If the initial position s(0) = -5 and initial velocity v(0) = -2, the position function of the object is -8cost + t^3/3 - 2t + 3. So the option D is correct.
We have to determine the position function of the object.
An object moves along a straight line with acceleration a(t) = 8cost + 2t.
Initial position s(0) = -5
Initial velocity v(0) = -2
Integration of a(t) given us s(t)
[tex]\int a(t)dt = \int (8cost + 2t) dt[/tex]
v(t) = 8sint + 2t^2/2 + C
v(t) = 8sint + t^2 + C
At v(0) = -2
v(0) = 8sin(0) + (0)^2 + C
-2 = 8 × 0 + 0 + C
C = -2
v(t) = 8sint + t^2 - 2
The integration of v(t) gives us s(t)
[tex]\int v(t)dt = \int (8sint + t^2 - 2)dt[/tex]
s(t) = -8cost + t^3/3 - 2t + D
At s(0) = -5
s(0) = -8cos(0) + (0)^3/3 - 2(0) + D
-5 = -8 × 1 + 0 - 0 + D
-5 = -8 + D
Add 8 on both side, we get
D = 3
s(t) = -8cost + t^3/3 - 2t + 3
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The middle school has 24 students less than 3 times the number of students at one of
the elementary schools.
The required equation is y=3x-24, where x is the number of elementary school students and y is the number of middle school students.
What is equation?An equation is a formula in mathematics that expresses the equality of two expressions by connecting them with the equals sign =. In its most basic form, an equation is a mathematical statement that shows that two mathematical expressions are equal. 3x + 5 = 14, for example, is an equation in which 3x + 5 and 14 are two expressions separated by a 'equal' sign. A mathematical equation that depicts the relationship between two expressions on opposite sides of the sign. It mostly consists of one variable and one equal to symbol. 2x - 4 = 2 is an example.
Here,
Let x be the number of students in elementary school and y be the number of students in middle school.
y=3x-24
The required equation is y=3x-24 where x be the number of students in elementary school and y be the number of students in middle school.
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After how many years will the loan be half-paid?
A. 15 years
B. 18 years
C. 21 years
D. 24 years
2. Consider this excerpt from chapter 39: "Something is discomforting about a sun that gives no
heat but keeps shining. " In this comparison, who is the sun?
O The tour guide
Maxine
Jade's mother
The symphony members
Jade's mother is the sun of Jade because she motivated Jade against race and gender, class and privilege, and fear and courage. Something is discomforting about a sun that gives no heat but keeps shining. " In this comparison, Jade's mother is the sun. So the option 3 is correct.
While expressing the complicated emotions of an aspirational, devoted girl, Jade's narrative voice offers riveting insights on the intricacies of race and gender, class and privilege, and fear and courage. Watson's story, which brims with empathy and wisdom, extols the ability of creative expression to reimagine and transform the world.
The many individuals who find themselves in the world looking for themselves are addressed in Watson's exquisitely written book. Piecing Me Together is a novel about how young people deal with the struggles and pain of daily life while remaining entire and true to themselves. It is both timely and timeless.
The reason why Jade's mother is said to as the sun of Jade is because she inspired Jade to overcome prejudices related to class, privilege, and fear.
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The complete question is:
Consider this excerpt from chapter 39:
Something is discomforting about a sun that gives no heat but keeps shining. " In this comparison, who is the sun?
1. The tour guide
2. Maxine
3. Jade's mother
4. The symphony members
How much money would you need to deposit at 7% annual interest compounded yearly to have $10,000 in the account at the end of 5 years? Round to the nearest cent.
The account balance after five years will be $10355.
What is compound interest?The interest that is paid on the principal and interest at regular intervals is known as compound interest. The difference between compound interest and simple interest starts to show after the first year, though.
The formula to calculate the compound interest is given below;-
[tex]A = P ( 1+\dfrac{R}{n})^{nt}[/tex]
Given that deposit at 7% annual interest compounded yearly to have $10,000 in the account at the end of 5 years.
The account balance after five years will be:-
[tex]A = P ( 1+\dfrac{R}{n})^{nt}[/tex]
[tex]A = 10000 ( 1+\dfrac{0.07}{1})^{5}[/tex]
A = 10000 x ( 1.07)⁵
A = $10355
Hence, the amount will be $10355.
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Given a rope 10 units in length, if side lengths must be in whole units, how many different triangles can be made?
A per the measurement, there is only form exactly 1 unique triangle.
The term triangle in math is known as a two-dimensional shape with three sides, three interior angles, and three vertices.
Here we have know that a rope 10 units in length, if side lengths must be in whole units.
And we need to find the number of different triangles can be made.
Here we know that length is 10 units, and the side length are whole units.
Which means that here we have 3 distinct value.
So as we all know that all of the triangles you make are the same triangle. Which means that if your three side lengths can form a triangle, then they can only form exactly 1 unique triangle.
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an engineer has designed a valve that will regulate water pressure on an automobile engine. the valve was tested on 100 engines and the mean pressure was 5.5 lbs/square inch. assume the standard deviation is known to be 0.7 . if the valve was designed to produce a mean pressure of 5.3 lbs/square inch, is there sufficient evidence at the 0.05 level that the valve performs above the specifications? state the null and alternative hypotheses for the above scenario.
There is sufficient evidence that the valve performs above the specifications.
Null Hypothesis (H0): The mean pressure of the valve is equal to 5.3 lbs/square inch
Alternative Hypothesis (H1): The mean pressure of the valve is greater than 5.3 lbs/square inch
To test whether the valve performs above the specifications, a hypothesis test can be used. The test statistic used will be a t-test since the sample size is below 30. The critical value at the 0.05 level is 1.645. The formula for the t-test is: t = (X-μ)/(s/√n) , where X is the sample mean, μ is the population mean, s is the sample standard deviation, and n is the sample size.
Plugging in the known values, the t-test is calculated as: t = (5.5-5.3)/(0.7/√100) = 2.571. Since this value is greater than the critical value at the 0.05 level (1.645), we can reject the null hypothesis and conclude that there is sufficient evidence that the valve performs above the specifications.
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A chef made a blend of cooking oil. 1/5 of his mix was olive oil and 4/5 was corn oil. Write this blend as a ratio of corn oil to olive oil
1 :1 is the blend as a ratio of corn oil to olive oil.
Now, According to the question:
A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0. A proportion is an equation in which two ratios are set equal to each other. For example, if there is 1 boy and 3 girls you could write the ratio as: 1 : 3 (for every one boy there are 3 girls)
"Information available from the question"
A chef made a blend of cooking oil.
1/5 of his mix was olive oil
and 4/5 was corn oil.
To find the blend as a ratio of corn oil to olive oil.
Now, Blend Ratio will be:
olive ratio + corn ratio
1/5 + 4/5
= 5/5 = 1/1
Hence, 1:1 is the blend as a ratio of corn oil to olive oil.
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Explain in words how to solve an equation with a variable on both sides of the equation.
Sofia is making a batch of slime using a recipe that includes glue, water, and a salt solution. She uses 7. 5 fl oz of glue. The amount of glue is 12. 5 times the amount of salt solution. There are 4. 2 less fluid ounces of salt solution than water.
How many fluid ounces of water does Sofia use to make the batch of slime?
Total amount of fluid ounces of water used by Sofia to make proportionate amount of slime is equal to 4.8 fluid ounces.
Let us consider 'x' amount of salt solution.
Amount of glue used by Sofia = 7.5 fluid ounces
Amount of glue = 12.5 times of salt solution
⇒ 7.5 = 12.5x
⇒ x = 7.5 / 12.5
⇒ x = 0.6
Fluid ounces of water used by Sofia to make the required batch of slime is:
Now, Amount of salt solution = Fluid ounces of Water - 4.2
⇒Fluid ounces of Water = x + 4.2
⇒ Fluid ounces of Water = 0.6 + 4.2
⇒ Fluid ounces of Water = 4.8 fluid ounces
Therefore, the fluid ounces of water used by Sofia with salt solution and glue to make a slime is equal to 4.8 fluid ounces.
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fred has ten feet of wire.he decides to cut it into equal length pieces. how many pieces will he get if each piece is 4 feet long?
Answer:
I don't know
Step-by-step explanation:
:)))))))))))))))))))))))))))))
Find the smallest pair of 4-digit numbers such that the difference between them is 303 and their HCF is 101. Show your steps.
Please give answer immediately
Based on the information provided, the two numbers whose HCF is 101 are 1010 and 1313.
What is the HCF?The HCF is the highest common factor or in other words, the highest number by which two numbers can be divided. Let's start by listing the four digits numbers that can be the HCF related to 101.
101 x 10 = 1010
101 x 11 = 1111
101 x 12 = 1212
101 x 13 = 1313
Now, from these numbers, there are two numbers whose difference is 303.
1313 - 1010 = 303
Based on this, the two numbers are 1010 and 1313
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Given the following data, fill out the table for V* n and V/n
(give your answers to 3 sig figs).
The table for V* n and V/n shows the various answers as
What is multiplication and Division?Multiplication is when you take one number and add it together a number of times.
The table appears as follows
Volume(V) Moles(n) V*n V/n
3 0.145 0.435 20.7
4 0.193 0.773 20.7
5 0.242 1.210 20.7
6 0.290 1.740 20.7
These figures are gotten by the multiplication and division of the numbers in the tables as given by the formulae
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What percent of 1 3/5 is 0.2? (im stu pid, sorry)
Answer: 12.5%
(Don't worry!)
There's a 1/6 chance that a student will be in Miss Jones math class if there are 30 students in her class how many students are there at all
If there is a 1/6 chance that a student will be in Miss Jones's math class, if there are 30 students in her class, then 180 students will be there at all.
Probability is a method to know how likely something is going to happen. Whenever we're uncertain about the outcome of an event, we can talk about the probabilities of certain outcomes. The analysis of events overseen by probability is called statistics.
Total number of students present in the miss jones class = 30
The chance that a student will be in Miss Jones's math class = 1/6
Let x be the students are there at all
According to the question,
1/6 × x = 30
⇒x = 30 × 6
⇒x = 180
Hence, 180 students are there at all.
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Question 32:
Write an equation in Slope-Intercept form for the
line that passes through (1,-3) and is parallel to
y+2 = 4(x-1)
The equation y+2 = 4(x-1) is already in slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept. In this equation, the slope is 4 and the y-intercept is -2.
For a line that is parallel to y+2 = 4(x-1), the slope (m) will be the same, which is 4.
To find the equation of a line that passes through a specific point (1,-3), we can use the point-slope form of a linear equation: y - y1 = m(x - x1)
So, using the point (1,-3) and the slope (4), we can write the equation as:
y - (-3) = 4(x - 1)
Simplifying this equation gives:
y + 3 = 4x - 4
Finally, we can write the equation in slope-intercept form by adding 4 to both sides and dividing both sides by 4:
y = 4x - 1
So the equation for the line that passes through (1,-3) and is parallel to y+2 = 4(x-1) is y = 4x - 1
i dont understand this
The given expression has sin A = BC/AC=36/85, cos A = AB/AC=77/85, tan A = BC/AB=36/77
How to find sin cos tan?In trigonometry, the values of sin, cos, and tan are the main functions we consider when solving trigonometric problems. Using these trigonometric values, the angles and sides of a right-angle triangle are calculated. In addition to sine, cosine, and tangent values, the other three significant values are cotangent, secant, and cosecant.
Normally, when calculating the sin, cos, and tan values for a triangle, the angles of 0°, 30°, 45°, 60°, and 90° are taken into consideration. These specific angles' values are easy to remember. What the trigonometric values are all about is knowing the standard angles for a specific triangle according to the trigonometric ratios (sine, cosine, tangent, cotangent, secant and cosecant).
We have, AB = 77 , BC = 36.and CA=85
When we consider the t-ratios of ∠A, we have
Base = AB = 77, Perpendicular = BC = 36, Hypotenuse = AC =85.
∴sin A = BC/AC=36/85 , cos A = AB/AC=77/85 , tan A = BC/AB=36/77
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Find the height of the figure.
12. A = 12 m²
4.8 m
13. A 11.0625 m²
3.75 m
The height of the figure is 66 m².
How to find height?Finding the triangle's height can be done in a variety of ways. There are numerous other formulas, but the one that uses a triangle's area is the one that is most widely used. You can determine the triangle's area given its sides using an equation known as Heron's formula. Once you are aware of the region, you can use the fundamental equation to determine the triangle's altitude.
You multiply 27.5 and 4.8. Which gets you 132. And because your finding the area of a triangle you have to divide 132 by 2 which gets you 66.
27.5 × 4.8
= 132
132/2
= 66
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Help please!!! (3x² - 4xy + y²)(4x + 3y)
The simplified form of the expression (3x² - 4xy + y²)(4x + 3y) is 12x³ - 7x²y + 8xy² + 3y³.
What is the simplified form of the expression?Given the expression in the question;
(3x² - 4xy + y²)(4x + 3y)
To simplify, apply distributive property by multiplying each term in the first expression by each term in the second expression.
(4x + 3y)(3x² - 4xy + y²)
4x (3x² - 4xy + y²) + 3y(3x² - 4xy + y²)
3x² × 4x - 4xy × 4x + y² × 4x + 3x² × 3y - 4xy × 3y + y² × 3y
12x³ - 16x²y + 4xy² + 9x²y - 12xy² + 3y³
Collect like terms
12x³ - 16x²y + 9x²y + 4xy² - 12xy² + 3y³
Add -16x²y and 9x²y
12x³ - 7x²y + 4xy² - 12xy² + 3y³
Add 4xy² and -12xy²
12x³ - 7x²y + 8xy² + 3y³
Therefore, the simplified form is 12x³ - 7x²y + 8xy² + 3y³.
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Tell whether the two rates form a proportion.
-0. 4 kilometer for every 15 minutes
-0. 6 kilometer for every 20 minutes
As the value of the ratio of both the quantities are NOT same so the given values .
No, The two rates not form a proportion.
Now, According to the question:
Two ratios are equivalent, if the fractions corresponding to them are equivalent. Four quantities are said to be in proportion, if the ratio of the first and the second quantities is equal to the ratio of the third and the fourth quantities.
A proportion is an equation that sets two ratios at the same value. For instance, you might express the ratio as follows:
1: 3 if there is 1 boy and 3 girls (for every one boy there are 3 girls) There are 1 in 4 boys and 3 in 4 girls. 0.25 are male (by dividing 1 by 4)
Now,
0. 4 kilometer for every 15 minutes equals to (0.4/15) = 0.026
So for every minute they travel 0.026km.
0. 6 kilometer for every 20 minutes equals (0.6/20) = 0.03
So for every minute they travel 0.03km.
Here, as the value of the ratio of both the quantities are NOT same so the given values .
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A recipe states that chicken needs to be cooked for 15 minutes per kg plus an extra 40 minutes. Express the relationship between mass and cooking time using function notation, and define the domain and range.
For the given statement, the domain and range are - Domain : x ,Range : f(x) 40.
What does a notation in mathematics mean?In mathematical notation, symbols are used in expressions and formulas to represent operations, unnamed numbers, relations, and any other mathematical objects. In mathematics, science, and engineering, mathematical notation is frequently used to communicate complicated ideas and properties in a clear, unambiguous manner.
A notation is a set of clear guidelines for using symbols to describe numbers and actions.
The sum of numerous linked terms is frequently represented by the sign (capital sigma) in shorthand notation. In statistics, sigma notation is frequently employed.
For each dividend number, the extended notation division method merely repeats the division, multiplication, and subtraction operations.
Given data :
x is the mass of the chicken (in kg)
f(x) : the cooking time ( in minutes )
Domain : x
Range : f(x) 40
f(x) = 15x + 40 - 15 minutes per kg (x) plus 40 more minutes
f (1) = 15 x 1 + 40 = 55
A 1 kg chicken needs 15 min + 40 min = 55 min
f (2) = 15 x 2 + 40 = 70
A 2 kg chicken needs 30min + 40 min = 70 min
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Classify the sequence {1, 6, 11, 16, 21, …}.
Answer:
Classify the sequence {1, 6, 11, 16, 21, …}.
The pattern is +5:
1 + 5 = 6
6 + 5 = 11
11 + 5 = 16
16 + 5 = 21
21 + 5 = 26
And so on
Step-by-step explanation:
You're welcome
Simplify this to help me out
When we simplify the expression (4x⁴y⁵ / 3xy²)⁵, the result obtained is 1024x¹⁵y¹⁵ / 243
How do I simplify (4x⁴y⁵ / 3xy²)⁵?To simplify the expression (4x⁴y⁵ / 3xy²)⁵, the laws of indices must be applied as illustrated below:
(4x⁴y⁵ / 3xy²)⁵
Recall
(Aᵐ)ⁿ = Aᵐⁿ
Thus,
(4x⁴y⁵ / 3xy²)⁵ = 1024x²⁰y²⁵ / 243x⁵y¹⁰
Recall
Aᵐ / Aⁿ = Aᵐ⁻ⁿ
Thus,
1024x²⁰y²⁵ / 243x⁵y¹⁰ = (1024 / 243)x²⁰⁻⁵y²⁵⁻¹⁰
1024x²⁰y²⁵ / 243x⁵y¹⁰ = (1024 / 243)x¹⁵y¹⁵
1024x²⁰y²⁵ / 243x⁵y¹⁰ = 1024x¹⁵y¹⁵ / 243
Therefore,
(4x⁴y⁵ / 3xy²)⁵ = 1024x¹⁵y¹⁵ / 243
From the above illustration, we can conclude that the simplified form of (4x⁴y⁵ / 3xy²)⁵ is 1024x¹⁵y¹⁵ / 243
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Mrs. Soriano baked 7 5/9 dozens of chocolate cookies. She gave 3 1/3 dozens to her friends. How many dozens of chocolate cookies were left ?
A. 4 3/9
B. 4 2/9
C. 4 5/9
D. 4 1/9
Answer:
4 2/9
Step-by-step explanation:
7 5/9 -3 1/3
68/9 -10/3
(68-30)/9
38/9
4 2/9
The graph of y = In(x) was transformed by shifting 8 units left and 12 units up. Write an equation( please help!!)
The parent function and transformed function will be y = ln x and y = ln (x + 8) + 12, respectively.
What is a function?A function is an assertion, concept, or principle that establishes an association between two variables. Functions may be found throughout mathematics and are essential for the development of significant links.
The function is given below.
y = ln x
The function is transformed by shifting 8 units left and 12 units up. Then replace x with (x + 8) and y with (y - 12). Then we have
y - 12 = ln (x + 8)
y = ln (x + 8) + 12
The parent function and transformed function will be y = ln x and y = ln (x + 8) + 12, respectively. The graph of the function is given below.
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What is the solution of the system of equations
Y=1/8x-1
-5x+4y= - 13
Answer:
(2.57, -0.07)
Step-by-step explanation:
To solve the system of equations, we can substitute the expression for y in the second equation:
-5x + 4(1/8x - 1) = -13
We can then simplify and solve for x:
-5x + (1/2)x - 4 = -13
-3.5x = -9
x = 2.57
We can then substitute this value of x back into the first equation to find the value of y:
y = 1/8(2.57) - 1
y = -0.07
So the solution of the system of equations is (x, y) = (2.57, -0.07)
If you were to sketch a circle graph for the data shown in the table below, approximately what
fraction of the circle would represent food?
Vacation Expenses Budget
Expense Amount Budgeted
Activities=600
Food= 450
Souvenirs=270
The fraction of the circle that would represent food is given as 34.09
How to solve for the fraction that would represent foodThe data we have here is given as
Activities = 600
Food = 450
Souvenirs = 270
We would have to sum this up
600 + 450 + 270 = 1320
The proportion that represents food is given as 450
= 450 / 1320
= 0.3409
Then we would have to convert this to percentage
0.341 * 100
= 34.09
34.09 x 360 = 123 degrees
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Multiple. Write your answer as a fraction or as a whole or mixed number.
3/4 x 8
Answer:
6
Step-by-step explanation:
3/4 x 8 = 3 x 8 / 4 x 1 = 24/4 = 6
Find the lateral area, and surface area of the figure.
Round your answers to the nearest thousandth, if necessary
Lateral Area = 108 square km
Surface Area = 120 square km
Think of the triangles as the floor and ceiling of this 3D room. The walls are three rectangular sides.
We have a 9 by 4 wall with an area of 9*4 = 36 square km
We have a 9 by 3 wall with an area of 9*3 = 27 square km
We have a 9 by 5 wall with an area of 9*5 = 45 square km
The lateral area is 36+27+45 = 108
The two triangles form the base faces of this prism.
Let's find the area of one of the triangles
area=0.5*base*height = 0.5*3*4 =6
One triangle has an area of 6, so both triangles in total have an area of 2*6 = 12 square km.
The total surface area is therefore 108+12 = 120 square km.
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PLEASE HELPPP
You are the grade 10 representative on the student council and you have been assigned the
task of finding a location to host a dance for the students of CISE. You have narrowed it down
to three options which are outlined below:
Ancient Abyss is a location that charges a $200 flat fee and $4 per person.
Beautiful Babylon is a location that charges a $99 flat fee and $6 per person.
Crazy Cleopatra is a location that charges a $280 flat fee and $3 per person.
Task:
You will analyze the three options and put together a proposal to submit to the student
council outlining your recommendations.
Based on the information provided, I have analyzed the three options for hosting a dance for the students of CISE, and have come to the following recommendations:
Ancient Abyss: This location charges a flat fee of $200 and $4 per person. This option may be suitable for smaller events with less than 50 attendees, as the flat fee is relatively high. However, for larger events with more than 50 attendees, the per person cost will become more significant and may make this option less cost-effective.
Beautiful Babylon: This location charges a flat fee of $99 and $6 per person. This option may be more cost-effective for larger events with more than 50 attendees, as the per person cost is lower than Ancient Abyss. However, for smaller events with less than 50 attendees, the flat fee may be relatively high.
Crazy Cleopatra: This location charges a flat fee of $280 and $3 per person. This option has the highest flat fee but the lowest per person cost. This option may be more cost-effective for larger events with more than 50 attendees, as the per person cost is lower than Beautiful Babylon. However, for smaller events with less than 50 attendees, the flat fee may be relatively high.
Based on the above analysis, I recommend that the student council consider Beautiful Babylon as the most cost-effective option for hosting the dance. However, I also recommend that the council consider the number of attendees expected at the event and adjust their decision accordingly.
In summary, The council should consider the number of attendees expected, Beautiful Babylon is a good option for larger events, for smaller events, Crazy Cleopatra is the better option.