To find the rate of change of the temperature difference between the two spacecraft, we need to first find the temperature at each spacecraft's position at time t=4.
For the first spacecraft, rt sin(t) = r4sin(4) and t=4, so its position is (4sin(4), 4, 0). Using the temperature function, we have T(4sin(4), 4, 0) = (4sin(4))(4)(5-2) = 48.08.
For the second spacecraft, rz cos(t) = r3cos(4) and t=-4/3, so its position is (3cos(4), -4/3, 7). Using the temperature function, we have T(3cos(4), -4/3, 7) = (3cos(4))(-4/3)(5-2) = -9.09.
Therefore, the temperature difference D between the two spacecraft at time t=4 is D = 48.08 - (-9.09) = 57.17.
To find the rate of change of D with respect to time, we use the Chain Rule. Let x = 4sin(t) and y = 4, so D = T(x, y, 0) - T(3cos(t), -4/3, 7). Then,
dD/dt = dD/dx * dx/dt + dD/dy * dy/dt
We already know that D = 48.08 - 9.09 = 57.17, so dD/dx = dT/dx = y(5-2x) = 4(5-2(4sin(4))) = -31.64.
We also have dx/dt = 4cos(4) and dy/dt = 0, since y is constant.
To find dD/dy, we take the partial derivative of T with respect to y, holding x and z constant: dT/dy = x(5-2y) = (4sin(4))(5-2(4)) = -28.16.
Putting it all together, we get:
dD/dt = dD/dx * dx/dt + dD/dy * dy/dt
= (-31.64)(4cos(4)) + (-28.16)(0)
= -126.56
Therefore, the rate of change of the temperature difference between the two spacecraft at time t=4 is -126.56.
Given the paths of the two spacecraft: r1(t) = (t sin(t), t, 0) and r2(t) = (t cos(t), -t, 7), and the temperature function T(x, y, z) = x * y * z^2, we want to determine the rate of change of the temperature difference D at time t=4 using the Chain Rule.
First, let's find the temperature for each spacecraft at time t:
T1(t) = T(r1(t)) = (t sin(t)) * t * 0^2
T1(t) = 0
T2(t) = T(r2(t)) = (t cos(t)) * (-t) * 7^2
T2(t) = -49t^2 cos(t)
Now, find the temperature difference D(t) = T2(t) - T1(t) = -49t^2 cos(t)
Next, find the derivative of D(t) with respect to t:
dD/dt = -98t cos(t) + 49t^2 sin(t)
Now, we need to evaluate dD/dt at t=4:
dD/dt(4) = -98(4) cos(4) + 49(4)^2 sin(4) ≈ -104.32
Thus, the rate of change of the temperature difference D at time t=4 is approximately -104.32 (in decimal notation, rounded to two decimal places).
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Ginny's family traveled
3
10
of the distance to her aunt’s house on Saturday. They traveled
3
7
of the remaining distance on Sunday. What fraction of the total distance to her aunt’s house was traveled on Sunday?
Ginny's family traveled 3/10 of the total distance to her aunt's house on Sunday.
What fraction of the total distance was traveled on Sunday?Let's say the total distance to Ginny's aunt's house is represented by the fraction 1.
On Saturday, Ginny's family traveled 3/10 of the distance, leaving 7/10 of the distance remaining.
Then, on Sunday, they traveled 3/7 of the remaining distance.
To find out what fraction of the total distance was traveled on Sunday, we need to multiply the distance traveled on Saturday and Sunday and divide by the total distance:
So, we have
Fraction = 3/7 * 7/10
Evaluate
Fraction = 3/10
Therefore, Ginny's family traveled 3/10 of the total distance to her aunt's house on Sunday.
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Which of the following options doesn't have the same value as the others explain? 10/100, 10%, 1/10, 0.01
Answer:
it should be 1/10 if that helps you
Answer:
0.01 does not have the same value as the others.
Step-by-step explanation:
10/100, 10%, and 1/10 is all the same. 0.01 is NOT the same because it is equal to 1/100, or 1% while the others were all equal to 10%. To figure this out, you must multiply 0.01 by 100 (or move the decimal point one space to the right two times) and we will get 1. This means that 0.01 is 1% which is also equal to 1/100, therefore it does not obtain the same value as the others.
Benjamin went shopping for a new phone
because of a sale. The price on the tag was
$28, but Benjamin paid $15. 40 before tax.
Find the percent discount
The percent discount on the phone because of a sale is 45%.
To find the percent discount, we need to calculate the difference between the original price and the discounted price, and then express that difference as a percentage of the original price.
First, let's find the difference between the two prices: $28 - $15.40 = $12.60. This means that Benjamin saved $12.60 on the phone.
Now, let's find the percent discount. We can do this by dividing the savings by the original price, and then multiplying the result by 100: ($12.60 / $28) * 100 = 45%.
So, Benjamin received a 45% discount on the phone before tax. This calculation shows that the sale allowed him to save a significant amount on his purchase. It's important to compare original and discounted prices to determine if a sale provides good value.
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What is 4x+2/39=5x-2/42?
We use the fundamental property of proportions where:
a/b = c/d if a • d = b • c[tex] \space [/tex]
[tex] \bf \frac{4x + 2}{39} = \frac{5x - 2}{42} \\ \\ \bf 39 \cdot (5x - 2) = 42 \cdot (4x + 2) \\ \\ \bf 195x - 78 = 168x + 84 \\ \\ \bf 195x - 168x = 84 + 78 \\ \\ \bf 27x = 162 \\ \\ \bf x = \frac{162}{27} \implies \bf \red{ \boxed{ \bf x = 6} } [/tex]
The number is 6.
Hope that helps! Good luck! :)
Determine whether the Mean Value there can be applied to to the dosed intervalectal that apply 100-V2--14:21 A. Yes, the Moon Value Theorem can be applied B. No, because is not continuous on the dosed inter
Based on the given information, we need to determine whether the Mean Value Theorem can be applied to the dosed interval [100-V2, 14:21].
The Mean Value Theorem states that for a function that is continuous on a closed interval [a, b] and differentiable on the open interval (a, b), there exists at least one point c in (a, b) where the slope of the tangent line to the function at c is equal to the average rate of change of the function over the interval [a, b].
In this case, we do not have enough information about the function or its continuity on the interval [100-V2, 14:21]. Therefore, we cannot determine whether the Mean Value Theorem can be applied or not.
However, we do know that for the Mean Value Theorem to be applicable, the function must be continuous on the closed interval. If the function is not continuous on the closed interval, then the Mean Value Theorem cannot be applied.
Therefore, the answer to the question is B. No, because we do not have enough information about the function's continuity on the dosed interval [100-V2, 14:21].
I understand you're asking about the Mean Value Theorem and whether it can be applied to a given interval. Due to some typos in your question, I'm unable to identify the specific interval and function. However, I can provide general guidance.
The Mean Value Theorem can be applied to a function if:
A. The function is continuous on the closed interval [a, b]
B. The function is differentiable on the open interval (a, b)
If the given function meets these two conditions, then the Mean Value Theorem can be applied. Otherwise, it cannot be applied.
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find the perimeter of the equilateral triangle whose area is 16root3/4
The perimeter of the equilateral triangle whose area is 16root3/4 is 15.9[tex]\sqrt{3/4} cm[/tex]
What is an equilateral triangle?You should understand that a triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry. A triangle with vertices A, B, and C is denoted
An equilateral triangle is a special case of an isosceles triangle in which all three sides have the same length
Let the sides of the triangle be a
a + a + a = 16root3/4
3a = 16[tex]\sqrt{3/4}[/tex]
a = 5.3[tex]\sqrt{3/4}[/tex]
Therefore the perimeter of the equilateral triangle is
5.3[tex]\sqrt{3/4} + 5.3\sqrt{3/4} +5.3\sqrt{3/4}[/tex]
Therefore, the perimeter is 15.9[tex]\sqrt{3/4} cm[/tex]
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find the next three terms in the sequence 3/4, 1/2, 1/4, 0
Answer:
[tex]\sf \bf \dfrac{-1}{4} \ ; \ \dfrac{-1}{2} \ ; \ \dfrac{-3}{4}[/tex]
Step-by-step explanation:
Arithmetic sequence:
Each term in the arithmetic sequence is obtained by adding or subtracting a common number with the previous term.
To find the next three terms, we need to find the common difference.
Common difference = second term - first term
[tex]\sf = \dfrac{1}{2}-\dfrac{3}{4}\\\\=\dfrac{2-3}{4}\\\\=\dfrac{-1}{4}\\\\\\\text{Each term is obtained by adding $\dfrac{-1}{4} $ with the previous term}[/tex]
Next three terms are,
[tex]\sf 0 + \left(\dfrac{-1}{4}\right)= 0 - \dfrac{1}{4}=\dfrac{-1}{4}\\\\\\\dfrac{-1}{4}+\left(\dfrac{-1}{4}\right)=\dfrac{-1}{4}-\dfrac{1}{4}=\dfrac{-2}{4}=\dfrac{-1}{2}\\\\\\\dfrac{-1}{2}+\left(\dfrac{-1}{4}\right)=\dfrac{-1}{2}-\dfrac{-1}{4}=\dfrac{-2-1}{4}=\dfrac{-3}{4}[/tex]
A farmer of a large apple orchard would like to estimate the true mean number of suitable apples produced per tree. He selects a random sample of 40 trees from his large orchard and determines with 95% confidence that the true mean number of suitable apples produced per tree is between 375 and 520. Which of these statements is a correct interpretation of the confidence level?
The correct interpretation of the 95% confidence level is that if we were to repeat this sampling process multiple times and construct confidence intervals in the same way, about 95% of the intervals would contain the true mean number of suitable apples produced per tree.
In other words, we are 95% confident that the true mean number of suitable apples produced per tree is between 375 and 520 based on this particular sample of 40 trees. However, we cannot say with certainty that the true mean falls within this interval, nor can we say that it falls outside of this interval with 95% confidence.
It's important to note that the confidence level refers to the long-run behavior of the method of constructing confidence intervals, rather than the probability that the true mean falls within the specific interval calculated from this one sample.
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What are the Actual dimensions of the house(in ft)
The house's real measurements are 18 feet by 20 feet.
What do we mean by dimensions?In everyday speech, a dimension is a measurement of an object's length, width, and height, such as a box.
The idea of dimension in mathematics is an expansion of the concepts of one-dimensional lines, two-dimensional planes, and three-dimensional space.
Examples of dimensions include width, depth, and height.
One dimension is that of a line, two dimensions are those of a square, and three dimensions are those of a cube. (3D).
So, scaling is the process of changing a figure's size to produce a picture.
Considering that a scale of 6 cm equals 12 ft.
Hence:
9 cm = 9 cm * (12 ft. per 6 cm) = 18 feet
10 cm = 10 cm * (12 ft. per 6 cm) = 20 feet
Therefore, the house's real measurements are 18 feet by 20 feet.
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Correct question:
A scale drawing of a house shows 9cm x10cm. If 6cm=12 ft, what are the actual dimensions?
Help with problem in photo
Answer:
(x-6)²+(y+3)²=17²
Step-by-step explanation:
The equation of a circle with center (a,b) and radius r is given by the formula:
(x - a)² + (y - b)² = r²
In this case, the center of the circle is (6,-3), and it passes through the point (-9,5). To find the radius of the circle, we need to calculate the distance between the center and the point on the circle. Using the distance formula, we get:
r = √[(x₂ - x₁)² + (y₂ - y₁)²]
= √[(-9 - 6)² + (5 - (-3))²]
= √[225 + 64]
= √289
= 17
So, the radius of the circle is 17. Now we can plug in the values for the center and radius into the equation of a circle:
(x - 6)² + (y + 3)² = 17²
Question 21
What fraction is equal to 40 % ?
A
B
C
D
45
58
2
1
25
Answer:
2/5
Step-by-step explanation:
To convert a percentage to a fraction, we divide the percentage by 100 and simplify the resulting fraction. For example, to convert 40% to a fraction, we divide 40 by 100 to get 0.4 and then simplify the fraction 2/5. Therefore, 40% is equal to 2/5.
Mathetmatics
Class - 6 question
Topic - Roman Numerals :-
Question:-
The number VCX is incorrect. Explain why?
Answer as fast as you can. I'l mark you as brainliest
In Roman Numerals, smaller numbers can be subtracted from larger numbers, but only to a certain extent.
The number VCX is incorrect in Roman Numerals because V (5) cannot be subtracted from X (10) to make 5, and C (100) cannot be subtracted from X (10) to make 90.
In Roman Numerals, smaller numbers can be subtracted from larger numbers, but only to a certain extent.
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Ten sixth-grade students reported the hours of sleep they get on nights
before a school day. Their responses are recorded in the dot plot. Looking
at the dot plot, Lin estimated the mean number of hours of sleep to be 8. 5
hours. Noah's estimate was 7. 5 hours. Diego's estimate was 6. 5
hours. Which estimate do you think is best? Solve for the mean to figure out
who was closer. *
Lin
ООО
Noah
Diego
Noah's estimate of 7.5 hours is closest to the actual mean number of hours of sleep reported by the ten sixth-grade students.
We have,
Compare the estimates given by Lin, Noah, and Diego.
Lin's estimate is 8.5 hours.
Noah's estimate is 7.5 hours.
Diego's estimate is 6.5 hours.
The average of these three estimates:
(8.5 + 7.5 + 6.5) / 3
= 22.5 / 3
= 7.5
It appears that Noah's estimate of 7.5 hours is the closest.
Therefore,
Noah's estimate of 7.5 hours is closest to the actual mean number of hours of sleep reported by the ten sixth-grade students.
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The complete question:
Which estimate of the mean number of hours of sleep reported by the ten sixth-grade students is closest to the actual mean: Lin's estimate of 8.5 hours, Noah's estimate of 7.5 hours, or Diego's estimate of 6.5 hours?
Cathy works at a restaurant. On Monday, she served 9 tables with 6 people at each table. On Tuesday, she served 86 people. She wants to know how many more people she served on Tuesday than on Monday.
Select the correct operations from the drop-down menus to represent this problem using equations.
9
Choose.
6 = m
86
Choose.
54 = d
Cathy served 32 more people on Tuesday than on Monday.
Given, on Monday, Cathy served 9 tables with 6 people at each table. On Tuesday, Cathy served 86 people. We have to find the number of people she served more on Tuesday than on Monday.
So, on Monday she served = 9 tables x 6 people per table
= 54 people.
To find out how many more people Cathy served on Tuesday than on Monday, we can subtract the number of people served on Monday from the number served on Tuesday.
i.e. 86 - 54 = 32.
Therefore, Cathy served 32 more people on Tuesday than on Monday.
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What would the balance be after 5 years if you deposited $1,000 in an account compounded monthly if the interest rate is 3. 7%?
$5,000. 00
$1,199. 21
$1,185. 00
$1,202. 88
A mouse is moving through a maze and must make four turns where it can go either left or
right. The mouse will escape the maze if it makes three lefts and one right, in any order.
(a) To the right, draw a tree diagram
of all possible routes the mouse
could take.
(b) Using your tree diagram, create
an organized list of the routes. For
example, a route of right, left, left,
right could be listed as RLLR.
(C) What is the probability the mouse
escapes the maze if all turns are
randomly made?
Hence, 25% is the likelihood that the mouse will succeed in escaping the maze if all turns are made at random.
what is probability ?The examination of random chance and the likelihood that they will occur is the focus of the mathematical field of probability. It is a gauge of how likely an event is to occur and is represented by a value between zero and 1. A probability of 1 indicates that an event will undoubtedly occur. The probability of an occurrence is zero if it cannot occur. An event's probability is 0.5, or 50%, when it possesses a 50/50 chance of occurring. The number of favourable outcomes is divided by the entire amount of possible results to determine probability.
given
Based on the tree diagram, the following is an orderly list of every route that might be taken:
Three left turns and one right turn, in whatever order, make up each route.
As there are two options (left or right) for each turn, there are a total of 24 = 16 potential sequences of four turns.
Only if the mouse makes precisely three left turns and one right out of these will it be able to escape the maze.
Three lefts and one right can be arranged in one of four distinct ways (LLL, LLR, LRL, RLL), so the likelihood that the mouse will elude the maze is:
P(escape) = Number of favourable results / Number of potential results = 4 / 16 = 0.25 = 25%
Hence, 25% is the likelihood that the mouse will succeed in escaping the maze if all turns are made at random.
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The graph of a quadratic function f is shown on the
grid. Which of these best represents the domain of f?
-4
Oy≥-12.25
All real numbers
All real numbers less than -4 or greater than 5
All real numbers will be the function's domain. D is the right answer in this case.
What are domain and range?The range of values that we are permitted to enter into our function is known as the domain of a function.
The x values for a function like f make up this set(x).
A function's range is the collection of values it can take as input.
After we enter an x value, the function outputs this sequence of values.
The range refers to all potential values of y, and the domain refers to all conceivable values of x.
Let a be the leading coefficient and the parabola's vertex be the point (h, k).
The parabola's equation will then be provided as,
y = a(x - h)² + k
The graph shows where the vertex of the parabola will be. (-1.5, -4.5). The equation is then presented as:
y = a(x + 1.5)² - 4.5
Therefore, all real numbers will be the function's domain. D is the right answer in the case.
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Correct question:
The graph of the quadratic function f is shown in the grid. Which of these best represents the domain of f?
A: y>=4.5
B: All real numbers less than -4 or greater than 1
C: -4<=x<=1
D: All real numbers
A large diamond with a mass of 481. 3 grams was recently discovered in a mine. If the density of the diamond is g over 3. 51 cm, what is the volume? Round your answer to the nearest hundredth.
The volume of the large diamond is approximately 3.51 cm³.
To find the volume of the large diamond with a mass of 481.3 grams and a density of (g/3.51 cm), you can use the formula:
Volume = Mass / Density
The volume of the large diamond, we can use the formula Volume = Mass / Density. Given that the mass is 481.3 grams and the density is (g/3.51 cm), we can substitute these values into the formula.
Simplifying the equation, we find that the volume is equal to 3.51 cm³. This means that the large diamond occupies a space of approximately 3.51 cubic centimeters.
1. First, rewrite the density as a fraction: g/3.51 cm = 481.3 g / 3.51 cm³
2. Next, solve for the volume by dividing the mass by the density: Volume = 481.3 g / (481.3 g / 3.51 cm³)
3. Simplify the equation: Volume = 481.3 g * (3.51 cm³ / 481.3 g)
4. Cancel out the grams (g): Volume = 3.51 cm³
So, the volume of the large diamond is approximately 3.51 cm³, rounded to the nearest hundredth.
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Answer:
Step-by-step explanation:
Density = mass
volume
We have density (3.51 cm) and we have mass (481.3)
We need to solve for V (volume)
3.51 = 481.3
V
Multiply both sides by V to clear the fraction:
3.51 V = 481.3
Divide both side by 3.51
3.51 V = 481.3
3.51 3.51
V = 137.122cm³
rounded to 137.12 cm³
Which of the following is an odd function? f(x) = x3 5x2 x f (x) = startroot x endroot f(x) = x2 x f(x) = –x
The limit of [tex]L_n[/tex] as n approaches infinity is 1/2, and it can be expressed as the definite integral of x from 0 to 1.
To express the limit of [tex]L_n[/tex] as n approaches infinity as a definite integral, we can use the fact that the limit of a Riemann sum is equal to the corresponding definite integral. Thus, we can rewrite [tex]L_n[/tex] as:
[tex]L_n[/tex] = 1/n * (0 + 1 + 2 + ... + (n-1))
This is a Riemann sum for the integral:
[tex]\int\limits^1_0 {x} \, dx[/tex]
with n subintervals of width 1/n. Therefore, we can write:
[tex]\lim_{n \to \infty} L_n = \lim_{n \to \infty} 1/n * (0 + 1 + 2 + ... + (n-1)) = \int\limits^1_0 {x} \, dx = [x^2/2] \ from \ 0 \ to \ 1 = 1/2[/tex]
So, the limit of Ln as n approaches infinity is 1/2, and it can be expressed as the definite integral of x from 0 to 1.
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What function does the graph represent?
Answer:
B
Step-by-step explanation:
Since the graph is facing down, there will be a negative sign.
In parenthesis it says (x + 1) which means you move one unit left
On the outside it says +2 which means you move the graph 2 units up
PLEASE WRITE THE EXPRESSION IN FORM OF |x-b|=c
Write the absolute value equations in the form |x-b|=c (where b is a number and c can be either number or an expression) that have the following solution sets:
Please do both problems
All numbers such that x≤−14.
All numbers such that x≥ -1. 3
The vertical distance the Mars Rover Curiosity has traveled is approximately 84.954 meters.
What will be the absolute value equations in the form |x-b|=c for x ≤ -14 and x ≥ -1.3?An absolute value equation is an equation that contains an absolute value expression, which is defined as the distance of a number from zero on the number line. The equation |x-b|=c represents the distance between x and b is c units. To write the absolute value equations in the form |x-b|=c, we need to determine the values of b and c based on the given solution sets.
For the solution set "All numbers such that x ≤ -14", we know that the distance between x and -14 is always a non-negative value. Therefore, the absolute value of (x-(-14)) or (x+14) is equal to the distance between x and -14. Since we want x to be less than or equal to -14, we can set the absolute value expression to be equal to -c, where c is a positive number. Hence, the absolute value equation is |x+14|=-c.
Similarly, for the solution set "All numbers such that x ≥ -1.3", the distance between x and -1.3 is always a non-negative value. Therefore, the absolute value of (x-(-1.3)) or (x+1.3) is equal to the distance between x and -1.3. Since we want x to be greater than or equal to -1.3, we can set the absolute value expression to be equal to c, where c is a positive number. Hence, the absolute value equation is |x+1.3|=c.
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A survey found that the relationship between the years of education a person has and that person's yearly income in his or her first job after completing schooling can be modeled by the equation y = 1200 x + 7000, where x is the number of years of education and y is the yearly income. According to the model, how much does 1 year of education add to a person's yearly income?
According to the model, each additional year of education adds $1200 to a person's yearly income in their first job after completing schooling.
We're given the equation y = 1200x + 7000, where x represents the number of years of education, and y represents the yearly income.
To find how much 1 year of education adds to a person's yearly income, we need to look at the coefficient of the variable x, which is 1200.
So according to the model, 1 year of education adds $1,200 to a person's yearly income.
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Find the surface area of the triangular prism shown below.
12
units²
10
10
14.
Answer:
The triangular prism has two triangular bases and three rectangular lateral faces.
First, we need to find the area of each triangular base. Using the formula for the area of a triangle:
base x height / 2
We can calculate the area of one triangular base as:
(10 x 12) / 2 = 60 units²
Now we need to find the area of each rectangular lateral face. All three faces have the same dimensions of 10 units by 14 units, so the area of each face is:
10 x 14 = 140 units²
To find the total surface area of the prism, we add up the areas of both triangular bases and all three rectangular faces:
Total surface area = 2 x (area of triangular base) + 3 x (area of rectangular face)
Total surface area = 2 x 60 units² + 3 x 140 units²
Total surface area = 120 units² + 420 units²
Total surface area = 540 units²
Therefore, the surface area of the triangular prism is 540 square units.
A teacher tells her students she is just over 1 and 1/2 billion seconds old.
a. Write her age in seconds using scientific notation (using for multiplication and for your exponent).
b. What is a more reasonable unit of measurement for this situation?
c. How old is she when you use a more reasonable unit of measurement?
a. The teacher's age in seconds can be written in scientific notation as 1.5 × [tex]10^{9}[/tex] seconds.
b. A more reasonable unit of measurement for this situation could be years, as it is a common unit used to express human age.
c. To convert the teacher's age from seconds to years, we can divide the number of seconds by the number of seconds in a year. There are 60 seconds in a minute, 60 minutes in an hour, 24 hours in a day, and approximately 365 days in a year. So,
1.5 × [tex]10^{9}[/tex] seconds ÷ (60 seconds/minute × 60 minutes/hour × 24 hours/day × 365 days/year) = approximately 47.5 years
Therefore, the teacher is approximately 47.5 years old when using the more reasonable unit of measurement.
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Dmitri practices his domra for 98 min during
the school week. this is 70% of the time he
must practice his instrument in one week.
The total or actual time he needs to practice is 140 min whereas he practiced for 98 min during the school week.
We need to find the total time he must practice for a week. To find the total time we assume that the total time is x min.
Given Data:
Dmitri practices time during the school week = 98 min
Dmitri practices amount of time = 70% of his total time
Total time = x
Then the equation is given as
70% × (x) = 98
0.70 × (x) = 98
x = 98 / 0.70
x = 140
Therefore, The total time of the practices is 140 min
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What is the lateral area of the cone to the nearest whole number? The figure is not drawn to scale.
*
Captionless Image
34311 m^2
18918 m^2
15394 m^2
28742 m^2
Answer:
π(70)(√(70^2 + 50^2)) = π(700√74) m^3
= 18,918 m^3
PLS HELP ME WITH THIS 50 POINTS!
Answer: The transformation is up one and to the left 5
(-5, 1)
Step-by-step explanation:
Please Give brainliest, have a great night!
Answer: h(x) = g(x+5)+1
Step-by-step explanation:
h(x) = g(x+5)+1
You went 5 in the negative direction x direction; take the opposite sign
Also went up 1 in the y direction so add 1 to equation
Sarah tells her mom that there is a 40% chance she will clean her room, a 70% she will do her homework, and a 24% chance she will clean her room and do her homework. What is the probability of Sarah cleaning her room or doing her homework?
To find the probability of Sarah cleaning her room or doing her homework, we can use the addition rule for probabilities. However, we need to be careful not to count the probability of Sarah cleaning her room and doing her homework twice. Therefore, we need to subtract the probability of Sarah cleaning her room and doing her homework from the sum of the probabilities of Sarah cleaning her room and doing her homework separately.
Let C be the event that Sarah cleans her room, and let H be the event that Sarah does her homework. Then we know:
P(C) = 0.40 (the probability that Sarah cleans her room)
P(H) = 0.70 (the probability that Sarah does her homework)
P(C and H) = 0.24 (the probability that Sarah cleans her room and does her homework)
Using the addition rule, we can find the probability of Sarah cleaning her room or doing her homework as follows:
P(C or H) = P(C) + P(H) - P(C and H)
= 0.40 + 0.70 - 0.24
= 0.86
Therefore, the probability of Sarah cleaning her room or doing her homework is 0.86, or 86%.
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A statistics class weighed 20 bags of grapes purchased from the store. The bags are advertised to contain 16 ounces, on average. The class calculated the 90% confidence interval for the true mean weight of bags of grapes from this store to be (15. 875, 16. 595) ounces. What is the sample mean weight of grapes, and what is the margin of error?
The sample mean weight is 15. 875 ounces, and the margin of error is 16. 595 ounces.
The sample mean weight is 16. 235 ounces, and the margin of error is 0. 360 ounces.
The sample mean weight is 16. 235 ounces, and the margin of error is 0. 720 ounces.
The sample mean weight is 16 ounces, and the margin of error is 0. 720 ounces
0.180 is the sample mean weight of grapes, and what is the margin of error
The sample mean weight is the midpoint of the confidence interval:
sample mean = (lower limit + upper limit) / 2 = (15.875 + 16.595) / 2 = 16.235
Therefore, the sample mean weight of grapes is 16.235 ounces.
The margin of error is half of the width of the confidence interval:
margin of error = (upper limit - sample mean) = (16.595 - 16.235) / 2 = 0.180
Therefore, the margin of error is 0.180 ounces.
So the correct answer is: "The sample mean weight is 16.235 ounces, and the margin of error is 0.180 ounces."
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Solve (t^2 + 4) dx/dt = (x^2 + 36), using separation of variables, given the inital condition 2(0) = 6.
To solve this differential equation using separation of variables, we can rearrange it as:
dx/(x^2 + 36) = (t^2 + 4)/dt
Now we can integrate both sides:
∫ dx/(x^2 + 36) = ∫ (t^2 + 4)/dt
To integrate the left side, we can use the substitution u = x/6, du/dx = 1/6 dx, and dx = 6 du:
∫ dx/(x^2 + 36) = ∫ du/u^2 + 1
= arctan(x/6) + C1
To integrate the right side, we can use the power rule:
∫ (t^2 + 4)/dt = (1/3)t^3 + 4t + C2
Putting these together, we have:
arctan(x/6) = (1/3)t^3 + 4t + C
Where C = C2 - C1 is the constant of integration.
Now we can solve for x:
x/6 = 6 tan((1/3)t^3 + 4t + C)
x = 36 tan((1/3)t^3 + 4t + C)
Using the initial condition 2(0) = 6, we have:
x(0) = 36 tan(C) = 6
tan(C) = 1/6
C = arctan(1/6)
Therefore, the solution to the differential equation with the given initial condition is:
x = 36 tan((1/3)t^3 + 4t + arctan(1/6))
First, let's rewrite the equation using the given terms and separating the variables:
(t^2 + 4) dx/dt = (x^2 + 36)
Now, separate the variables:
dx/x^2 + 36 = dt/t^2 + 4
Next, we'll integrate both sides:
∫(1/(x^2 + 36)) dx = ∫(1/(t^2 + 4)) dt
Using the substitution method, we find:
(1/6) arctan(x/6) = (1/2) arctan(t/2) + C
Now, we'll use the initial condition 2(0) = 6 to find the value of C. Since 2(0) = 0, we have:
(1/6) arctan(6/6) = (1/2) arctan(0/2) + C
This simplifies to:
(1/6) arctan(1) = C
Therefore, the solution to the differential equation is:
(1/6) arctan(x/6) = (1/2) arctan(t/2) + (1/6) arctan(1)
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