The first derivative of g(a) is [tex]g'(x) = 18x^2 - 18x - 36.[/tex]
To find the first derivative of g(a), we need to use the power rule and the constant multiple rule.
First, we use the power rule to take the derivative of each term:
[tex]- The derivative of 6x^3 is 18x^2
- The derivative of -9x^2 is -18x
- The derivative of -36x is -36[/tex]
Next, we use the constant multiple rule to combine these derivatives:
g'(a) = 18x^2 - 18x - 36
Therefore, the first derivative of g(a) is [tex]g'(x) = 18x^2 - 18x - 36.[/tex]
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66. Which value of m makes the inequality true?
A. 4
B. 5
3m-4 < 11
C. 6
D. 7
Answer:
The answer to the question provided is choice A, 4.
The value of m which makes the inequality true is, 4
What is Inequality?A relation by which we can compare two or more mathematical expression is called an inequality.
Given that;
The inequality is,
⇒ 3m - 4 < 11
Now,. We can simplify as;
⇒ 3m - 4 < 11
⇒ 3m < 11 + 4
⇒ 3m < 15
⇒ m < 5
Thus, The value of m which makes the inequality true is, 4
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Bob earns $60,000 a year at an accounting firm. Each year, he receives a raise. Bob
has determined that the probability that he receives a 10% raise is 0. 7, the probability that he earns
a 3% raise is 0. 2, and the probability that he earns a 2% raise is 0. 1.
A competing company has offered Bob a similar position for $65,000 a year. Bob wonders if he
should take the new job or take his chances with his current job. SHOW ALL WORK!
A) Find the mathematical expectation of the dollar amount of his raise at his current job
The mathematical expectation of the dollar amount of Bob's raise at his current accounting firm is $4,680. Therefore, Bob should take the new job at the competing company.
To find the mathematical expectation of the dollar amount of Bob's raise at his current accounting firm, we'll first calculate the expected raise percentages using the given probabilities. Then, we will multiply those percentages by his current salary to determine the expected dollar amount.
A) Step 1: Calculate the expected raise percentages using probabilities
- 10% raise with a probability of 0.7: (0.1 * 0.7) = 0.07
- 3% raise with a probability of 0.2: (0.03 * 0.2) = 0.006
- 2% raise with a probability of 0.1: (0.02 * 0.1) = 0.002
Step 2: Add up the expected raise percentages
0.07 + 0.006 + 0.002 = 0.078
Step 3: Multiply the expected raise percentage by Bob's current salary
Expected dollar amount of raise = $60,000 * 0.078 = $4,680
The mathematical expectation of the dollar amount of Bob's raise at his current accounting firm is $4,680.
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Find the critical numbers of the function. (Enter your answers as a comma-separated list.) h(x) = sin^2 x + cos x, 0 < x < 2π x =
To find the critical numbers of h(x) = sin^2(x) + cos(x) in 0 < x < 2π steps are first to find the derivative h'(x), set h'(x) equal to zero and solve for x and check if solutions are within the given interval. The critical numbers are x = π, π/3, and 5π/3.
To find the critical numbers of the function h(x) = sin^2(x) + cos(x) in the interval 0 < x < 2π, we will follow these steps:
Find the derivative of the function, Set the derivative equal to zero and solve for x, Set h'(x) equal to zero and solve for x, Check if the solutions are within the given interval.
1: Differentiate h(x) with respect to x.
h'(x) = d(sin^2(x) + cos(x))/dx
Using chain rule, we get:
h'(x) = 2sin(x)cos(x) - sin(x)
2: Set h'(x) equal to zero and solve for x.
0 = 2sin(x)cos(x) - sin(x)
Factor out sin(x):
0 = sin(x)(2cos(x) - 1)
So, either sin(x) = 0 or 2cos(x) - 1 = 0.
3: Solve for x and check if the solutions are within the interval 0 < x < 2π.
For sin(x) = 0, x = π (since 0 < π < 2π).
For 2cos(x) - 1 = 0, cos(x) = 1/2.
x = π/3 and 5π/3 (since 0 < π/3 < 2π and 0 < 5π/3 < 2π).
Therefore, the critical numbers of the function h(x) = sin^2(x) + cos(x) in the interval 0 < x < 2π are x = π, π/3, and 5π/3.
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The model q(t) = 2. 5.00E+00. 0168t predicts the world population, in billions, t years after 1955. What was the population of the world in 1955 based
on this model?
The population of the world in 1955 based on the model q(t) = 2.500[tex]e^{0.0168t}[/tex] is 2.54 billion.
The model q(t) = 2.500[tex]e^{0.0168t}[/tex] represents the world population in billions
Here, t represents the years after 1955 and e is exponential constant its value is approximately 2.718.
Here the population is growing exponentially means population is growing at faster rate.
To find the population of the world in 1955 we will take
t = 1
on putting the value of t in the given function q(t)
q(t) = 2.500e[tex]e^{0.0168(1)[/tex]
on solving the function q(t) we get
q(t) ≈ 2.54
so, the population of the world in 1955 is 2.54 billion
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Grace and Kelly can create math problems for a particular course in 20 hours. Alone, Grace can do write all of the problems 4 hours faster than Kelly could if she were to work alone. How long would it take each person to write the problems if they worked alone?
From the word problem given, it will take Grace 0.05 hours and Kelly 4.05 to complete the task
How long will it take for each person to write the problem if they worked alone?To solve this problem, we need to write an equation for the word problem.
Let x = time it takes for Kelly
let y = time it takes for Grace
From the problem;
y = x - 4 ...eq(i)
Since they can complete the work in 20 hours;
1/x + 1/y = 20 ...eq(ii)
Solving for both equations
From equ(ii)
1/x + 1/(x - 4) = 20
Solving for x;
x = 4.05 or x = 0.049
Put the value in and solve for y
y = x - 4
y = 4.05 - 4 = 0.05 or y = 0.0049 - 4 = insignificant
The value of y = 0.5 hours
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Keilantra was given a large box of 24 chocolates for her birthday. If she eats exactly 3 chocolates each day, how many chocolates would Keilantra have remaining 6 days after her birthday?
Answer: 6 chocolates
Step-by-step explanation:
Keilantra had 24 chocolates to begin with, and she ate six lots of three. so the first step is 6 x 3 = 18. Now that we know how many chocolates Keilantra ate, we need to figure out how many chocolates she has left. So we take our product (18) and we subtract it from the total (24). So we end up with 24 - 18 = 6.
Finding Positive Numbers In Exercise, find three positive integers x, y, and z that satisfy the given conditions. The sum is 32, and P= xy^2z is a maximum. =
To find three positive integers x, y, and z that satisfy the given conditions, we need to use the concept of maximizing a function subject to certain conditions. Solving for y and z, we have y = 15 and z = 16.
In this case, we want to maximize the function P= xy^2z, subject to the condition that the sum of x, y, and z is 32.
To maximize P, we need to find the values of x, y, and z that make P as large as possible. One way to do this is to use the method of Lagrange multipliers, which involves finding the critical points of a function subject to a constraint.
In this case, we have the function P= xy^2z and the constraint x+y+z=32. Using Lagrange multipliers, we can set up the following equations:
∂P/∂x = λ∂(x+ y+ z)/∂x
y^2z = λ
∂P/∂y = λ∂(x+ y+ z)/∂y
2xyz = λ
∂P/∂z = λ∂(x+ y+ z)/∂z
xy^2 = λ
x+y+z=32
Solving these equations simultaneously, we get:
y^2z/x = 2xyz/y = xy^2/z = λ
Simplifying, we get:
y^2z/x = 2yz = xy^2/z
Rearranging, we get:
x = 2y^3/z
y = (x/2z)^(1/3)
z = (x/4y^2)^(1/3)
Substituting these expressions for x, y, and z into the constraint x+y+z=32, we get:
2y^3/z + (x/2z)^(1/3) + (x/4y^2)^(1/3) = 32
Solving this equation for x, y, and z, we get:
x = 16
y = 4
z = 2
Therefore, the three positive integers x, y, and z that satisfy the given conditions are x=16, y=4, and z=2. These values make P= xy^2z a maximum, since any other values of x, y, and z that satisfy the constraint x+y+z=32 would yield a smaller value of P.
To find three positive integers x, y, and z that satisfy the given conditions, we need to consider the following:
1. The sum of x, y, and z is 32: x + y + z = 32
2. The product P = xy^2z is a maximum.
First, let's express z in terms of x and y using the sum condition:
z = 32 - x - y
Now, substitute this expression for z into the product P:
P = xy^2(32 - x - y)
To maximize P, we should make y as large as possible, since it has the largest exponent in the product formula. Let's allocate the majority of the remaining sum to y. For example, if x = 1, we get:
1 + y + z = 32
Solving for y and z, we have y = 15 and z = 16. Now let's check the product:
P = (1)(15^2)(16) = 3600
This is one possible solution for x, y, and z that gives a maximum product P with the given conditions. The three positive integers are x = 1, y = 15, and z = 16, and the maximum product P = 3600.
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Find the probability that a point chosen randomly inside the rectangle is in each given shape. Round to the nearest tenth.
1. The probability that the point chosen is in the triangle is 0.1 (nearest tenth)
2. The probability that the point is in the square is 0.2( nearest tenth)
What is probability?A probability is a number that reflects the chance or likelihood that a particular event will occur. The certainty for an event is 1 which is equivalent to 100%.
Probability = sample space / total outcome
total outcome is the area of rectangle , which is
A = l× w
= 12 × 8
= 96
area of the rectangle = 1/2 bh
= 1/2 × 4 × 5
= 2 × 5
= 10
Area of the square = 4×4
= 16
1. Probability the the point will be in the triangle= 10/96 = 5/48
= 0.1( nearest tenth)
2. probability the the point will be in the square =
16/96 = 1/6
= 0.2 ( nearest tenth)
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HELP DUE TOMORROW!!!
The equation of the attached graph is
y = 1 cos (1x) + 0 How to write the equation of the graphThe equation is written by the general formula
y = A cos (Bx + C) + D
where:
A = amplitude.
B = 2π/T
where T = period
C = phase shift.
D = vertical shift.
A = amplitude
A = (maximum - minimum) / 2
Using the graph,
maximum = 1
minimum = -1
A = [1 - (-1)] / 2 = 2/2 = 1
B = 2π/T
where T = 2π
B = 2π/(2π) = 1
C = phase shift = 0
D = vertical shift
D = 1 - 1 = 0
substituting results to
y = 1 cos (1x + 0) + 0
this is written as
y = 1 cos (1x) + 0
y = cos (x)
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Pls help quickly i’ll give brainlyist
Answer:
Angle Q measures 55°, so angle M measures 55°.
39 + 55 + x = 180
94 + x = 180
x = 86
The real number properties can be used to simplify numerical expressions. in this section, you will identify which properties were used to simplify several expressions.
which properties were used to simplify the following expression? select all that apply.
4 + 3(9 + 2)
4 + (3 × 9) + (3 × 2)
4 + 27 + 6
4 + 6 + 27
10 + 27
37
The property was not explicitly used in this example, but it is worth noting that adding 0 to any number leaves it unchanged (i.e., a + 0 = a).
How many properties are used to simplify the expression 4 + 3(9 + 2) into 37?The properties that were used to simplify the expression 4 + 3(9 + 2) into 37 are:
Distributive property: The expression was rewritten as 4 + (3 × 9) + (3 × 2) by distributing the 3 over the parentheses.
Associative property: The order of the terms (3 × 9) and (3 × 2) was rearranged without changing the result because of the associative property of multiplication.
Commutative property: The order of the terms 4, 27, and 6 was rearranged without changing the result because of the commutative property of addition.
Identity property: The property was not explicitly used in this example, but it is worth noting that adding 0 to any number leaves it unchanged (i.e., a + 0 = a).
The properties used to simplify the expression are Associative property of addition, Commutative property of addition, and Distributive property and Identity property of addition. Therefore, the correct option is A, C, E and F.
The properties used to simplify the expression are as follows.
1. Distributive property (E): 4 + 3(9 + 2) = 4 + (3 × 9) + (3 × 2)
This property is applied when a number is multiplied with the sum of two or more numbers. In this case, the number 3 is distributed over the numbers 9 and 2.
2. Identity property of addition (F): 4 + 27 + 6 = 4 + 6 + 27
This property states that adding zero to any number does not change its value. Although this property isn't explicitly shown in the given steps, it is implied by the fact that we can rearrange the terms in the addition without changing their value.
3. Commutative property of addition (C): 4 + 6 + 27 = 10 + 27
This property states that changing the order of numbers in an addition does not change the sum. Here, the numbers 4 and 6 were rearranged to make it easier to add them together.
4. Associative property of addition (A): (10 + 27) = 37
This property states that the grouping of numbers in an addition does not affect the sum. In this case, the parentheses are unnecessary since the numbers were already grouped correctly.
In summary, the properties used to simplify the expression are: A) Associative property of addition, C) Commutative property of addition, and E) Distributive property and F) identity property of addition.
Note: The question is incomplete. The complete question probably is: The real number properties can be used to simplify numerical expressions. in this section, you will identify which properties were used to simplify several expressions. Which properties were used to simplify the following expression? select all that apply.
4 + 3(9 + 2)
4 + (3 × 9) + (3 × 2)
4 + 27 + 6
4 + 6 + 27
10 + 27
37
A) associative property of addition B) associative property of multiplication C) commutative property of addition D) commutative property of multiplication E) distributive property F) identity property of addition G) identity property of multiplication
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students in mr gonzales class are researching situations of exponitial decay and creating their graphs mr gonzales asked his students what the situations have in common and their responses are shown below
Therefore , the solution of the given problem of unitary method comes out to be it is consistently a constant proportion or percentage of the preceding value.
A unitary method is what?The task can be completed using the well-known minimalist technique, actual variables, and any essential components from the very first Diocesan specialised question. In response, customers can be given another opportunity to use the item. If not, significant effects on our comprehension of algorithms will disappear.
Here,
According to the students' responses, all instances of exponential decay share the following characteristics:
They begin with a baseline value. (y-intercept).
They get smaller with time. (or successive periods).
They get closer to a horizontal asymptote, which stands for the function's minimum or limit value.
The graphs also demonstrate that, although the rate of decay—or the rate at which values decrease—can vary from circumstance to circumstance,
it is consistently a constant proportion or percentage of the preceding value.
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Which correctly compares the numbers? 158,364 > 158,379 > 158,397 158,364 > 158,379 > 158,397 518,317 > 518,246 > 518,197 518,317 > 518,246 > 518,197 290,061 > 289,937 > 290,324 290,061 > 289,937 > 290,324 678,200 > 678,194 > 678,227
The correct comparison of the numbers is:
678,200 > 678,194 > 678,227
Therefore, the answer is the last option, "678,200 > 678,194 > 678,227".
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Select all the correct answers.
Isosceles trapezoid ABCD is shown.
Which three statements are correct?
In the given Isosceles trapezoid ABCD, the following three statements are correct:
∠ADC ≅ ∠BCD
AD ≅ BC
AC ≅ BD
An isosceles trapezoid is a trapezoid with equal base angles and hence equal left and right side lengths. Non-parallel sides on isosceles trapezoids have the same lengths. Hence, AD ≅ BC
A triangle with two equal sides is said to be isosceles. The two angles facing the two equal sides are also equal. Hence, ∠ADC ≅ ∠BCD.
The diagonals of the isosceles trapezoid are also equal. Hence, AC ≅ BD.
Thus, three correct statements in the given question are:
∠ADC ≅ ∠BCD
AD ≅ BC
AC ≅ BD
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A car accelerates away from the starting line at 3. 6 m/s2 and has the mass of
2400 kg. What is the net force acting on the vehicle?
If A car accelerates away from the starting line at 3. 6 m/s2 and has a mass of 2400 kg, Therefore, the net force acting on the vehicle is 8640 N.
The net force acting on the vehicle can be calculated using Newton's second law of motion, which states that the force applied to an object is equal to its mass multiplied by its acceleration:
Net force = mass x acceleration
In this case, the mass of the car is 2400 kg and the acceleration is 3.6 m/s^2. Thus, we can calculate the net force as:
Net force = 2400 kg x 3.6 m/s^2
Net force = 8640 N
Therefore, the net force acting on the vehicle is 8640 N.
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the line whose equation is 3x-5y=4 is dilated by a scale factor of 5/3 centered at the origin. Which statement is correct?
The correct statement is: "The line whose equation is 3x-5y=4 is dilated by a scale factor of [tex]y= (\frac{5}{3} )x[/tex] centered at the origin, and the equation of the dilated line is y= (\frac{5}{3} )x
When a line is dilated by a scale factor of k centered at the origin, the equation of the dilated line is given by y = kx, if the original line passes through the origin. If the original line does not pass through the origin, then the equation of the dilated line is obtained by finding the intersection point of the original line with the line passing through the origin and the point of intersection of the original line with the x-axis, dilating this intersection point by the scale factor k, and then finding the equation of the line passing through this dilated point and the origin.
In this case, the equation of the original line is 3x - 5y = 4. To find the intersection point of this line with the x-axis, we set y = 0 and solve for x:
3x - 5(0) = 4
3x = 4
[tex]x = \frac{4}{3}[/tex]
Therefore, the intersection point of the original line with the x-axis is (4/3, 0). Dilating this point by a scale factor of 5/3 centered at the origin, we obtain the dilated point:
[tex](\frac{5}{3} ) (\frac{4}{3},0) = (\frac{20}{9},0)[/tex]
The equation of the dilated line passing through this point and the origin is given by [tex]y= (\frac{5}{3} )x[/tex]. Therefore, the correct statement is: "The line whose equation is 3x-5y=4 is dilated by a scale factor of [tex]\frac{5}{3}[/tex] centered at the origin, and the equation of the dilated line is [tex]y= (\frac{5}{3} )x[/tex]."
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A sector with a central angle measure of 4/ 7π(in radians) has a radius of 16 cm. what is the area of the sector.
The area of the sector is approximately 73.14 square centimeters.
The formula to calculate the area of a sector is given by A = (θ/2) × r^2, where θ is the central angle measure in radians, and r is the radius of the circle.
Substituting the given values in the formula, we get A = (4/7π/2) × 16^2
Simplifying this expression, we get A = (8/7) × 16^2 × π/2
A = 128π square centimeters/7
Using the approximation π ≈ 3.14, we can calculate the value of A as follows:
A ≈ (128 × 3.14) square centimeters/7 ≈ 573.44 square centimeters/7 ≈ 73.14 square centimeters (rounded to two decimal places)
Therefore, the area of the sector is approximately 73.14 square centimeters.
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In triangle ABC, the length of side AB is 12 inches and the length of side BC is 20 inches. Which of the following could be the length of side AC?
Applying the triangle inequality theorem, the possible length of side AC is: C. 18 inches.
How to Determine the Length of a Triangle Using Triangle Inequality Theorem?The triangle inequality theorem states that lengths of the two sides of a triangle, when added together must be greater than the third side of any given triangle.
Therefore, to determine the possible length of side AC, we can use the triangle inequality theorem, stated above and applying this to triangle ABC, we have the following:
AC < AB + BC
AC < 12 + 20
AC < 32
This implies that, length of side AC must be less than 32 inches. Thus, the answer is: C. 18 inches.
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What is the maximum volume of a square pyramid that can fit into a cube with a side length of 30cm ?
A square pyramid with the maximum volume that can fit inside a cube has a same base as a cube ( 30 cm x 30 cm ) . The height of the pyramid is also same as a side length of a cube ( h = 30 cm ).
The volume of the pyramid:
V = 1/3 · 30² · 30 = 1/3 · 900 · 30 = 9,000 cm³
Answer:The maximum volume of the pyramid is 9,000 cm³.
Please answer the question correctly and neatly. Please find the
exact answer. Will upvote if correct.
Find the volume of the solid obtailed by rotating the region bounded by the given curves about the specified axis. y= x, y = 1 about y = 3
The region bounded by the given curves is a triangle with vertices at (0,0), (1,1), and (1,0). When this region is revolved around the line y=3, we obtain a solid with a hole in the middle.
To find the volume of this solid, we can use the method of cylindrical shells. Imagine slicing the solid into thin cylindrical shells with radius r and height Δy. The volume of each shell is approximately 2πrΔy times the thickness of the shell.
The distance between the axis of rotation (y=3) and the line y=1 is 2 units. Therefore, the radius of each cylindrical shell is r = 3 - y. The height of each shell is Δy = dx, where x is the distance from the y-axis.
To set up the integral, we need to express x in terms of y. Since the region is bounded by y=x and y=1, we have x=y for 0<=y<=1. Therefore, the integral for the volume of the solid is:
V = ∫[0,1] 2π(3-y)x dx
= 2π ∫[0,1] (3-y)y dx
Evaluating this integral, we get:
V = 2π [3y^2/2 - y^3/3] from 0 to 1
= 2π (3/2 - 1/3)
= 2π/3
Therefore, the volume of the solid obtained by rotating the region bounded by y=x, y=1 about y=3 is (2/3)π cubic units.
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The rectangular model is made up of squares each square is a equal size what percent of the model shaded
The percentage of the model is shaded is 45% if the total number of square is 80 option (H) is correct.
What is the percentage?It is defined as the ratio of two numbers expressed in the fraction of 100 parts. It is the measure to compare two data, the % sign is used to express the percentage.
Total No. of squares = 10×8 = 80
Total No. of squares shaded = 36
Percentage of the model is shaded = (36/80)×100
= 0.45×100
= 45%
Thus, the percentage of the model is shaded is 45% if the total number of square is 80 option (H) is correct.
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Full Question:
Although part of your question is missing, you might be referring to this full question:
See attached image.
helpp me with this question please
Answer:
24
Step-by-step explanation:
add all of them up
Solve the following pair of equations by substitution method:
0.2x + 0.3y − 1.1 = 0, 0.7x − 0.5y + 0.8 = 0
Answer:
(x, y) = (1, 3)
Step-by-step explanation:
You want to solve this system of equations by substitution:
0.2x +0.3y -1.1 = 00.7x -0.5y +0.8 = 0Expression for xWe can solve the first equation for an expression in x:
x = (1.1 -0.3y)/0.2 = (11 -3y)/2
SubstitutionSubstituting for x in the second equation gives ...
0.7(11 -3y)/2 -0.5y +0.8 = 0
7.7 -2.1y -y +1.6 = 0 . . . . . . . . . multiply by 2, eliminate parentheses
-3.1y +9.3 = 0 . . . . . . . . . . . . collect terms
y -3 = 0 . . . . . . . . . . . . . . . divide by -3.1
y = 3 . . . . . . . . . . . . . . . add 3
x = (11 -3(3))/2 = 2/2 = 1 . . . . . find x
The solution is (x, y) = (1, 3).
__
Additional comment
A graphing calculator confirms the solution.
A UPS driver need to drive 600 miles. The drivers average speed for the first 160 miles is b miles per hour. The drivers average speed for the rest of the trip is c miles per hour. Write an equation for the total time, t, in hours it took the UPS driver to complete the trip.
Lucy’s dog weighs nine and seventy-five hundredths kilograms. what is the weight, in kilograms, of lucy’s dog written in expanded notation?
The weight of Lucy's dog, written in expanded notation, is 9 kilograms and 0.75 kilograms.
Expanded notation is a way of writing a number as the sum of each digit multiplied by its place value. In this case, the number is 9.75. The digit 9 is in the tens place, so it represents 9 tens or 90. The digit 7 is in the ones place, so it represents 7 ones or 7.
The digit 5 is in the tenths place, so it represents 5 tenths or 0.5. The digit 7 is in the hundredths place, so it represents 7 hundredths or 0.07. Therefore, the weight of Lucy's dog in expanded notation is 90 kilograms plus 7 kilograms plus 0.5 kilograms plus 0.07 kilograms, which simplifies to 9 kilograms and 0.75 kilograms.
Mathematically, we can represent the given number as 9.75 = 9 x 10 + 7 x 1 + 5 x 0.1 + 7 x 0.01 = 90 + 7 + 0.5 + 0.07 = 9.57. Thus, the weight of Lucy's dog written in expanded notation is 9 kilograms and 0.75 kilograms.
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Americans consume on average 32. 3 lbs of cheese per year with a standard deviation of 8. 7 lbs. Assume that the amount of cheese consumed each year by an American is normally distributed. An American in the middle 70% of cheese consumption consumes per year how much cheese?
An American in the middle 70% of cheese consumption consumes per year between 23.252 and 41.348 lbs of cheese.
To find the amount of cheese consumed by an American in the middle 70%, we need to find the range of values that contain the middle 70% of the distribution.
First, we need to find the z-scores corresponding to the lower and upper boundaries of the middle 70% of the distribution. We can use the standard normal distribution for this, by converting the raw score of 32.3 lbs to a z-score:
z = (x - μ) / σ = (32.3 - 32.3) / 8.7 = 0
The z-score for the mean is zero, which means the mean is the midpoint of the normal distribution.
Next, we need to find the z-scores that correspond to the lower and upper boundaries of the middle 70% of the distribution. We can use the standard normal distribution table or calculator to find the z-scores. For a middle 70% range, the z-scores are approximately -1.04 and 1.04.
Finally, we can use the z-scores and the formula z = (x - μ) / σ to find the corresponding values of x, which represent the range of cheese consumption that contains the middle 70% of the distribution:
Lower boundary: z = -1.04
-1.04 = (x - 32.3) / 8.7
x - 32.3 = -9.048
x = 23.252 lbs
Upper boundary: z = 1.04
1.04 = (x - 32.3) / 8.7
x - 32.3 = 9.048
x = 41.348 lbs
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Find the length of the curve. y = ∫√25sin^2t - 1 dt, 0 < x < т/2
I apologize, but there seems to be some confusion in your question. The function given, y = ∫√25sin^2t - 1 dt, is not a curve but rather an indefinite integral expression. In order to find the length of a curve, we need a function defined explicitly in terms of x (or y) and its bounds. Could you please provide more information or clarify your question?
To find the length of the curve given by y = ∫√(25sin^2(t) - 1) dt from 0 to π/2, we need to calculate the definite integral.
First, let's set up the integral:
Length = ∫√(25sin^2(t) - 1) dt, with bounds from 0 to π/2
Unfortunately, this integral cannot be solved analytically using elementary functions. You will need to use a numerical method, such as the Trapezoidal Rule or Simpson's Rule, to approximate the value of the integral, and thus find the length of the curve.
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Which equation defines a linear
function?
A y = 2/4x + 12
B y = x2 + 4x - 6
C x2 + y2 =16
D 1/x2 + 1/y2 = 4
The equation defines a linear function is A y = 2x/4 + 12
Which equation defines a linear function?A y = 2x/4 + 12 is the equation that defines a linear function because it can be simplified to y = 1/2x + 12,
Which has a constant slope of 1/2 and a constant rate of change.
The other options are not linear functions because they involve exponents or do not have a constant slope.
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Amita, Monica and Rita are three sisters.
Monica is x years old.
Amita is 3 years older than Monica.
Rita is twice the age of Amita.
If the mean age of the three sisters is 15, how old is Amita?
Answer:
So Monica is 9 years old.
To find Amita's age, we substitute x into the expression for Amita's age:
Amita's age = 9 + 3 = 12
Therefore, Amita is 12 years old.
what value of x is y/z
a-13
b-77
c-103
d-154
Answer:
I got you
Step-by-step explanation:
it's c -103 cause you first have to get 180 degrees
