The standard deviation of the sampling distribution is approximately 0.3292.
What is central limit theorem?The behaviour of the sampling distribution of the mean is described by the central limit theorem, a key conclusion in statistics. It asserts that regardless of how the population distribution is shaped, if a random sample of size n is taken from a population with mean and standard deviation, the distribution of sample means will tend towards a normal distribution as n increases.
Because it enables us to utilise the normal distribution to draw conclusions about the population mean based on sample means, the central limit theorem has significant practical ramifications. Additionally, it offers a foundation for confidence interval estimation and statistical hypothesis testing.
The standard deviation is given by the formula:
SD = σ/√(n)
Now, substituting the value of σ = 40, n = 147,400 we have:
SD = σ/√(n) = 40/√(147400) ≈ 0.3292
Hence, the standard deviation of the sampling distribution is approximately 0.3292.
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The total square footage of your house is 1500 square feet. You want to put new carpet in every room, hallway, and closet, except for the kitchen, dining room and bathroom. If the kitchen is 8 ft by 10 and the dining room is 12ft and 14ft and the bathroom is 4ft by 6 ft, how many square feet of carpet do you need for the house?
Answer:
1228
Step-by-step explanation:
To find the total square footage of carpet needed for the house, we first need to calculate the total square footage of the areas where we do not need carpet and then subtract that from the total square footage of the house.
The kitchen is 8 ft by 10 ft, so its area is:
8 ft x 10 ft =80 square feetThe dining room is 12 ft by 14, ft so its area is:
12 ft x 14 ft = 168 square feetThe bathroom is 4 ft by 6 ft, so its area is:
4 ft x 6 ft = 24 square feetTherefore, the total square footage of the areas where we do not need carpet is:
80 + 168 + 24 = 272 square feetTo find the total square footage of carpet needed for the house, we can subtract this from the total square footage of the house:
1500 - 272 = 1228 square feetTherefore, we need 1228 square feet of carpet for the house.
To calculate the amount of carpet needed, subtract the square footage of the rooms where you don't want new carpet (kitchen, dining room, bathroom) from the total house size. This results in 1228 square feet of carpet required.
Explanation:First, let's determine the total square footage of the spaces where you don't want new carpet. The kitchen is 8 ft by 10 ft, which equals 80 square feet. The dining room is 12ft by 14ft, giving us 168 square feet. The bathroom is 4ft by 6 ft, equal to 24 square feet. When you add these together, that is a total of 272 square feet that should not be carpeted.
Since your total house size is 1500 square feet, we subtract the square footage of the kitchen, dining room, and bathroom from this total. So, 1500 square feet - 272 square feet equals 1228 square feet. Therefore, you need 1228 square feet of carpet for the house.
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The halt-lime performance of a marching band includes a performance in which the band members form a circle with point J at the center. This formation can he modeled by the equation 2° +1? + 10z 12y - 83 = 0.
The required values are as follows:
Center = (-5, 6), Radius = 12, Domain: x ∈ (-17, 7), Range: y ∈ (-6, 18)
Given equation: x² + y² + 10x - 12y - 83 = 0
To convert it into standard form, complete the square for both the x and y terms:
(x² + 10x) + (y² - 12y) = 83
(x² + 10x + 25) + (y² - 12y + 36) = 83 + 25 + 36
(x + 5)² + (y - 6)² = 144
Comparing this with the standard form, we have:
Center (h, k) = (-5, 6)
Therefore, the coordinates for the point J are (-5, 6).
The radius represents the distance from each band member to the center of the circle. In this case, the radius of the circle is the square root of the constant term on the right side of the standard form equation:
Radius = √144 = 12
The domain of the circle is the set of all possible x-values that lie on the circle. Since the circle is centered at (-5, 6) and has a radius of 12, the domain can be expressed as:
Domain: x ∈ (-5 - 12, -5 + 12) or -17 ≤ x ≤ 7
The range of the circle is the set of all possible y-values that lie on the circle. Using the same information, the range can be expressed as:
Range: y ∈ (6 - 12, 6 + 12) or -6 ≤ y ≤ 18
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using formula : if a block of wood has dimensions of 4.55cm x 9.1cm x 2.54cm
a) the volume of the block of wood (V = I x w x h)
b) the total surface area of the block of wood (SA = 2lh + 2wh + 2lw)
show work please
The volume of the block of wood is 104.7634 cm³ and the total surface area is 186.4502 cm².
Volume is the measure of the amount of space occupied by a three-dimensional object. It is typically measured in cubic units such as cubic meters (m³), cubic centimeters (cm³), or cubic inches (in³).
The volume of the block of wood will be;
V = l x w x h = 4.55 cm x 9.1 cm x 2.54 cm
= 104.7634 cm³
Therefore, the volume of the block of wood is 104.7634 cm³.
The total surface area of the block of wood will be;
SA = 2lh + 2wh + 2lw
= 2(4.55 cm x 2.54 cm) + 2(9.1 cm x 2.54 cm) + 2(4.55 cm x 9.1 cm)
= 58.0094 cm² + 46.4314 cm² + 82.0094 cm²
= 186.4502 cm²
Therefore, the total surface area is 186.4502 cm².
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help me quick and right answers only. algebra
The function that has a range of all real numbers is given as follows:
f(x) = -x + 2.
What are the domain and range of a function?The domain of a function is the set that contains all possible input values of the function, that is, all the values assumed by the independent variable x in the function.The range of a function is the set that contains all possible output values of the function, that is, all the values assumed by the dependent variable y in the function.Hence the range for each function in the context of this problem is given as follows:
f(x) = -x + 2 -> all real values.f(x) = -x²: y ≤ 0.f(x) = 2^x + 1: y ≥ 1.More can be learned about domain and range at brainly.com/question/26098895
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you are renting a condominium at 1,700 a month. Your annual expenses are insurance, $325; lost interest, $50 and utility bills, $5,940. You also pay a monthly fee for all maintenance and what is his average monthly expense?
Answer:
$526.25, and your total monthly expense (including rent and maintenance fee) is $2,326.25.
Step-by-step explanation:
To calculate your average monthly expense, we need to first add up all of your annual expenses and divide by 12 (the number of months in a year) to find the monthly average.
Annual expenses:
Insurance: $325
Lost interest: $50
Utility bills: $5,940
Total annual expenses = $325 + $50 + $5,940 = $6,315
To find the average monthly expense, we divide the total annual expenses by 12:
Average monthly expense = Total annual expenses / 12
Average monthly expense = $6,315 / 12
Average monthly expense = $526.25
In addition to the annual expenses, you also pay a monthly rent of $1,700 and a monthly fee for all maintenance. Let's assume that the monthly maintenance fee is $100.
Therefore, your total monthly expense would be:
Total monthly expense = Monthly rent + Monthly maintenance fee + Average monthly expenses
Total monthly expense = $1,700 + $100 + $526.25
Total monthly expense = $2,326.25
So, your average monthly expense is $526.25, and your total monthly expense (including rent and maintenance fee) is $2,326.25.
pleasee help me due tomorrow
The true statements include
B The x-coordinate of point T' is 5.E The length of segment Q' R' is the same length as segment QR.What is rigid transformation?Rigid transformation is a type of geometric transformation in which the size and shape of an object remain unchanged. Rigid transformations include
translations, rotations, and reflections.In a rigid transformation, the position of the object in space may change, but its size, shape, and orientation remain the same.
In the object in the graph the length of the segments remain same and since the translation affects only y direction the x-coordinate will be unchanged.
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what is the simplified answer to 49^{1/2}
Answer:
7
Step-by-step explanation:
A cube is shown. Describe the shape resulting from a horizontal cross section, a vertical cross section, and an angled cross section.
horizontal cross section: _____
vertical cross section: _____
angled cross section: _____
The shape resulting from a horizontal cross section, a vertical cross section, and an angled cross section of the cube are:
horizontal cross section: square.
vertical cross section: square.
angled cross section: rectangle.
How to determine the cross section?In this exercise, you are required to use a graphing tool to investigate and determine the cross-sections of the given three-dimensional geometric object (cube), by passing different planes through them.
By critically observing the cross-sections of the three-dimensional geometric object (cube) I used, we can reasonably infer and logically deduce the following types of quadrilateral based on the cross-sections;
A horizontal cross section would produce a square.
A vertical cross section would produce a square.
An angled cross section would produce a rectangle.
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A triangle is shown with its exterior angles. The interior angles of the triangle are angles 2, 3, 5. The exterior angle at angle 2 is angle 1. The exterior angle at angle 3 is angle 4. The exterior angle at angle 5 is angle 6. Which statements are always true regarding the diagram? Select three options. m∠5 + m∠3 = m∠4 m∠3 + m∠4 + m∠5 = 180° m∠5 + m∠6 =180° m∠2 + m∠3 = m∠6 m∠2 + m∠3 + m∠5 = 180°
The statements that are always true regarding the diagram are:
m∠1 + m∠5 = 180°
m∠2 + m∠3 = m∠6
m∠3 + m∠4 + m∠5 = 180°
Explain the term diagram
It refers to a value or position that is higher or greater than another value or position. It is often used in comparisons or to describe the relative positions of objects or points on a graph or coordinate plane. The opposite of "above" is "below," which refers to a value or position that is lower or lesser.
According to the given information
We know that the sum of the measures of the three interior angles of a triangle is always 180°. Therefore, we have:
m∠2 + m∠3 + m∠5 = 180°
From the given information, we know that:
m∠2 + m∠1 = 180° (linear pair of angles)
m∠3 + m∠4 = 180° (linear pair of angles)
m∠5 + m∠6 = 180° (exterior angle theorem)
Rearranging these equations, we get:
m∠1 = 180° - m∠2
m∠4 = 180° - m∠3
m∠6 = 180° - m∠5
Substituting these expressions into the above equation for the sum of the interior angles, we get:
m∠2 + m∠3 + m∠5 = m∠2 + (180° - m∠1) + m∠5
m∠3 + m∠4 + m∠5 = (180° - m∠3) + m∠4 + m∠5
Simplifying these equations, we get:
m∠1 + m∠5 = 180°
m∠2 + m∠3 = m∠6
Therefore, the statements that are always true regarding the diagram are:
m∠1 + m∠5 = 180°
m∠2 + m∠3 = m∠6
m∠3 + m∠4 + m∠5 = 180° (which is equivalent to option 2)
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help my compters dieing
its at 3 percent HELP PLEASE
Answer: The first number is the X-axis and the second is the Y-axis.
Step-by-step explanation:
5, 1, 4, and 2 belong in X. 35, 7, 28, and 14 belong in Y.
The rule is that X always goes first the Y goes after.
Given f’(x)=-4x - 5 compute. F(3)- f(-1)
Answer:
-36
Step-by-step explanation:
To solve this problem, we need to integrate f'(x) to find f(x), and then evaluate f(3) and f(-1) to compute the expression f(3) - f(-1).
Integrating f'(x)=-4x - 5 with respect to x, we get:
f(x) = -2x^2 - 5x + C
Where C is the constant of integration.
To find the value of C, we can use the initial condition f(0) = 1. Substituting x = 0 and f(x) = 1 into the equation above, we get:
1 = -2(0)^2 - 5(0) + C
1 = C
So, we have:
f(x) = -2x^2 - 5x + 1
Now, we can evaluate f(3) and f(-1) and compute f(3) - f(-1):
f(3) = -2(3)^2 - 5(3) + 1 = -32
f(-1) = -2(-1)^2 - 5(-1) + 1 = 4
f(3) - f(-1) = (-32) - 4 = -36
Therefore, f(3) - f(-1) = -36.
Answer:
-36
Step-by-step explanation:
You want F(3) -F(1) given f'(x) = -4x -5.
IntegralThe desired difference is the definite integral ...
[tex]\displaystyle \int_{-1}^3{(-4x-5)}\,dx=\left[-2x^2-5x\right]_{-1}^3=-2(9-1)-5(3+1)\\\\=\boxed{-36}[/tex]
<95141404393>
Which monomial has a degree of 3?
A.
3x
B.
3
C.
3x2
D.
–2x3
The only option given that has a variable raised to the third power is D. -2x³, so the correct answer is D.
What is monomial?In algebra, a monomial is an expression that consists of a single term, which is a product of a constant coefficient and one or more variables raised to non-negative integer powers. In each of these expressions, there is only one term, and each term is a product of a constant coefficient and one or more variables raised to non-negative integer powers. Monomials are important in algebra because they can be combined using various operations such as addition, subtraction, multiplication, and division, to form more complex expressions.
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Felix exercises by spending 12 minutes warming up and then running for 20 minut
He has exercised a total of 240 minutes this month.
Felix has spent a total time of 11.4 hours (or 684 minutes) running this month.
HOW CAN WE CALCULATE TOTAL TIME?we can calculate the total time Felix has spent running this month.
Given:
Warm-up time: 12 minutes
Running time: 20 minutes
Total exercise time in a month: 240 minutes
Step 1: Calculate the total time spent running
Let x be the total time spent running in minutes.
According to the given information, Felix spends 12 minutes on warm-up and 20 minutes on running.
So, the equation would be:
12 + 20x = 240
Step 2: Solve for x
Subtract 12 from both sides of the equation:
20x = 240 - 12
20x = 228
Divide both sides by 20:
x = 228 / 20
x = 11.4
So, Felix has spent a total of 11.4 hours (or 684 minutes) running this month.
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Which choice is equivalent to the product below when x≥ 0?
√10x² √5x
A. 5x√2x
B. x√15
C. √15x²
D. 5x√2
SUBMIT
Answer:
Step-by-step explanation:
We can simplify the given product using the properties of radicals:
√10x² √5x = √(10*5)x^(2+1) = √50x^3
We can further simplify the radical by factoring out the largest perfect square from 50, which is 25:
√50x^3 = √(25*2)x^3 = 5x√2
Therefore, the product √10x² √5x is equivalent to 5x√2, when x≥0.
To simplify the product √10x² √5x, we can combine the square roots and simplify:
√10x² √5x = √(10x² * 5x) = √(50x³) = √(25x² * 2x) = 5x√2x
Therefore, the choice that is equivalent to the original product when x≥0 is A. 5x√2x.
If f(x) = 2x2-x-4 and g(x) = x² + 5x + 2, find an express
a ）f(x) + xg(x)
b）[f(x)]²
c） f²(x)
d）gf(x).
a) [tex]f(x) + xg(x) = x^{3} + 7x^{2} + x - 4.[/tex]
b) [tex][f(x)]² = 4x^{4} - 4x^{3} - 15x^{2} + 8x + 16[/tex]
c) [tex]f^{2}(x) = 4x^{4} - 4x^{3} - 15x^{2} + 8x + 16[/tex]
d) [tex]gf(x) = 2x^{4} + 8x^{3} - 13x^{2} - 3x - 8.[/tex]
what is expression ?
It is possible to do mathematical operations like addition, subtraction, division, and multiplication. An expression is put together as follows: Number, expression, and mathematical operator.
a) f(x) + xg(x)
First, we need to find xg(x), which is x multiplied by g(x):
[tex]xg(x) = x(x^{2} + 5x + 2) = x^{3} + 5x^{2} + 2x\\\\f(x) + xg(x) = 2x^{2} - x - 4 + x^{3} + 5x^{2} + 2x\\\\f(x) + xg(x) = x^{3} + 7x^{2} + x - 4[/tex]
Therefore, [tex]f(x) + xg(x) = x^{3} + 7x^{2} + x - 4.[/tex]
b) [f(x)]²
To square f(x), we can simply multiply it by itself:
[f(x)]² = (2x² - x - 4)(2x² - x - 4)
[tex][f(x)]² = 4x^{4} - 4x^{3} - 15x^{2} + 8x + 16[/tex]
c) f²(x)
Since f²(x) means f(x) times f(x), we can use the distributive property of multiplication:
[tex]f^{2} (x) = f(x) * f(x)\\\\f^{2}(x) = (2x^{2} - x - 4)(2x^{2} - x - 4)[/tex]
[tex]f^{2}(x) = 4x^{4} - 4x^{3} - 15x^{2} + 8x + 16[/tex]
d) gf(x)
To find gf(x), we need to multiply g(x) by f(x):
[tex]gf(x) = (x^{2} + 5x + 2)(2x^{2} - x - 4)[/tex]
Multiplying each term of g(x) by each term of f(x), and simplifying:
gf(x) = 2x⁴ + 8x³ - 13x² - 3x - 8
Therefore, [tex]gf(x) = 2x^{4} + 8x^{3} - 13x^{2} - 3x - 8.[/tex]
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100 Points! Algebra question. Find each value if f(x)=5/x+2and g(x)=-2x+3. Only looking for an answer to question A. Please show as much work as possible. Photo attached. Thank you!
Therefore, the value of f(m-2) is 5/(m-2) + 2, and the value of function g(1/2) is 2.
What is function?In mathematics, a function is a rule or correspondence between two sets, where each input value from the first set (called the domain) corresponds to exactly one output value in the second set (called the range). A function is often represented by a formula, equation, or graph.
Here,
1. To find f(m-2), we substitute (m-2) for x in the expression for f(x):
f(m-2) = 5/(m-2) + 2
So the value of f(m-2) is 5/(m-2) + 2.
2. To find g(1/2), we substitute 1/2 for x in the expression for g(x):
g(1/2) = -2(1/2) + 3
So the value of g(1/2) is -1 + 3, which simplifies to 2.
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Karla invests $10,000 into an account with a 2.2% interest that is compounded annually.
How much money will she have in this account if she keeps it for 5 years? Round your answer to the nearest dollar. Do not round at any other point in the solving process; only round your answer.
Karla will have approximately $11,149 in the account after 5 years, rounded to the nearest dollar.
How much money will Karia have in this account if she keeps it for 5 years?The formula accrued amount in a compounded interest is expressed as;
A = P( 1 + r/n )^( n × t )
Where A is accrued amount, P is principal, r is interest rate and t is time.
Given that:
Principal P = $10,000Compounded annually n = 1Time t = 5 yearsInterest rate r = 2.2%Accrued amount A = ?First, convert R as a percent to r as a decimal
r = R/100
r = 2.2/100
r = 0.022
Plug the given values into the above formula and solve for A.
A = P( 1 + r/n )^( n × t )
A = 10,000( 1 + 0.022/1 )^( 1 × 5 )
A = 10,000( 1 + 0.022 )^( 5 )
A = 10,000( 1.022 )^( 5 )
A = $11,149
Therefore, the accrued amount after 5 years is $11,149.
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A triangle has two angles with measures of 118 and 18 degrees. The side across from the 18 degree angle has a length of 8 millimeters.
Which figure represents this triangle?
The figure that represent the triangle described in the question is option (C).
Understanding TriangleTriangle is a basic geometric shape that consists of three straight sides and three angles.
We can say triangle is a polygon with three sides and three vertices, and is one of the simplest and most fundamental shapes in geometry.
Class of Triangle based on sides
Equilateral: triangle with all sides of equal lengthIsosceles: triangle with two sides of equal lengthScalene: triangle with no sides of equal lengthClass of Triangle based on their angles
Acute triangles: all angles are less than 90 degreesRight triangles: one angle is exactly 90 degreesObtuse triangles: one angle is greater than 90 degreesLearn more about triangle here:
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Sam wants to invest $6000 in a savings account for 5 years.
Account A pays simple interest at a rate of 6% per year.
Work out the amount of profit he will make with this account.
poppy seed muffins 1
cinnamon rolls 3
bran muffins 2
apple fritters 2
croissants 2
Considering this data, how many of the next 20 pastries served should you expect to be bran muffins?
Answer:3/10
Step-by-step explanation:
What is a rigid transformation and what are three types of rigid transformations?
*
10 points
Rigid Transformations are movement of figures where the size and shape change. Examples are translations, reflections and rotations.
Rigid Transformations have congruent preimages and images. Examples include translations, reflections, and rotations.
Rigid transformation have non-congruent preimages and images. Examples include reflections, rotations and translations.
Rigid Transformations use scale factors to create new images from preimages. Examples include maps, diagrams and drawings.
A rigid transformation and the three types of rigid transformations are: B. Rigid Transformations have congruent preimages and images. Examples include translations, reflections, and rotations.
What is a transformation?In Mathematics and Geometry, a transformation can be defined as the movement of a point from its initial position to a new location. This ultimately implies that, when a geometric figure or object is transformed, all of its points would also be transformed.
Generally speaking, there are three (3) main types of rigid transformation and these include the following:
TranslationsReflectionsRotations.In conclusion, rigid transformation are movement of geometric figures where the size and shape does not change because they have congruent preimages and images.
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the lcm of two numbers is 60 and their sum is 27
what are the numbers?
Answer: The two numbers are 5 and 12
Step-by-step explanation:
As the least common multiple of two numbers is
60
, the two numbers are factors of
60
.
Factors of
60
are
{
1
,
2
,
3
,
4
,
5
,
6
,
10
,
12
,
15
,
20
,
30
,
60
}
As one of the numbers is
7
less than the other, the difference of two numbers is
7
Among
{
1
,
2
,
3
,
4
,
5
,
6
,
10
,
12
,
15
,
20
,
30
,
60
}
,
3
&
10
and
5
&
12
are the only two pair of numbers whose difference is
7
. But Least common multiple of
3
and
10
is
30
.
Hence, the two numbers are
5
and
12
.
Please help me solve these question(giving 50 points)
The restrictions on the polynomial expression [tex]\frac{x^2 - 25}{x - 1} \div \frac{x^2 - x - 30}{x^2 - 4x - 12}[/tex] are at x = -5, -2, 1 and 6
Simplifying the expressionFrom the question, we have
[tex]\frac{27x^2y^3}{45x^4}[/tex]
Divide the variables
So, we have
[tex]\frac{27y^3}{45x^2}[/tex]
Divide 27 and 45 by 9
So, we have
[tex]\frac{3y^3}{5x^2}[/tex]
Hence, the solution is [tex]\frac{3y^3}{5x^2}[/tex], x ≠ 0
The simplest form of a rational expressionGiven that
[tex]\frac{x + 2}{x^2 - 5x - 14}[/tex]
Factorize the numerator
So, we have
[tex]\frac{x + 2}{(x + 2)(x - 7)}[/tex]
Divide
[tex]\frac{1}{x - 7}[/tex]
So, the solution is [tex]\frac{1}{x - 7}[/tex] , where x ≠ 7
The possible functionThe hole is given as (2, 1/3)
This means that the graph is undefined at (2, 1/3)
One possible equation from the list of options is
[tex]f\left(x\right)\:=\:\frac{x\:-\:2}{x^2\:-\:x\:-\:2}[/tex]
Restrictions on the polynomialThe expression is given as
[tex]\frac{x^2 - 25}{x - 1} \div \frac{x^2 - x - 30}{x^2 - 4x - 12}[/tex]
The restrictions on the polynomial is the domain
When solved graphically, we have the restrictions to be at x = -5, -2, 1 and 6
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Suppose that a and b are positive numbers for which log, (a) = log15(b) = log25 (a + 2b). What is the value of a
Answer: The value of "a" is given by a = 25 - 2b, where "b" is a positive number.
Step-by-step explanation:
Given that log(a) = log15(b) = log25(a + 2b), we can use the properties of logarithms to solve for the value of a.
Since log(a) = log15(b), we can equate the bases and eliminate the logarithms:
a = 15^log15(b) .....(1)
Similarly, since log(a) = log25(a + 2b), we can equate the bases and eliminate the logarithms:
a = (a + 2b)^log25(a + 2b) .....(2)
Now, we can equate the right-hand sides of equations (1) and (2) since they are both equal to a:
15^log15(b) = (a + 2b)^log25(a + 2b)
Taking the logarithm of both sides with base 15, we get:
log15[15^log15(b)] = log15[(a + 2b)^log25(a + 2b)]
Using the property that loga(a^x) = x, we can simplify the left-hand side:
log15(b) = log15[(a + 2b)^log25(a + 2b)]
Now, we can equate the bases and eliminate the logarithms:
b = (a + 2b)^log25(a + 2b)
Taking the logarithm of both sides with base (a + 2b), we get:
log(a + 2b)(b) = log(a + 2b)[(a + 2b)^log25(a + 2b)]
Using the property that loga(a^x) = x, we can simplify the right-hand side:
log(a + 2b)(b) = log25(a + 2b)
Since log(a + 2b)(b) = log(a + 2b)/logb(a + 2b) by the change of base formula, we can rewrite the equation as:
log(a + 2b)/logb(a + 2b) = log25(a + 2b)
Now, we can equate the numerators and denominators separately:
log(a + 2b) = log25(a + 2b)
1 = log25(a + 2b)/(log(a + 2b))
Since loga(a) = 1, we can rewrite the equation as:
log25(a + 2b) = log(a + 2b)/(log(a + 2b))
Using the property that loga(a^x) = x, we get:
log25(a + 2b) = 1
This implies that 25^1 = a + 2b, since we are using the definition of logarithm which states that loga(b) = c is equivalent to a^c = b.
Therefore, a + 2b = 25.
Given that a and b are positive numbers, we can deduce that a + 2b > 0.
Solving for a, we get:
a = 25 - 2b
Since a and b are both positive, a = 25 - 2b > 0.
So, the value of a is greater than zero and is given by a = 25 - 2b, where b is a positive number.
The volume of a cube is increasing at a rate of 56 in∧3/sec. At what rate is the length of each edge of the cube changing when the edges are 6 in. long? (Recall that for a cube,
V = x∧3.)
Answer: The rate at which the length of each edge is changing is approximately 0.5185 inches per second when the edges are 6 inches long.
Step-by-step explanation:
Let's denote the volume of the cube as V and the length of each edge as x. Given that the volume of a cube is V = x^3, we can find the rate at which the length of each edge is changing.
We're given that the rate of change of the volume is dV/dt = 56 in³/sec. We want to find the rate of change of the length of each edge, which is dx/dt, when the length of each edge is 6 inches.
First, we differentiate the volume equation with respect to time t:
V = x^3
dV/dt = d(x^3)/dt
Using the chain rule:
dV/dt = 3x^2 * (dx/dt)
Now, we know that dV/dt = 56 in³/sec and x = 6 in. Plugging these values into the equation, we get:
56 = 3 * (6)^2 * (dx/dt)
Solving for dx/dt:
56 = 108 * (dx/dt)
dx/dt = 56 / 108
dx/dt ≈ 0.5185 in/sec (rounded to four decimal places)
So, the rate at which the length of each edge is changing is approximately 0.5185 inches per second when the edges are 6 inches long.
nasim is working two summer jobs making $9 per walking dogs and $8 per hour cleaning tables. Nasim must earn no less than $130 this week. Write an inequality that would represent the possible values for the number of hours walking dogs d and the hours cleaning tables c that nasim can work in a given week
The inequality that would represent the possible values for the number of hours walking dogs is 9d + 8c ≥ 130
How can the inequality be written?Inequalities in mathematics can be described as one that is been used in the expression of the relationship between two values that are not equal
It should be noted thed that Inequality implies not equal with the symbol (≠)” symbols ≥ < > ≤. From the question , number of hours walking dogs (d) Let number of hours clearing tables an be represented by( c) Hence the appropriate inequality is 9d + 8c ≥ 130.
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For which equations is 8 a solution? Select the four correct answers. x + 6 = 2 x + 2 = 10 x minus 4 = 4 x minus 2 = 10 2 x = 4 3 x = 24 StartFraction x Over 2 EndFraction = 16 StartFraction x Over 8 EndFraction = 1
The equations for which 8 is a solution:
are x minus 4 = 4
2 x = 4
StartFraction x Over 8 EndFraction = 1
x + 6 = 2
How find which equations is 8 a solutionThe equations for which 8 is a solution are:
x - 4 = 4 (if we substitute x=8, we get 8-4=4 which is true)
2x = 4 (if we substitute x=8, we get 2*8=16 which is true)
StartFraction x Over 2 EndFraction = 16 (if we substitute x=8, we get 8/2=4 which is not true)
StartFraction x Over 8 EndFraction = 1 (if we substitute x=8, we get 8/8=1 which is true)
So, the correct answers are:
x minus 4 = 4
2 x = 4
StartFraction x Over 8 EndFraction = 1
x + 6 = 2
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To the nearest millimeter, a cell phone is 135 mm long and 69 mm wide. What is the ratio of the width to the length?
The ratio of the width to the length is (Type the ratio as a simplified fraction.)
The ratio of the width to the length of the cell phone is 23/65.
What is ratio?
Ratio is the quantitative relation between two amounts showing the number of times one value contains or is contained within the other.
To find the ratio of the width to the length of the cell phone, we use the formula below.
Formula:
n = W/L............................. Equation 1Where:
n = Ratio of width to length of the cell phoneW = Width of the cell phoneL = Length of the cell phoneFrom the question,
Given:
W = 69 mmL = 135 mmSubstitute these values into equation 1
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57% chance child is born with disease, a woman has 3 kids what is the probability all 3 get the disease?
The probability that all 3 children will be born with the disease is approximately 0.195 or 19.5%.
We have,
Assuming that the probability of a child being born with the disease is independent of whether or not their siblings are born with the disease, we can use the multiplication rule of probability:
P(all 3 children have the disease)
= P(first child has the disease) x P(second child has the disease) x P(third child has the disease)
Since each child has a 57% chance of being born with the disease:
P(all 3 children have the disease)
= 0.57 x 0.57 x 0.57
Now,
P(all 3 children have the disease)
= 0.195
Therefore,
The probability that all 3 children will be born with the disease is approximately 0.195 or 19.5%.
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Fill in the table using this function rule. y = - 3x-3 -4 ? - 2 ?
The missing values of function rule, Y for corresponding value of X= (-4 ) and (-2) will be 9 and 3 respectively.
[tex]X|-4 |- 2|\\ Y|\quad9\; | \quad3\;|[/tex]
How to calculate the value of function?The function is commonly expressed as [tex]f(x) =........[/tex]If you wish to calculate the function for a variable or expression, replace x with that value.Use addition, subtraction, multiplication, and division as well as any other applicable mathematical operations to simplify the statement.If you like, you may use variables to keep the result in a generic form or use particular values in place of the variable to get a numerical result.Now for the given fucntion ,
By substituting the values of x into the equation [tex]y = -3x - 3[/tex] and solving for y, we can determine the values of y for [tex]x = -4\; and -2[/tex].
[tex]For \;x = -4:\\y = -3(-4) - 3\\y = 12 - 3\\y = 9[/tex]
Hence, for x =(-4), y= 9
[tex]For\; x = -2:\\y = -3(-2) - 3\\y = 6 - 3\\y = 3[/tex]
Hence, for x =( -2), y = 3
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Correct Question:Fill in the table using this function rule. y = - 3x-3
[tex]X|-4 |- 2|\\ Y|\quad?\; | \quad?\;|[/tex]