There are [tex]8^5\\[/tex] cubes in the Container.
What is Exponents and Power?Exponents and powers are ways used to represent very large numbers or very small numbers in a simplified manner.
For example, if we have to show 3 x 3 x 3 x 3 in a simple way, then we can write it as [tex]3^4[/tex], where 4 is the exponent and 3 is the base.
Given:
Volume of Container = [tex]8^7[/tex] cm³
Volume of Each cube = 8² cm³
So, the number of cubes in the container
= Volume of Container / Volume of Each cube
= [tex]8^7[/tex] cm³ / 8² cm³
Now, using Exponents property
[tex]a^m / a^n= a^{m-n[/tex]
Then, number of cubes in the container
= [tex]8^7[/tex] cm³ / 8² cm³
= [tex]8^{7-2[/tex]
= [tex]8^5\\[/tex]
Hence, the number of cubes are [tex]8^5\\[/tex].
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Find $QR$.
A triangle Q S T is drawn. A line pass through vertex T intersects the side Q S at point R. Angle T R Q is marked right angle. Length of side Q T is labeled 4. 7, length of side T S is labeled 4. 7 and length of segment R S is labeled 1. 3
In the given triangle QST where TRQ represents as a right angled triangle the value of QR is equal to 1.36 .
As given in the question,
In the triangle QST,
Line passing through vertex Q intersect QS at R such that TRQ is a right angled triangle.
RS = 1.3
QT = ST ( both are 4.7 )
⇒ ∠Q ≅∠S
⇒∠Q and ∠S are not right angle.
⇒ In ΔTRQ , TR ⊥ QS
In ΔTRS,
Using Pythagoras theorem,
ST² = RS² + RT²
⇒ 4.7² = ( 1.3 )² + RT²
⇒RT = 4.5
In ΔTRQ,
QR² = QT² - RT²
⇒QR = √ 4.7² - 4.5²
⇒QR = 1.36
Therefore, the value of QR in the given triangle with given conditions is equal to 1.36.
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is this nonlinear,linear or nonproportional?
Answer:
This equation is Linear.
Step-by-step explanation:
How do you find f (- 2 on a graph?
To find the value of f(-2) on a graph, you would locate the point (-2, y) on the graph, where y is the value of the function at x = -2. The value of y is the y-coordinate of the point on the graph.
In a cartesian coordinate system, the x-axis and y-axis are perpendicular to each other. The x-axis is the horizontal axis and the y-axis is the vertical axis. When a function is graphed, the x-coordinate is input into the function and the y-coordinate is the output of the function. So, when you are trying to find the value of f(-2) on a graph, you are looking for the y-coordinate of the point where x = -2. To find this point, you would move horizontally along the x-axis until you reach the value of -2. Then, you would move vertically from that point until you reach the point on the graph. The y-coordinate of that point is the value of f(-2)
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Let g be a vertical shrink by a factor of 1/3 followed by a translation 3 units right
of the graph of f(x) = srqt of x + 5.
Answer:
g(x) = ([tex]\sqrt{x-3}[/tex])/3 + 5
Step-by-step explanation:
f(x) = [tex]\sqrt{x}[/tex] + 5
[tex]\sqrt{x}[/tex] + 5 ==> 1/3 * [tex]\sqrt{x}[/tex] + 5 ==> vertical shrink is when the function's y-coordinates shrink from the y-intercept (5 is the y-int) by a factor of 1/3
[tex]\sqrt{x}[/tex]/3 + 5 ==>( [tex]\sqrt{x-3}[/tex])/3 + 5 ==> in order to translate the graph 3 units to the right, subtract x by 3 since x is being affected when the graph moves left/right. In addition, x now has to be 3 units greater in order for the function to have the same value:
[tex]\sqrt{4-3}[/tex] = [tex]\sqrt{1}[/tex]
4 > 1 and 4 = 1 + 3
Hence, g(x) = ([tex]\sqrt{x-3}[/tex])/3 + 5
You are given quadrilateral PQRS, such that
ABCD = T (0, -8)(Ro 180°(R y-axis (PQRS)))
What are the new coordinates for ABCD?
On solving the provided question, we can say that from the graphs
the new coordinates for ABCD (-1,-2),(2,-3),(-4,-6),(-3,8)
What is graphs?Mathematicians use graphs to logically convey facts or values using visual representations or charts. A graph point will typically reflect a relationship between two or more things. Nodes, or vertices, and edges make form a graph, a non-linear data structure. Glue together the nodes, often referred to as vertices. This graph has vertices V=1, 2, 3, 5, and edges E=1, 2, 1, 3, 2, 4, and (2.5), (3.5). (4.5). Statistical charts (bar charts, pie charts, line charts, etc.) graphical representations of exponential growth. a logarithmic graph in the shape of a triangle
here,
ABCD = T (0, -8)(Ro 180°(R y-axis (PQRS)))
from the graphs
the new coordinates for ABCD
(-1,-2),(2,-3),(-4,-6),(-3,8)
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Describe the equation x=3.
a. What does the graph look like?
b. What is the slope?
The graph of the equation, x = 3, would be a vertical line that intersects the x axis at x = 3.
The slope of the graph would be undefined.
What is the slope of a vertical line ?Vertical lines have an undefined slope because slopes are based on the change in the horizontal climb of a line. Seeing as vertical lines have no horizontal change, it means that the slope in undefined.
The line, x = 3 is a vertical line because the x - axis is the horizontal line. A line that would intersect it at x = 3 would therefore have to be a vertical line which is straight or it would not remain at x = 3 in perpetuity.
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Last week, Alex took 90 selfies and Vic took 75 selfies. Today,
they each decided that some of these selfies were not very good
and deleted them. Alex deleted three times as many selfies
as Vic. Now, Alex has half as many selfies as Vic. How many
selfies did Alex delete?
The number of selfies deleted by Alex is 63.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
The solution of an equation is the set of all values that, when substituted for unknowns, make an equation true.
Given that, last week, Alex took 90 selfies and Vic took 75 selfies.
Let the number of selfies deleted by Vic be s.
Alex deleted three times as many selfies as Vic.
So, the number of selfies deleted by Alex =3s
Alex has half as many selfies as Vic.
Now, 90-3s = 1/2 (75-s)
180-6s=75-s
5s=105
s=21
The number of selfies deleted by Alex =3s
= 63
Therefore, the number of selfies deleted by Alex is 63.
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pls helppp
One-third of the cars in the parking
lot are silver. There are 165 cars in
the lot. How many cars are silver?
Answer: 55
Step-by-step explanation:
Its 55 because 55 is one third of 165! Hope this helps :)
What are the 7 properties of logarithms?
properties of logarithms -Logarithm Base Properties
Product Property
Quotient Property
Power rule
Change of Base rule
Reciprocal rule
Exponent law vs Logarithm law
Natural Logarithm properties.
properties of logarithms functions are used to solve logarithm problems. We have learned many properties in basic math such as commutative, associative and distributive, which are applicable for algebra.
The properties of logarithms are used to simplify the complex problems involving logarithmic functions. These properties help in converting the functions into easily computable parts.
The logarithmic number is associated with exponent and power, such that if x n = m, then it is equal to log x m=n. Hence, it is necessary that we should also learn exponent law.
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please answer quick , and explain
Calculate the areas of each simpler figure, then sum the areas to determine the overall area of the composite figure.
What does Area of Composite Shapes mean?As specified by any composite shape, the area of composite shapes is the space it occupies. The assemblage of simple shapes creates a composite shape. As a result, the area of the composite shape is calculated by separately adding each of the fundamental shapes.Simple geometric forms are assembled into a composite figure. Divide a composite figure or other figure with an atypical shape into straightforward, non-overlapping figures to determine its area. Calculate the areas of each simpler figure, then sum the areas to determine the overall area of the composite figure.To learn more about areas refer to:
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A door manufacturer specifies the width of a front-entrance door as 36 inches with a tolerance of ±0.0625 inches. When designing a prefabricated home, what should you ensure the width of the door opening is greater than?
- 33.75 inches
- 35.9375 inches
- 36.0625 inches
- 37.0625 inches
- 38.75 inches
Based on mathematical operations, when designing a prefabricated home, you must ensure that the width of the door opening is greater than A. 33.75 inches, given the sample mean of 36 inches with a tolerance (margin of error) of ±0.0625 inches.
What is the margin of error?The margin of error is the tolerance level that creates the confidence interval for the sample mean.
With a sample mean of 36 inches for the door opening and a tolerance level of ±0.0625 inches, the width can be designed to measure between 35.9375 inches and 36.0625 inches.
This measurement implies that the upper limit for the width (confidence interval) is 36.0625 inches while the lower limit is 35.9375 inches.
Thus, the width of the door opening must be greater than Option A.
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Problem No. 7 Three equidistant dots on each of two parallel lines (see sketch for illustration purposes only) are joined in all possible ways. How many triangles can be formed?
Three equidistant dots on each of two parallel lines (see sketch for illustration purposes only) are joined in all possible ways. The number of triangles that can be formed is 20 triangles
How do we determine the value?A "Three equidistant dots" refers to three points that are evenly spaced apart on a line. These three points could represent the vertices of a triangle, and in this case, the question is asking how many triangles can be formed by connecting each of the three dots on one line to each of the three dots on a parallel line.
In total, there are 3 dots on one line and 3 dots on the other line, for a total of 6 dots, and the question is asking how many ways the dots can be connected to form triangles.
To find the number of triangles that can be formed, we use the formula for the number of combinations of n things taken 3 at a time, which is n! / (r!(n-r)!). In this case, n = 6 and r = 3.
So, there are 6! / (3! * 3!) = 20 triangles that can be formed.
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Fill in the Blanks
Evaluate the following trigonometric expressions.
a. 2 cos^2(pi/8) -1=
b. 2tan(11/pi)/1-tan^2(11pi/12)=
2 cos^2(pi/8) -1= ,
x=(2n + 1) π/4 + π/8, where n is an integer.
What is meant by integer?
An integer, pronounced "IN-tuh-jer," is a whole number that can be positive, negative, or zero and is not a fraction.Integer examples include: -5, 1, 5, 8, 97, and 3,043. 1.43, 1 3/4, 3.14, and other numbers that are not integers are some examples.The Latin word integer, from the prefix in ("not") plus tangere, means "whole" or (literally) "untouched" ("to touch").An integer is any number that may be expressed without using any fractions. Since there are no fractions in integers, they are essentially entire numbers that can be positive, zero, or negative.An integer field can have 3, 5, 10, or 20 digits, with length being defined in terms of the number of digits. One byte of storage is required for a 3-digit field.x=(2n + 1) π/4 + π/8, where n is an integer.
We use the double angle identity 2[tex]cos^{2}[/tex]A−1 = cos2A
if x − π/8 =A, then 2[tex]cos^{2}[/tex] (x− π/8) −1 = cos(2(x − π/8)) = cos(2x − π/4)
Hence cos(2x − π/4) = 0
and 2x − π/4 = (2n + 1) π/2, where n is an integer
or 2x = (2n+1) π/2 + π/4
or x = (2n + 1) π/4 + π8, where n is an integer.
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Match the situation to the expression that represents the number of inches the plant grew this week.
A plant measured x inches tall last week, and 8 inches tall this week. answers x/8,x-8, 8-x
The Height of the plant is (8-x) inches
What is Expression?A mathematical operation such as subtraction, addition, multiplication, or division is used to combine terms into an expression. In a mathematical expression, the following terms are used:
An absolute numerical number is referred to as a constant.Variable: A symbol without a set value is referred to as a variable.Term: A term can be made up of a single constant, a single variable, or a mix of variables and constants multiplied or divided.Coefficient: In an expression, a coefficient is a number that is multiplied by a variable.Given:
A plant measured x inches tall last week, and 8 inches tall this week.
So, to find the exact growth of plant from x inches to 8 inches then we have to find the difference between these two heights.
Then, the height of tree per week
= height of plant this week - height if plant previous week.
= 8- x
Hence, the expression is 8-x.
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I need help with this.
Answer:
the answer is in the picture
How do you solve log2x 2?
He coined a term from the two ancient Greek terms logos, meaning proportion, and Arithmos, meaning number; compounding them to produce the word “logarithm.
An exponential equation is an equation in which the variable appears in an exponent.
A logarithmic equation is an equation that involves the logarithm of an expression containing a variable.
To solve exponential equations, first see whether you can write both sides of the equation as powers of the same number.
Divide each term in
log(2)x=2
by log(2).
log(2) x log(2)=2log(2)
Simplify the left side.
Cancel the common factor of
log(2).
x=2log(2)
The result can be shown in multiple forms.
Exact Form:
x=2log(2)
Decimal Form:
x=6.6438561
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statistics uses methods that generalize results obtained from a sample to the population and measure the reliability of the results. t or f
Inferential statistics use techniques that extrapolate results from a sample to the population and assess the accuracy of the findings.
What is the difference between a population and a sample?The entire group about whom you want to make conclusions is referred to as a population.
The particular group from which you will gather data is known as a sample. The sample size is always smaller than the population as a whole.
It is crucial to separate, handle, and organize all data that is given to us in order to streamline work. Descriptive statistics refer to the reading of the given data that supports characterizing or supplying the well-behaved data for analysis.
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Is X² and 2x like terms?
No, X² and 2x are not like terms. Like terms are terms that have the same variables and exponents, but different coefficients. X² and 2x have the same variable (x) but different exponents (2 and 1, respectively).
Like terms are terms that have the same variables and exponents, but different coefficients. X² and 2x are not like terms because they have the same variable (x) but different exponents (2 and 1, respectively). When two terms have the same variable and exponent, they are considered like terms. For example, 3x² and 4x² are like terms because they have the same variable (x) and exponent (2). However, if the terms have different variables or different exponents, they are not like terms. For example, X² and 2y are not like terms because they have different variables (x and y). Similarly, 2x and x² are not like terms because they have different exponents (1 and 2, respectively). To sum up, like terms must have the same variables and exponents in order to be considered as such.
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in most cases, the product of a monomial and a binomial is a ___.
In most cases, the product of a monomial and a binomial is a trinomial.
A monomial is an algebraic expression that is a single term, such as 2x or 5y^3. A binomial is an algebraic expression that is a sum or difference of two terms, such as x+y or 2x-3y. When a monomial is multiplied by a binomial, the result is an expression with three terms, which is called a trinomial.
For example, when we multiply the monomial 2x with the binomial x+y, we get:
(2x)(x+y) = 2x^2 + 2xy
This is a trinomial because it has three terms: 2x^2, 2xy and the constant term is missing.
It's worth noticing that, this is a general rule but not always true, there are some cases when the product of a monomial and a binomial is a binomial, like when the monomial has a factor that cancels out one of the terms in the binomial.
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the hair on your head grows 1in 1 inch per month discreet or continuous
Answer: Continuous
Step-by-step explanation: I say it is continuous as the hair will grow continuously but we can't determine how exactly it'll grow 1 inch a month and the inches won't be integers if the hair is grown more than an inch.
What is the slope intercept form of 2x y =- 2?
The slop-intercept form of 2x + y = -2 is y = -2x - 2.
The slope-intercept form of a linear equation is y = mx + b, where m is the slope of the line and b is the y-intercept (the point where the line crosses the y-axis).
To convert the equation 2x + y = -2 into slope-intercept form, we can follow these steps:
1. Isolate y on one side of the equation. We can do this by subtracting 2x from both sides: y = -2x - 2
2. Now we have y = -2x - 2, which is in slope-intercept form.
So, the slope-intercept form of 2x + y = -2 is y = -2x - 2. The slope of the line is -2 and the y-intercept is (-2,0).
Therefore, the slope-intercept form of the equation 2x + y = -2 is y = -2x - 2.
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a girl borrowed Rs 128000 from a bank to buy a piece of land. If the land charges 15% p.a, compounded half yearly, what will she have to pay after 1½ years? Also find fhe compound interest.
The compound interest would be Rs. 35835.51.
What is compound interest?
Compound interest is the interest on a loan or deposit calculated based on both the initial principal and the accumulated interest from previous periods.
To calculate the total amount to be paid after 1.5 years at 15% p.a. compounded half-yearly, the formula is:
A = P(1 + r/n)^(nt)
Where:
A = total amount
P = principal amount (Rs 128000)
r = interest rate (15%)
n = number of times the interest is compounded per year (2 times per year)
t = number of years (1.5 years)
So, the total amount to be paid after 1.5 years would be:
A = 128000 * (1 + 0.15/2)^(2*1.5) = Rs 163835.51
The compound interest can be calculated by subtracting the principal amount from the total amount:
CI = A - P = 163835.51 - 128000 = Rs 35835.51
Hence, the compound interest would be Rs. 35835.51.
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how to tell the difference between no solution, infinite solutions, and one solution
Answer:if you try to solve the equation and get a variable or a number equal to itself.
Step-by-step explanation:
What is truth?
Supposed to be philosophy but nobody cares.
The truth also called as property of sentences , assertions and beliefs.
What is Declaration of truth and false in the mathematics?
Declaration of truth and false in mathematics are 1 and 0 respectively.
Questions on fact and falsity saturate our lifestyles as humans. while we may not continually understand what's actual, we've intuitive thoughts of what it might mean for some thing to be actual and work very difficult to get “nearer” to it. We often make claims approximately what's authentic apparently with little to no problem. but we find ourselves in a consistent conflict with falsehoods. Our paintings, our love lives, or even our most loved leisure times are laden with discovering fact over falsehood. Is that concept real.
Hence, The truth is property of sentences , assertions and beliefs.
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you have an ant farm with 29 ants. The population of ants in your farm will double every 3 months. The table shows the population growth of the ants over nine months. Decide whether the table represents a linear function or a nonlinear function. After one year, how many ants will there be in the ant farm?
The number of ants after 1 year=464 and the table will follow no-linear function as the equation will be a exponential equation for the growth of ants.
What is a exponential equation?
An exponential equation is an equation with exponents where the exponent (or) a part of the exponent is a variable. For example, 3^x = 81, 5^x - 3 = 625, 6^2y - 7 = 121 etc are some examples of exponential equations. We may come across the use of exponential equations when we are solving the problems of algebra, compound interest, exponential growth, exponential decay, etc.
Now,
The exponential equation that will be followed by given ant's growth will be
y=29(2)^t/3
where 29=initial population
t=Number of months
and It will represent a non-linear function as a exponential function is a no-linear function.
Population after 1 year
y=29(2)^12/3
=29*16
=464
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An online sales store started its business with 15 sales per week. If their sales increased by 18% each week, use an exponential growth model to find the week in which they exceeded 1,000 sales per week
They made more than 1,000 sales per week for 26 weeks.
A sale is a transaction that involves exchanging products or services for a certain sum of money. To put it another way, a sale is any action that includes giving the buyer possession of a thing or commodity in return for payment.
The first sale is 15 units.
Sales are rising at a weekly rate of 18%.
1000 are the final sales.
The next week is when sales reach 1,000 or more:
[tex]1000=15 \times\left(1+\frac{18}{100}\right)^t \\\frac{1000}{15}=\left(\frac{118}{100}\right)^t \\\frac{200}{3}=(1.18)^t[/tex]
Solving further we get,
[tex](\left.\log\frac{200}{3}\right)=t \log 1.18[/tex]
Thus we get,
t=25.37
In the twenty-fifth week, the company makes 1000 in sales.
As a result, the company's revenues exceeded 1000 in the 26th week.
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two distinct circles and a square lie in the plane. what is the maximum number of points of intersection of two or more of these three figures?
The maximum number of points of intersection of two distinct circles and a square is 18.
The maximum possible intersection points of a circle and a line is 2. A square comprises 4 line segments, hence, the maximum possible intersection points of a circle and a square is 2 x 4 = 8 points.
The condition for 8-point intersection is that the diameter of the circle must be between s and s√2, where s is the length of the sides of the square, or it can be written as:
s < d < s√2
In the problem, there are two circles and a square. Let's denote the circles as C1 and C1, while the square as S
- Maximum number of intersection points of C1 and C2 is 2
- Maximum number of intersection points of C1 and S is 8
- Maximum number of intersection points of C2 and S is 8
Hence, the maximum possible intersection points of these figures is 2 + 8 + 8 = 18 points.
The possible construction where these three figures have maximum intersection points is depicted on the attached picture.
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Which of the following equations is equivalent to -5(x-1)=2x+15
Select one:
-7x =14
-7x =20
-7x =10
-7x =16
Answer:
-7x = 10
Step-by-step explanation:
step 1: multiply each term inside the parentheses by -5, to get:
-5x + 5 = 2x + 15
you can subtract 2x from each side of the equation to get:
-7x + 5 = 15
now you subtract 5 from each side to get:
-7x = 10
Where is log x defined?
Log x is defined for all positive real numbers (x>0). Exponential functions increase exponentially (x^y) and logarithmic functions decrease logarithmically (log x).
Log x is defined as the inverse of the exponential function. Exponential functions increase exponentially (x^y) and logarithmic functions decrease logarithmically (log x). The logarithm of a number is the exponent to which another fixed number must be raised to produce that number. Log x is defined for all positive real numbers (x>0). This means that any number that is greater than 0 can have a logarithm associated with it. For example, log 10 = 1 because 10^1 is equal to 10. The logarithm of a number can also be expressed in terms of other logarithms. For example, log 10 = log 10^2 = 2 log 10. Log x can also be used to solve equations and find the value of unknown variables.
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Understand the Pythagorean
You can use the Pythagorean Theorem to write an equation that describes how the side lengths are related as 20² + 15² = 25².
What is Pythagorean theorem?The Pythagorean theorem can be defined as a mathematical expression in Euclidean geometry that can be used to solve for any of the three (3) side lengths of a right triangle.
Mathematically, Pythagorean's theorem is given by this mathematical expression:
a² + b² = c²
20² + 15² = 25².
400 + 225 = 625
625 = 625 (proof).
In conclusion, you would know that the geometric proof of the Pythagorean Theorem can be applied to all right triangles because the square of the hypotenuse is always equal to the sum of the square of the opposite side and the adjacent side of a right triangle.
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