Lena is not correct in her statement that she will use more pages if she puts 5 stickers on a page instead of 10 stickers on a page.
Is it true that if you put 8 stickers on a page instead of 4, you will use less pages?
Yes, it is true that if you put 8 stickers on a page instead of 4, you will use less pages. The total number of stickers divided by the number of stickers per page determines the number of pages needed. In general, the more stickers per page, the less pages will be needed to hold the same number of stickers.
If Lena puts 10 stickers on a page, she will need fewer pages than if she puts 5 stickers on a page.
For example, if she has 50 elephant stickers, she would need 5 pages if she put 10 stickers on a page, but she would need 10 pages if she put 5 stickers on a page.
This is because the total number of stickers divided by the number of stickers per page determines the number of pages needed. In general, the fewer stickers per page, the more pages will be needed to hold the same number of stickers.
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If m∠ABD=83°, what are m∠ABC and m∠DBC
Answer: m∠ABC = 54° and m∠DBC= 30°
Step-by-step explanation: To find the measures of each angle, you have to make it into an equation to solve for .
In this case, the equation is (3x + 3) + (6x - 1) = 83°
First you combine like terms. In this case the 3x and the 6x have to be combined. 3x + 6x = 9x. The 3 and -1 have to be combined as well. 3 - 1 = 2.
Now you have 9x + 2 = 83°
Subtract 2 from each side and you are left with 9x = 81°.
Now divide each side by 9 and you are left with x = 9.
Now that you know the value of x, you will have to apply it to the equation for each angle.
m∠ABC = 6(9) - 9 = 53
m∠ABC = 53°
m∠DBC = 3(9) + 3 = 30
m∠DBC = 30°
In conclusion, the measure of angle ABC 53° and the measure of angle DBC is 3°.
Hoped this helped!!
Answer:
m∠ABC = 54° and m∠DBC= 30°
If a sequence is defined recursively by f(0)=3 and f(n+1)=-3f (n)+2 for n≥2 then f(2), is equal to
By using the recursive formula for the sequence, we will see that the second term is:
f(2) = -4
How to find the second term of the sequence?We know that the sequence is defined by the recursive formula:
f(1) = 3
f(n + 1) = -3*f(n) + 2
(notice that the formula is written incorrectly in the question, as it not completely defines a sequence).
We want to find the second term of the sequence, which is f(2).
Using the second part of the formula, we will get:
f(2) = -3*f(1) + 2
And we know that f(1) = 3
Then:
f(2)= -3*3 + 2
f(2) = -6 + 2 = -4
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Choose the expressions that are sums or differences of two cubes. 64 + a12b51 –t6 + u3v21 8h45 – k15 75 – n3p6 –27 – xz9
The expressions that are sums or differences of two cube:
A. 64 + a¹²b⁵¹
B. –t⁶ + u³v²¹
C. 8h⁴⁵ – k¹⁵
What is expression?An expression or mathematical expression is a finite collection of symbols that is well-formed according to context-dependent norms. In mathematics, an expression is a phrase that has at least two numbers or variables and at least one arithmetic operation. Addition, subtraction, multiplication, or division are all examples of math operations. A number, a variable, or a combination of numbers, variables, and operation symbols constitutes an expression. An equation consists of two expressions joined by an equal sign. Example of a word: the sum of 8 and 3. Example of a word: The product of 8 and 3 equals 11. 8 + 3 is an expression.
Here,
The following phrases are sums or differences of two cubes:
A. 64 + a¹²b⁵¹
=4³+(a⁴b¹⁷)³
B. –t⁶ + u³v²¹
=(-t²)³+(uv⁷)³
C. 8h⁴⁵ – k¹⁵
=(2h¹⁵)³-(k⁵)³
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The density curve for a continuous random variable X has which of the following properties? The probability of any event of the form X = constant is 0. The probability of any event is the area under the density curve and above the values of X that make up the event. The total area under the density curve for X must be exactly 1. All of the above
The total area under the density curve for X must be exactly 1.
The region below the density curve and above the values of X that make up the event is the likelihood of any event. There must be exactly one area under the density curve for all instances of X.
A Density Curve: What Is It?
The general shape of a distribution is depicted by a density curve. The percentage of all observations falling in a certain period is represented by the area under the curve and above any interval of values on the horizontal axis. A density curve's median is the location where the area to the left and right are equal.
A graph that displays probability is known as a density curve. All probabilities are represented by 100% of the curve's area under the curve. You can alternatively state that the area is equal to 1 because 100% is a decimal, which is how we typically express probabilities.
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Compute the Laplace transforms, F(s), of the functions f(t) below f(t) - e8 sin 5 t F(s) =
f(t) - eSt sinh 7t F(s) = f(t)-7t cosh 5t F(s)= (t) = 9t sin ut . Fu(s)
To compute the Laplace transform of a function, we use the integral definition , F(s) = L{f(t)} = ∫ f(t) e^(-st) dt.
What is integral definition ?
The integral definition of the Laplace transform is a mathematical method used to find the Laplace transform of a function. It is defined as,
F(s) = L{f(t)} = ∫ f(t) e^(-st) dt , Where F(s) is the Laplace transform of the function f(t), s is a complex variable known as the frequency domain variable, and t is the time domain variable.
Given the functions f(t) provided ,
f(t) = e^(-8t)sin(5t)
F(s) = L{e^(-8t)sin(5t)} = ∫ e^(-8t)sin(5t) e^(-st) dt = (5/(s+8+5i))(e^(-8-s)) - (5/(s+8-5i))(e^(-8-s))
f(t) = e^(-st)sinh(7t)
F(s) = L{e^(-st)sinh(7t)} = ∫ e^(-st)sinh(7t) e^(-st) dt = (7/(s^2+49))(e^(-s-7i)) - (7/(s^2+49))(e^(-s+7i))
f(t) = -7t cosh(5t)
F(s) = L{-7t cosh(5t)} = ∫ -7t cosh(5t) e^(-st) dt = (-7/s^2)(e^(-s-5)) - (7/s^2)(e^(-s+5))
f(t) = 9t sin(ut)
F(s) = L{9t sin(ut)} = ∫ 9t sin(ut) e^(-st) dt = (9/(s^2 + u^2))(e^(-su)) - (9/(s^2 + u^2))(e^(su))
Note that in all cases, we should check if the integral converges, and that the limits of integration are appropriate.
To compute the Laplace transform of a function, we use the integral definition , F(s) = L{f(t)} = ∫ f(t) e^(-st) dt.
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An ordinary (fair) die is a cube with the numbers 1 through 6 on the sides (represented by painted spots). Imagine that such a die is rolled twice in succession and that the face values of the two rolls are added together. This sum is recorded as the outcome of a single trial of a random experiment.
Compute the probability of each of the following events.
Event : The sum is greater than 6.
Event : The sum is divisible by 5 or 6 (or both).
The probabilities are 5/36 and 9/36, respectively, if the sum is bigger than 6 and if the amount is divisible by 5 or 6 (or both).
what is probability ?Probability theory is the study of how likely it is that an event will occur or that a statement is true. A number between 0 and 1, roughly 0 signifying how unlikely an event is to occur and 1, signifying certainty, is the probability of an event occurring. The likelihood or likelihood that a particular event will occur is expressed numerically as a probability. It is also possible to express probabilities as percentages between 0% and 100% or as percentages between 0 and 1. the percentage of all possible outcomes divided by the total number of events in a complete collection of equally likely alternatives that result in a specific occurrence.
given
It may take the following forms:
(4,6),(5,5),(5,6),(6,5),(6,6)
the likelihood that the total exceeds 9 is 1/36+1/36+1/36+1/36.
=5/36.
B) The following are some possible scenarios:
(1,4),(4,1),(3,3),(3,2),(4,2),(5,1),(1,5),(6,4),(4,6)
The likelihood that the number will be divisible by five, six, or both is
1/36 plus eight times
=9/36
Therefore, The probabilities are 5/36 and 9/36, respectively, if the sum is bigger than 6 and if the amount is divisible by 5 or 6 (or both).
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Plsss I need help I can’t fail algebra I don’t even need an explanation I just need the answers
The function is A = 120[tex](1.016)^{4t}[/tex] and the balance after 6 years is $175.64.
What is compound interest?
The interest that is calculated using both the principal and the interest that has accrued during the previous period is called compound interest. It differs from simple interest in that the principal is not taken into account when determining the interest for the subsequent period with simple interest.
Here the principal = $120
Rate of interest = 6.4% = 6.4/100 = 0.064C. Then,
Now using compound interest formula then,
Amount A = P[tex](1+\frac{r}{n} )^{nt}[/tex]
Here n=4 compound quarterly
A = 120[tex](1+\frac{0.064}{4} )^{4t}[/tex]
=> A= 120[tex](1+0.016)^{4t}[/tex]
=> A = 120[tex](1.016)^{4t}[/tex]
The function is A = 120[tex](1.016)^{4t}[/tex]. Now years t = 6 then
=> A = A = 120[tex](1.016)^{4*6}[/tex] = 120[tex](1.016)^{24}[/tex]
=> A = $175.64
Hence the function is A = 120[tex](1.016)^{4t}[/tex] and the balance after 6 years is $175.64 .
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Pedro and Bella are reading the same book for their language-arts class. On Saturday, Pedro starts the day at page 20 and reads at an average rate of 25 pages per hour. Bella starts reading at the same time, but she starts at page 60 and reads at an average rate of 18 pages per hour.
Answer: If Pedro starts reading at page 20 and reads at an average rate of 25 pages per hour, and Bella starts reading at the same time but starts at page 60 and reads at an average rate of 18 pages per hour,
We can use the formula: distance = rate x time
To find out when they will meet we need to find out when they are on the same page.
let's say t be the time in hours, Pedro will be reading t25 pages, and Bella will be reading t18 pages.
So we can write the equation: 20+t25 = 60+t18
Solving this equation we get t = 2
So, they will meet after 2 hours.
Pedro will be on page 20+225 = 70, and Bella will be on page 60+218 = 96
So they will meet at page 70 when Pedro reaches that page after 2 hours of reading, which means Bella will have read 26 pages more than Pedro on that point.
Step-by-step explanation:
Find the indicated side of the
triangle.
7
a
b
45°
a = [?]
Enter
Answer:
[tex]a=7[/tex]
Step-by-step explanation:
The legs of an isosceles right triangle are congruent.
The Pythagorean Theorem may be used to calculate the length of side a: [tex]a^{2}[/tex] = 72 + [tex]b^{2}[/tex] = 49 + [tex]b^{2}[/tex]. When we solve for a, we obtain a = (49 + [tex]b^{2}[/tex]). As a result, the length of side an equals the square root of 49 multiplied by the square of side b.
What is Pythagorean Theorem?The Pythagorean Theorem is a mathematical equation that asserts that the square of the length of the hypotenuse (the side opposite the right angle) in a right triangle is equal to the sum of the squares of the other two sides. The Pythagorean Theorem is stated in equation form as [tex]a^{2}[/tex] + [tex]b^{2}[/tex] = [tex]c^{2}[/tex], where a and b are the lengths of the triangle's legs (the two sides that meet at a right angle) and c is the length of the hypotenuse.
In the given question,
a = 7 * sin(45°)
= 7 * 0.707
= 4.949
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Triangle GHC is similar to triangle JKC? What is the length of GC?
The length of GC could be 7.2 when Triangle GHC is similar to triangle JKC.
What is a triangle ?
Triangle can be defined in which it contains 3 sides and 3 angles and the sum of three angles is 180 degrees .
Given
Triangle GHC is similar to triangle JKC
JK = 15
KC = 20
JC = 18
GH = 6
SO,
△GHC ~ △JKC
we know that
(GH/GC) = (JK/JC)
(6/GC) = (15/18)
GC= 6 * 18 / 15
GC = 36 / 5
GC = 7.2
Hence , the length of GC could be 7.2 when Triangle GHC is similar to triangle JKC.
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Families that attended a concert featuring music from the early 1900s were surveyed
about which type of music from the concert they preferred. The table shows the results
of the survey. What percent of the children surveyed preferred ragtime music?
30%
Adults
Children
Total
60%
Concert Music Preferred
Blues
15
6
21
Jazz
14
36
50
89%
Ragtime
11
18
29
Total
40
60
100
18%
Answer:
30%
Step-by-step explanation:
Given table:
[tex]\begin{array}{|c|c|c|c|c|}\cline{1-5} & \sf Jazz&\sf Blues & \sf Ragtime & \sf Total\\\cline{1-5} \sf Adult & 14& 15&11 & 40\\\cline{1-5} \sf Children &36 &6& 18& 60\\\cline{1-5} \sf Total &50 &21 &29 & 100\\\cline{1-5}\end{array}[/tex]
From observation of the table:
The number of children that preferred ragtime music is 18.The total number of children is 60.To find the percent of the children surveyed that preferred ragtime music, divide the number of children that preferred ragtime music by the total number of children:
[tex]\begin{aligned}\implies \sf Percent&=\dfrac{\sf Children\;who\;preferred\;ragtime}{\sf Total\;children}\\\\&=\dfrac{18}{60}\\\\&=\dfrac{18 \div6}{60\div 6}\\\\&=\dfrac{3}{10}\\\\&=\dfrac{3 \times 10}{10 \times 10}\\\\&=\dfrac{30}{100}\\\\&=30\%\end{aligned}[/tex]
A triangle has side measures of 15,15 and 15 . Choose the term that describes the triangle .
1 . Right 2. Equilateral 3. Scalene 4. Isosceles
Answer:
Equilateral Triangle
Step-by-step explanation:
Answer:
Equilateral
Step-by-step explanation:
The Answer to this given question is a Equilateral
Reason : The sides of an equilateral triangle are congruent, which means that all sides are of equal length.
Can someone tell me what sin(a) is, I will give brainliest
The values of trigonometric functions are sinα = -10 and cotα = -10/24.
What is the trigonometric functions?
In mathematics, the trigonometric functions (also called circular functions, angle functions or goniometric functions[) are real functions that relate an angle of a right-angled triangle to ratios of two side lengths.
They are widely used in all sciences that are related to geometry, such as navigation, solid mechanics, celestial mechanics, geodesy, and many others. They are among the simplest periodic functions, and as such are also widely used for studying periodic phenomena through Fourier analysis.
We have given,
tanα = -(24/10) and π α < 2π
To Find: sinα =? & cotα = ?
[tex]{\displaystyle \tan \theta ={\frac {\sin \theta }{\cos \theta }}=\cot \left({\frac {\pi }{2}}-\theta \right)={\frac {1}{\cot \theta }}}\tan \theta ={\frac {\sin \theta }{\cos \theta }}=\cot \left({\frac {\pi }{2}}-\theta \right)={\frac {1}{\cot \theta }}[/tex]
cotα = -10/24
sinα = -10
Therefore, the values of trigonometric functions are sinα = -10 and cotα = -10/24.
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rkKeys 34 134 134 Your development company recently purchased 12.5 acres of land. According to local regulations, each housing lot must be at least 54, 450 square feet. In a of the purchased land must be left undeveloped. What is the maximum number of housing lots that you can develop on the land? A C 10 11 D. 13 18 A ; for Review & Tools a O Contrast 은 * Clear Highlights ? Help (H) n Text To Speech « Prev TAO Software 3.4.0-sprint140 © 2013-2023 by Open Assessment Technolo DOLL 3 $ 4 % 5 € ∞♪ g y h u k b m
Price divided by size is the formula for calculating the price per square foot (in square feet). For instance, if a 2,000-square-foot property is being sold for $300,000, the price per square foot would be $150 if you took the overall price and divided it by the size.
What do you mean by rectangular area?
A rectangle's sides determine its area. In essence, the length and breadth of the rectangle multiplied together gives the area of the rectangle.A shape called a quadrilateral has two opposing sides that are equal and parallel. It is a four-sided polygon with four 90-degree angles. Rectangles have a two-dimensional form.The area of a rectangle is the region contained by its four sides or boundaries.This is how the whole process occurs in a company which recently purchased 12,5 acres of the given land.To know more about rectangular area here
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Suppose we randomly select a coffee drinker. Let C be
the event that the coffee drinker uses cream and S be
the event that the coffee drinker uses sugar.
What is the probability that a randomly selected coffee
drinker does not use sugar or cream?
What is the probability that a randomly selected coffee
drinker uses sugar or cream?
Answer:
0.10 and 0.90 are the correct answers.
Step-by-step explanation:
what is the value of the numerical expression 5/8-(3-1/4)+2/3
Answer:
-35/24
Step-by-step explanation:
5/8 - (3 - 1/4) + 2/3 =
Distribute the negative sign to 3 and -1/4. When a negative sign is distributed to a negative number, that number becomes positive:
- (3 - 1/4) ==> -3 + 1/4
5/8 - 3 + 1/4 + 2/3 =
Now multiply the equation by 24/24 = 1. Multiplying anything by 1 results in the same equation. For example, 8 * 1 = 8.
Also multiply the equation by 24/24 because 24 is the LCM (Least Common Multiple) of the denominators 8, 4, and 3: 8*3=24. 6*4=24.
(5/8 - 3 + 1/4 + 2/3) * 24/24 =
(5*24/8 - 3*24 + 1*24/4 + 2*24/3) / 24 = ==> multiply each term by 24 and
divide the entire expression by 24
(120/8 - 72 + 24/4 + 48/3) / 24 = ==> simplify
(15 - 72 + 6 + 16) / 24 =
(-57 + 22) / 24 = -35/24
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The value of the numerical expression 5/8 - (3 - 1/4) + 2/3 is -35/24.
What is an expression?When used to represent a quantity or a mathematical relationship, symbols and numbers are combined to form an expression in mathematics. It may contain exponents, brackets, variables, constants, and mathematical operations like addition, subtraction, multiplication, and division.
To simplify the expression 5/8 - (3 - 1/4) + 2/3, we need to follow the order of operations (also known as PEMDAS):
First, we need to simplify the expression inside the parentheses (3 - 1/4):
3 - 1/4 = 12/4 - 1/4 = 11/4
Next, we need to subtract 11/4 from 5/8:
5/8 - 11/4 = 5/8 - 22/8 = -17/8
Finally, we need to add 2/3 to the result:
-17/8 + 2/3
To add these two fractions, we need to find a common denominator. The least common multiple of 8 and 3 is 24, so we can rewrite the fractions with a denominator of 24:
-17/8 + 2/3 = (-51/24) + (16/24) = -35/24
Therefore, the value of the numerical expression 5/8 - (3 - 1/4) + 2/3 is -35/24.
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Tamika and her friend sold their old toys at a yard sale earning x dollars. Tamika had to pay her parents back the $25 they gave her for making change. She then divided the rest of the money between her and her friend. What algebraic expression can you write for this scenario? Explain what each term means in regards to this scenario.
The algebraic expression that she can use to represent the scenario would be = $x-25/2
What is algebraic expressions?Algebraic expression is defined as the expression that can be used to represent a constant algebraic number, variables, and the algebraic operations.
The amount of money Tamika and her friend sold their old toys= X dollars
The amount of money that Tamika had to pay back to her parents = $25
Therefore the remaining amount = X - 25
The amount of money that she divided between her friend and her = $ x-25/2
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59) When scrap iron in a boat is thrown overboard in a swimming pool, the pool level
A) rises.
B) falls.
C) remains unchanged.
As rain drop and sink through the rock, it often solvates some of the iron. It conveys that iron along with it as it continues to seep through the rock and soil.
When the rainwater becomes groundwater or dart into freshwater sources like lakes and rivers, it may become the part of the local water supply.
Municipal water systems that get their water from these sources can end up with high levels of iron in their water, and the riddle they have set up to remove bacteria and other harmful contaminants may not always riddle it out.
Wells that portray water from aquifers with high iron content may contain high iron concentrations as well.
Iron in water generally takes two types of ferrous iron, which is soluble in water, and next one is ferric iron, which is insoluble.
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The area of the right triangle shown is 24 square feet. Which equations can be used to find the lengths of the legs of the triangle? Select three options. 0.5(x)(x + 2) = 24 x(x + 2) = 24 x2 + 2x – 24 = 0 x2 + 2x – 48 = 0 x2 + (x + 2)2 = 100
There are only three correct equations for the area of the right triangle which are:
0.5(x)(x + 2) = 24x² + 2x - 48 = 0x² + (x + 2)² = 100.Area of a triangleThe area of a triangle is calculated by dividing the product of the base and height of the triangle.
base of the triangle = x
height of the triangle = x + 2
area of the triangle = 1/2(x)(x + 2)
so
1/2(x)(x + 2) = 24...(1)
1/2 is also 0.5, so the equation 0.5(x)(x + 2) = 24 is correct.
by cross multiplication, equation (1) becomes;
x(x + 2) = 48
x² + 2x = 48 {expand the left hand side}
x² + 2x - 48 = 0 {subtract 48 from both sides}
so the equation x² + 2x - 48 = 0 is correct.
Considering the last equation, x² + (x + 2)² = 100
x² + x² + 4x + 4 = 100
2x² + 4x = 100 - 4 {collect like terms}
2x² + 4x = 96 {divide through by 2}
x² + 2x = 48
x² + 2x - 48 = 0
so the equation x² + (x + 2)² = 100 is equivalent to the equation (1) and so is also correct.
Therefore, the equations 0.5(x)(x + 2) = 24, x² + 2x - 48 = 0, and x² + (x + 2)² = 100 are correct and can be used to find the length of sides for the right triangle.
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Write an equation of a line that is parallel to 2x - 5y = 10 and passes through the point (5,8).
Answer:
y=2/5x+6
Step-by-step explanation:
work attached here
if the correlation between two variables is 1.00, the standard error of estimate equals 0.
A. True
B. False
If the correlation between 2 variables is 1.00, the standard error of estimate equals 0 statement is True.
The statistical measure of correlation, which is expressed as a number, describes the magnitude and direction of a relationship between two or more variables. A correlation between two variables does not, however, automatically mean that a change in one variable was what led to changes in the values of the other.
The two events are causally related, which means that causation demonstrates that one event is the result of the occurrence of the other event. It is also known as the cause-and-effect principle.
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Can someone help please? It's urgent.
Answer:
he earns $500 from the lessons from both groups of students.
Step-by-step explanation:
To summarize:
There are 14 students in set R (piano students)
There are 10 students in set R (piano students) who are not in set S (saxophone students)
There are 11 students in set S (saxophone students)
There are 14 + 11 = 25 total students in both sets R and S
There are 4 students who are common to both R and S, that are taking saxophone for free
The music teacher will get $280 for the piano students
The music teacher will get $220 for the saxophone students.
So the total he earns is $280 + $220 = $500 from the lessons from both groups of students.
SIMPLE INTEREST PLEASE HELP DUE SOONN
the interest Bianca will collect is $3127.50.
What is simple interest?
A quick and simple way to figure out interest on money is to use the simple interest technique, which adds interest at the same rate for each time cycle and always to the initial principal amount. Any bank where we deposit our funds will pay us interest on our investment. One of the different types of interest charged by banks is simple interest. Now, before exploring the idea of basic curiosity in further detail,
The formula for simple interest is:
S = p*t*r/100
where P is the principal amount of money, R is the interest rate as a decimal, T is the time.
p = 3000
r =4.25%
t =1
S = 3000*4.25*1/100 = 127.50
Hence the interest Bianca will collect is $3127.50.
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4/7 = 12/g 21 15 24 3
Answer:
4/7 = 12/g cannot be true, as the numbers on the right side of the equation are not related to the numbers on the left side of the equation and cannot be used to solve for the variable "g".
The correct way to solve for the variable in an equation like this is by cross-multiplying and simplifying the equation.
4/7 = 12/g
multiply both sides by 7g
4*g = 12
Divide both sides by 4
g = 3
So in this case the value of g is 3, but the given numbers 21 15 24 3 are not related to this equation.
Step-by-step explanation:
Answer:12/21
Step-by-step explanation:
cross-multiply 4/7 = 12/g so 4g = 84 . 4 x3 =12 7x3=21 So the answer is 12/21.
Please help quick!! 16 points + brainly for right answer!!
What is the area of this figure?
Enter your answer in the box.
[__] yd²
Please answer Asap. Math algebra 2
Answer:
Domain: [0, ∞)
Range: [√5, ∞)
Step-by-step explanation:
Find the domain by finding where the piecewise is defined. The piecewise range is the set of values that correspond with the domain.
Domain: [0, ∞)
Range: [√5, ∞)
hope that helps...
140-100
Need help with this maths
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A pharmacy has 8 pints of cough syrup. A prescprtion calls for 3/4 pint of cough syrup. How many full prescriptions can be filled?
Answer:
The pharmacy has 8 pints of cough syrup and a prescription calls for 3/4 of a pint, so to find the number of full prescriptions that can be filled, you would divide 8 (the total amount of cough syrup) by 3/4 (the amount of cough syrup per prescription). This would be 8 / (3/4) = 8 * (4/3) = 8 * 1.33 = 10.67.
Therefore, they can fill 10 prescriptions, they will have 0.67 left.
Step-by-step explanation:
What is the fewest number of regions that three lines can separate a plane into? Describe the configuration of lines that gives you this many regions.
As long as they are not all on the same line, three points can define a plane in a three-dimensional space.
How many different numbers of regions can three lines divide a plane into?Intersecting Space with Planes A plane just divides space into two distinct regions. Space is divided into a maximum of four sections by two planes. Space can only be divided into eight sections by three planes.
One line has the ability to split a plane into two regions; two non-parallel lines have the ability to divide a plane into four regions; three non-parallel lines have the ability to divide a plane into seven regions; and so on.
Four unique, nonintersecting zones can be created by selecting three separate points on a circle and connecting each pair of them with a chord.
Three points can define a plane in a three-dimensional space as long as they are not all on the same line.
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One line can divide a plane into two regions, two non-parallel lines can divide a plane into 4 regions and three non-parallel lines can divide into 7 regions.
What is the maximum number of regions can divide a plane?The maximum number Ln of regions in the plane that can be defined by n straight lines in the plane is: Ln=n(n+1)2+1. This sequence is A000124 in the On-Line Encyclopedia of Integer SequenceOne line can divide a plane into two regions, two non-parallel lines can divide a plane into 4 regions and three non-parallel lines can divide into 7 regionsIf three planes meet pairwise in three parallel lines they create 7 regions. A plane not parallel to these lines doubles the number of regions, a plane parallel to them creates at four more regions. Thus all triples of planes meet in one pointAn infinite number of regions can be formed in a circle by the number of chords of the circle. How many regions can be formed by a circle and two chords? There are two options for a circle and two chords, depending on whether the chords intersect or not.
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Which equation could be used to find the missing side of the triangle shown?
10 m
am
5 m
O a² +52
10²
O 5² + 10² a²
O2 (5) +2 (10) = 2a
O a² + 10² 5²
=
O a² + 10² 5² =25 + 100 =2a ,2a=125 , a=\sqrt{125} , a=11.18 m
Therefore, the missing side (a) is 11.18 m.
Calculate the missing side (a) of the triangle
We are trying to find the missing side (a) of the triangle shown in the diagram.
To do this, we will use the Pythagorean Theorem, which states that the sum of the squares of the two shorter sides of a right triangle is equal to the square of the longest side.
The two shorter sides of the triangle are 5 m and 10 m.
We will use the Pythagorean Theorem to calculate the missing side (a).
First, we need to square the lengths of the two shorter sides:
5² = 25
10² = 100
Next, we add the squares of the two shorter sides together:
25 + 100 = 125
Finally, we take the square root of the sum to find the length of the missing side:
√125 = 11.18 m
Therefore, the missing side (a) is 11.18 m.
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