Equivalents are things that are equal or have the same value. in mathematics, for example, the fraction 3/4 and the decimal ______________ are the same value
Equivalents are things that are equal or have the same value. in mathematics, for example, the fraction 3/4 and the decimal 0.75 are the same value
Any 2 terms in mathematics are said to be equivalent if the are identical in terms of values. They do not necessarily have to be "equal"
For example, 8 can be said to be equal to 8 but 8 is "equivalent" to
4 + 4
1 + 7
10 - 2 etc.
This can also be considered for conversion systems.
For example- 1 kg is equvalent to 1000 grams.
Just like in all the examples we considered before, equivalency can be drawn when fractional forms are converted into decimal forms.
1/2 is equivalent to 0.5
Hence for 3/4, we need to write a decimal value for the same
3/4 = 75/100 = 0.75
Hence 3/4 will be equivalent to 0.75
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Which ordered pair is the solution to the linear functions graphed?
The ordered pair that is the solution to the linear functions graphed is (b) (5, 25)
How to determine the solution to the system?A system of linear equations is a collection of at least two linear equations.
In this case, the system of equations is given as
The lines on the graph
Next, we interpret the graph of the system of equations
In this case, the point of intersection of the equations represent the solution to the system
From the graph, the lines intersect at (5, 25)
Hence, the solution is (5, 25)
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How do you find the scale factor of two similar circles?
The scale factor of two similar circles is equal to the ratio of their radii.
This can be expressed mathematically as a fraction, where the numerator is the radius of the larger circle, and the denominator is the radius of the smaller circle. For example, if the radii of the two circles are 3 cm and 6 cm, then the scale factor is 3/6 or 1/2. To find the scale factor, divide the radius of the larger circle by the radius of the smaller circle. For example, if the radii of the two circles are 10 cm and 4 cm, then the scale factor is 10/4, or 5/2.
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which statements describe scientific laws but not theories or hypothesis check all that apply
The assertions are thought to be established truths since they explain scientific laws rather than speculations or Fourier's hypotheses and do not offer justifications for their veracity.
What are the laws of science?Scientific rules are those that have been established by experimenters or scientists after years of observations and experiments for scientific purposes. Laws are not established facts. They don't even offer an explanation for why scientific rules hold true.
What are the five scientific laws?The five most well-known scientific laws are: Bernoulli's law of fluid dynamics; Dalton's law of partial pressures; Hooke's law of elasticity; and Fourier's law of heat conduction.
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The correct question is -
Which statements describe scientific laws but not theories or hypotheses? Check all that apply.
They are likely to change as new evidence is discovered.
They do not provide explanations for why they are true.
They are considered to be proven facts.
They have not yet been tested.
They are the bases for experiments instead of the results.
jacks computer prints 36 pages in 2 minutes and 24 sec At that rate how many more seconds will it take for 5 more pages
The time taken to print the 5 more pages will be 1.25 seconds.
Define the unitary method?The unitary strategy involves calculating the value of an individual unit, from which we can derive the values of the appropriate number of units.For the stated question-
The printer at Jack's prints 36 pages in 2 minutes and 24 seconds.
This can be written as;
2*60 + 24 seconds ---> 36 pages
120 + 24 seconds ---> 36 pages
144 seconds ---> 36 pages
Time taken to print 1 page.
1 page ---> 36 / 144 seconds.
Thus, to print 5 more pages.
5 page ---> 36 / 144 * 5 seconds.
5 page ---> 1.25 seconds.
Thus, the time taken to print the 5 more pages will be 1.25 seconds.
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An amusement park attraction has a sign that indicates that a person must be 48 inches tall to ride the attraction. The following box plot shows the heights of a sample of people who entered the amusement park one day. Based on the box plot, approximately what percent of the people who entered the amusement park met the height requirements for the attraction?
Based on the attached boxplot, approximate percentage of the people who entered the amusement park met the height requirement for the attraction is 50%.
What is a boxplot and how to read it?A boxplot is a way to present a five number summary in a box chart. The main part of the box shows where the middle portion of the data, the interquartile range. At the ends of the box, we will find the first quartile (Q1 or the 25% mark) and the third quartile (Q3 or the 75% mark). The bottom of the box is the minimum (the smallest number in the set) and the top of the box is the maximum (the largest number in the set). And, the median is represented by a line in the center of the box.
From the boxplot can be seen that:
Minimum = 43
Maximum = 64
Q1 (first quartile) = 46
Q3 (third quartile) = 58
Median = 48
In the passage, given that a person must be at least 48 inches tall to ride the attraction. So, this is the same number as median value, that is 48. Thus, 50% the amusement visitors are eligible for the requirement, and the 50% others are not.
Hence, the percentage of the people who entered the amusement park met the height requirement for the attraction is 50%.
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Simplify the expression 2v+8v-5v
[tex]2v+8v-5v[/tex]
Combine Like Terms:
[tex](2v+8v-5v)[/tex]
[tex]\fbox{5v}[/tex]
Use upper and lower sums to approximate the area of the region using the given number of subintervals (of equal width). (round your answers to three decimal places. ) y = 3x.
The area of the region is between the upper and lower sums, which are 0.5625 and 0.5.
Calculate Area Using SumsTo use upper and lower sums to approximate the area of a region, we need to first divide the region into subintervals of equal width. Once we have the subintervals, we can then use the function values at the upper and lower bounds of each subinterval to calculate the upper and lower sums.
In this case, we are given that y = 3x, and we are asked to use n = 4 subintervals to approximate the area of the region.To find the width of each subinterval, we can use the formula:width = (b - a) / n, where a and b are the lower and upper bounds of the region, and n is the number of subintervals.
Let's assume the region is between x = 0 and x = 1.Therefore, the width of each subinterval is (1 - 0) / 4 = 0.25.Next, we can use the upper and lower bounds of each subinterval to calculate the upper and lower sums.The upper sum is calculated by multiplying the function value at the upper bound of each subinterval by the width of the subinterval and summing up the results:Upper sum = 0.25 × f(0.25) + 0.25 × f(0.5) + 0.25 × f(0.75) + 0.25 × f(1)The lower sum is calculated by multiplying the function value at the lower bound of each subinterval by the width of the subinterval and summing up the results:Lower sum = 0.25 × f(0) + 0.25 × f(0.25) + 0.25 × f(0.5) + 0.25 × f(0.75)Since we know y = 3x, we can use this to calculate the function value at each bound:Upper sum = 0.25 × 30.25 + 0.25 × 30.5 + 0.25 × 30.75 + 0.25 × 31 = 0.5625Lower sum = 0.25 × 30 + 0.25 × 30.25 + 0.25 × 30.5 + 0.25 × 30.75 = 0.5Therefore the area of the region is between the upper and lower sums, which are 0.5625 and 0.5 respectively.Learn more about Lower and Upper Sums here:
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Solve (x - 5)² = 3.
A. x-5± √√3
B. x = 8 and x = -2
C. x=-5± √√3
D. x=3 ± √√5
Answer:
A
Step-by-step explanation:
(x-5)^2 = 3
Take the square root of both sides
You are now left with: x-5 = sqrt(3)
Add 5 to both sides
x= 5 + or - sqrt(3)
Answer: A
Step-by-step explanation:
(x - 5)^2 = 3
take square root of both sides
(x - 5) = +-sqrt 3
you can remove the parentheses
x - 5 = +-sqrt 3
isolate the x variable
x = +-sqrt 3 + 5
6r - 6t = 6 and 3r - 6t = 15
Answer: r = -3, t = -4
Step-by-step explanation:
6r-6t=6
3r-6t=15
Using the elimination method, you can get
3r=-9
r=-3
Substitute -3 for r, and you get
-9-6t=15
-6t=24
t=-4
r=-3,t=-4
Answer:
r,t=-3,-4
Step-by-step explanation:
[1] 6r - 6t = 6
[2] 3r - 6t = 15
If you have a rewards card at Biggby, you earn a free drink after every 12 drinks you buy. Can the total amount of money spent at Biggby after ordering n drinks be considered arithmetic? Why or why not?
For the following system, if you isolated x in the second equation to use the substitution method, what expression would you substitute into the first equation? 2x + y = 8 −x − 3y = −12 a 3y + 12 b −3y + 12 c 3y − 12 d −3y − 12
Isolating x in the second equation, the expression that would be replaced into the first equation to solve the system of equations is given as follows:
b. -3y + 12.
How to solve the system of equations?The system of equations for this problem, with variables x and y, is defined as follows:
2x + y = 8.-x - 3y = -12.The second equation of the system is given as follows:
-x - 3y = -12.
The first step to isolate x is move the -3y term to the opposite side of the equality, with an addition symbol, which is the inverse of the negative symbol, hence:
-x = 3y - 12.
As the leading coefficient of x is negative, the entire expression must be multiplied by -1, hence:
x = 12 - 3y.
x = -3y + 12(commutative property).
Meaning that the correct option is given by option b.
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Answer: (b) -3y + 12.
To use the Substitution Method, we would isolate x in the second equation, which gives:
-x = 3y - 12
Multiplying both sides by -1, we get:
x = -3y + 12
We can then substitute this expression for x into the first equation, which gives:
2(-3y + 12) + y = 8
Simplifying this expression, we get:
-5y + 24 = 8
Subtracting 24 from both sides, we get:
-5y = -16
Finally, dividing both sides by -5, we get:
y = 16/5
Therefore, if we isolate x in the second equation, we would substitute x = -3y + 12 into the first equation.
So the expression we would substitute into the first equation is -3y + 12.
Help! Determine the Volume of the following rectangular prism using the formula V = lwh
Therefore , the solution to the given problem of volume comes out to be Volume of the prism = 15x^7 cube unit.
What is meant by volume?The term "volume" describes the amount of muti space that a thing takes up. Volume, in contrast to mass, varies with the environment. The term "density" describes the mass that a material has in a specific volume. It explains how mass and volume are related.
Here,
Given: The rectangular prism must have a 4.5 inch width.
As follows are the terms for the rectangular prism's volume:
V = l*w*h
where the prism's dimensions are l for length, w for width, and h for height.
Volume of prism equals 5x3 * 3x2 * x2,
or 15x7.
Therefore , the solution to the given problem of volume comes out to be Volume of the prism = 15x^7 cube unit.
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HELP QUICK!! please <3.
Answer:
67
Step-by-step explanation:
.__. that it
2x + 3 - x - (-1) = 2x - 2 - x
Answer: The equation is false.
Step-by-step explanation:
2x+3-x-(-1) = 2x-2-x
2x+3-x+1=2x-2-x
x+4=x-2
4 ≠ -2
The lateral surface area of a cylinder of length 14m is 220m². Find the volume of the cylinder.
The volume of the cylinder is 275m³.
We have given that,
Lateral surface of cylinder = 220m²
Height (h) = 14m
Let radius of cylinder = r
Then 2πrh = 220m²
⇒ × 22/7 × r × 14 = 220m²
[tex]$ \Rightarrow \text r = \frac{220 \times 7}{2 \times 22\times 14}[/tex]
[tex]$ \Rightarrow \text r = \frac{220 \times 7}{2 \times 22\times 14}[/tex]
[tex]$ \Rightarrow \text r = \frac{5}{2} = 2.5[/tex]
Now we can find the volume,
Volume of cylinder = πr²h
= 22/7 × (2.5)² × 14
= 22 × 6.25 × 2
= 275m³
Thus, the volume of the cylinder is 275m³.
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The volume of the cylinder is 274.75 cubic meter.
What is lateral surface area?All of the sides of the object are the lateral p of an object, except its base and top (when they exist). The lateral surface area is the lateral surface zone. This is to be distinguished from the overall surface area, which, along with the base and top areas, is the lateral surface area.
Given that, the lateral surface area of a cylinder of length 14m is 220 m².
We know that, the lateral surface area of a cylinder is 2πrh.
Here, 2πrh=220
2×3.14×r×14=220
87.92r=220
r=220/87.92
r=2.5 meters
We know that, the volume of a cylinder is πr²h
Here, volume = 3.14×2.5²×14
= 3.14×6.25×14
= 274.75 cubic meter
Therefore, the volume of the cylinder is 274.75 cubic meter.
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A set of 3 cards, spelling the word ADD, are placed face down on the table. Determine P(A, A) if two cards are randomly selected with replacement.
one third
one ninth
two thirds
two sixths
The probability of the two cards being A and A, P(A, A), is 1/9.
The correct option is the second option, one ninth.
What is the probability?The Probability in mathematics is the possibility of an event in time. In simple words, how many times that incident is happening in any given time interval.
Given:
A set of 3 cards, spelling the word ADD, are placed face down on the table.
And we have to determine P(A, A) if two cards are randomly selected with replacement.
From the formula for probability, we have that
P(A) = Number of favorable outcomes / Total number of possible outcomes
P(A) = 1/3
Then,
The probability of selecting two cards that have A and A with replacement is,
P(A, A) = P(A) × P(A)
P(A, A) = 1/3 × 1/3
P(A, A) = 1/9
Therefore, the probability is 4/9.
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simplify the following-
8^6 ÷ 8
Answer:
32768
Step-by-step explanation:
8^6 ÷ 8
8^6= 262144
262144 ÷ 8 = 32768
32768
Hope this helps.
10. Below are the results for
finding the solution to a
system of equations. State
how many solutions the
different results yield and
explain why.
-5 = -5
What are all of 2 factors?
The factor of 2 is 1 and 2.
What is a factor?
In mathematics, an integer m that can be multiplied by another integer to create n is known as a divisor of an integer n, also known as a factor of n. One can also state that n is a multiple of m in this situation.
Factors are also known as divisors. This means they can divide evenly into the number they're a factor of.
Here,
We have to find the possible factors of 2.
We concluded that the factor of 2 is 1 and itself.
Factors of 2 are all the numbers which on multiplying give the result of 2. Factors of 2 are 1 and 2 only.
Hence, the factor of 2 is 1 and 2.
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simplify: (c+1) (c-7)
(c+1) (c-7) = cc - 7c + c - 7 = c^2 - 7c - 7
So the simplified form of (c+1) (c-7) is c^2 - 7c - 7
Answer:
[tex]c^2-6c-7[/tex]
Step-by-step explanation:
[tex](c+1) (c-7)[/tex]
Apply the FOIL mothed.
[tex]cc+c\left(-7\right)+1\cdot \:c+1\cdot \left(-7\right)[/tex]
[tex]c^2-6c-7[/tex]
What is the solution set of the given systems? 5x + 2y = 7 and y = x + 1
The solution set of the given system is (5/7, 12/7).
Now, According to the question:
The given equations are:
5x + 2y = 7 …. (1)
y = x + 1 ….. (2)
Let us solve the system of linear equations using the substitution method.
Substituting equation (2) in (1)
5x + 2(x + 1) = 7
By further calculation
5x + 2x + 2 = 7
So we get
7x = 7 - 2
7x = 5
Divide both sides by 7
x = 5/7
Substitute the value of x in equation (2)
y = 5/7 + 1
Taking LCM
y = (5 + 7)/7
y = 12/7
Therefore, the solution set of the given system is (5/7, 12/7).
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David has a weekend job cleaning windows. He charges different amounts for different size windows. Choose the statement below that is true. A The size of the window depends on the price charged. B The price charged depends on the size of the window. C The size of the window depends on how long it takes to wash. D The time it takes to wash a window depends on the price charged.
The price charged depends on the size of the window.
Option (B) is correct.
What is a direct proportion?
Direct proportion is a relationship between two variables, where the ratio of their values is always constant. This means that if one variable increases, the other variable will also increase in the same ratio.
B) The price charged depends on the size of the window.
The statement that is true is that the price charged by David for cleaning windows depends on the size of the windows. It means that the larger the window, the more David charges for cleaning it. The size of the window is a factor in determining the price and not the other way around.
Hence, the correct statement would be "The price charged depends on the size of the window.".
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Part E
The solution to the system of equations representing Aiden’s and Natalie’s data is shown on the graph.
Analyze the solution to the system to determine whether there is a catapult arm length that Aiden and Natalie can both use to launch their tennis balls the same distance. Explain your reasoning
Both Aiden's and Natalie's tennis balls can cover the same distance of the catapult length is 40.
What is a linear equation?A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included.
Given:
As, we know the linear intercept form,
y = mx + b
Where m is the rate of change (slope) and b is the initial value of y.
Now, From the graph of both Aiden's and Natalie's data, we can see that the point of intersection is at (-40, 90).
Also, which shows x axis at 40 is the distance.
So, Both of them Aiden's and Natalie's tennis balls can cover the length of 40.
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Ms. Higgins has 28 students in her gym class. She puts them in 4 equal groups. How many students are in each group?
Answer:
each group will have 7 students in it.
Step-by-step explanation:
Ms. Higgins has 28 students in her gym class and wants to put them in 4 equal groups.
divide the total number of students by the number of groups.
28 students / 4 groups = 7 students per group.
So, each group will have 7 students in it.
What is substitution technique?
The substitution technique includes simplifying the given equation, solving one of the equations for any unknown value, substituting the step 2 solution in another equation, solving the new equation, and finally solving the equation to find the second variable.
The substitution method is the algebraic method to solve different linear equations. In this technique, the value of one variable from either of the equation is substituted in the other equation.
In this technique the following steps are used to solve an equation by substitution method:
Step 1. Simplify the given equation by removing the parenthesis.
Step 2. Solve one of the equations for any unknown value.
Step 3. Substitute step 2 result in the other equation.
Step 4. Now solve the equation which gets from step 3 obtained using elementary arithmetic operations.
Step 4. Finally, solve the final equation for the second variable.
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Which of the following is a factor of xy 3y − 7x − 21?
The factor of xy 3y − 7x − 21 is x − 3.
xy 3y − 7x − 21 = x(y 3y − 7) − 21 = x(y 3y − 7) − 3(7) = (x − 3)(y 3y − 7)
The expression xy 3y − 7x − 21 can be simplified by factoring out the greatest common factor, which in this case is x. We can factor out an x by dividing the entire expression by x. This gives us y 3y − 7 − 21/x. Now, we can look for a common factor between the two terms. In this case, the factor is -3. We can factor out -3 from both terms to get -3/x and y 3y − 7. This can be rewritten as (x − 3)(y 3y − 7). Therefore, the factor of xy 3y − 7x − 21 is x − 3.
To explain further, factoring is the process of breaking down an expression into its factors. A factor is a number, variable, or expression that can be multiplied to produce the original expression. In this case, we are looking for the factors of xy 3y − 7x − 21. To find these factors, we first simplify the expression by factoring out the greatest common factor, which in this case is x. We then look for a common factor between the two terms, which is -3. We factor out -3 and rewrite the expression as
(x − 3)(y 3y − 7). This means that the factor of xy 3y − 7x − 21 is x − 3.
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it costs £101.50 to buy 7 dresses. how much does it cost to buy 10 dresses give you answre in pounds
Answer:
£145
Step-by-step explanation:
£101.5 divided by 7 gives you £14.5 per each dress then times the £14.5 by 10 and that will give you in total £145 for 10 dresses
What are the solutions of the inequality 2x² x 6 0?
The solutions of the inequality [tex]2x^{2} + x - 6 = 0[/tex] are 3/2, -2. This can be found by using the Quadratic Formula, which states that for any quadratic equation of the form [tex]ax^{2} +bx + c = 0[/tex], the solutions are [tex]x = -b +/-\sqrt{b^{2} -4ac} /2a[/tex].
Discriminant: b² - 4 a c = 1 - 4(2)(-6) = 1 + 48 = 49
Solution 1: x = [tex]-b + \sqrt{b^{2} -4ac} /2a[/tex] = (-1 + √49)/(2×2) = (-1 +7)/4 = 6/4 = 3/2
Solution 2: x = [tex]-b-\sqrt{b^{2} -4ac} /2a[/tex]= (-1 - √49)/(2×2) = -8/4 = -2
So, the two solutions are 3/2 and -2.
The equation can also be written as,
[tex]2x^{2} +4x -3x-6=0[/tex]
[tex]2x(x+2) -3(x+2) = 0[/tex]
[tex](2x-3)(x+2) = 0[/tex]
x = 3/2, -2
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3 customers entered a store over the course of 12 minutes. Fill out a table of equivalent ratios and plot the points on the coordinate axes provided.
A table of equivalent ratios for the number of customers and minutes for customers that entered the store are as follows:
Customers Hours
1 4
12 6
10 40
What is a proportional relationship?In order to have a proportional relationship and equivalent ratios, the number of customers (x) and the number of minutes (y) must have the same constant of proportionality.
Next, we would determine the constant of proportionality (k) as follows:
Constant of proportionality (k) = y/x
Constant of proportionality (k) = 12/3
Constant of proportionality (k) = 4.
When minutes y = 4, the number of customers (x) is given by:
x = y/k
x = 4/4
x = 1.
When the number of customers (x) = 10, the number of minutes (y) is given by:
y = kx
y = 4(10)
y = 40.
Next, we would use an online graphing calculator to plot the points on a coordinate axes as shown in the image attached below.
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