Here is a theorem: If A:B with B isn't equal to 0 and C:D with D isn't equal to 0 are equivalent, then they have the same value:A/B = C/D. This is essentially stating that if two ratios are equivalent, then their values are the same (when they have values). Can you provide any counterexamples to the theorem above?
Answers
Examples of the given theorem are \(\frac{2}{4} \ \& \ \frac{3}{6}\) , \(\frac{4}{16} \ \& \ \frac{8}{32}\) and so on .
Equivalent fractions can be defined as fractions that have different numerators and denominators but represent the same value. Two or more fractions are said to be equivalent if they simplify to the same fraction. Equivalent fractions are fractions that have the same value regardless of the numerator and denominator.For example, the equivalent fractions of 1/5 are 5/25, 6/30, and 4/20, which on simplification, result in the same fraction, that is, 1/5.According to the theorem .
if two ratios are equivalent, then their values are the same .
Let one ratio be \(\frac{2}{4}\) and other be \(\frac{3}{6}\) .
On simplifying and equating these ratios , we get
\(\frac{2}{4} =\frac{3}{6} \\\\\frac{1}{2} =\frac{1}{2}\)
As the ration is same hence \(\frac{2}{4} \ \& \ \frac{3}{6}\) are equivalent fractions .
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Related Questions
A marine biologist measured one dish that was 1 1/4 of a foot and a second fish that was 3/4 of a foot long. How much longer was the first fish
Answers
Answer:
1/3 foot longer
Step-by-step explanation:
2/3-1/3=1/3
Mr, Obrien needs to buy 8 television for the school. Each television costs $795. Mr. O'Brien has 120 fifty-dollar bills that he can use to pay for the televisions.
Part A.
How much will the 8 televisions cost?
Part B.
Does Mr. Obrien have enough money to buy all televisions he needs? If not, how many can he buy?
Answers
Answer:
A. $6360, B. He doesn't have enough money.
Step-by-step explanation:
Answer:
This answer is for only part A
1tv=$795
8 x 795 = 6,360
Pleaseeeeeeeee help meeeeEEEEEEEE IM HAVING A BREAKDOWN JUST PLEAAE HELPPPP
Answers
Answer:
all you got to do at the Sheldon also picks tomatoes from his garden. He picked 5 310 kg, but 1.5 kg were rotten and had to be thrown away. How many kilograms of tomatoes were not rotten? Write an equation that shows how you reached your answer.
Step-by-step explanation:
Sheldon also picks tomatoes from his garden. He picked 5 310 kg, but 1.5 kg were rotten and had to be thrown away. How many kilograms of tomatoes were not rotten? Write an equation that shows how you reached your answer.
I need help the question is solve the equation n+75=155
Answers
Answer:
80
Step-by-step explanation:
155-75=80
1. The first quartile (1) of the ages of the 256 employees of CCNHS – Main Campus is 39 years old. What does it imply?
Answers
If the first quartile is 39 years old, it means that approximately one-fourth of the employees at CCNHS – Main Campus are 39 years old or younger.
The first quartile (Q1) of the ages of the 256 employees of CCNHS – Main Campus being 39 years old implies that 25% of the employees have an age equal to or less than 39 years old.
In statistical terms, the first quartile represents the point below which 25% of the data falls. It divides the data set into four equal parts, with each part containing 25% of the data. Therefore, if the first quartile is 39 years old, it means that approximately one-fourth of the employees at CCNHS – Main Campus are 39 years old or younger.
This information provides insight into the age distribution of the employees at the institution. It indicates that a significant portion of the employees are relatively young, with a quarter of them falling below the age of 39. Understanding the age demographics of the workforce can be useful for various purposes, such as planning professional development programs or implementing age-specific policies.
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Which of these choices is a solution to the equation (x + 4)(x - 3) = -10?
a) 4
b) 3
C) -2
d) -1
Answers
The solution of the given equation (x + 4)(x - 3) = -10 is -2.
Thus, option C is correct.
Two algebraic expressions separated by an equal symbol in between them and with the same value of the expression are called equations.
Example = 2x +4 = 12
Here, 4 and 12 are constants and x is variable
Given equation:
Multiply the brackets,
(x + 4)(x - 3) = -10
\(x^2-3x+4x-12 = -10\)
x^2 +x -12+10 =0
x^2 +x -2=0
x(x+2)-1(x+2)=0
(x+2)(x-1)=0
x= -2, x=1
Thus, option C is correct.
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Write a system of equations to describe the situation below, solve using any method, and fill in the blanks. Today's cafeteria specials at a high school in Ashland are a deluxe turkey sandwich and a chef salad. During early lunch, the cafeteria sold 14 turkey sandwiches and 61 chef salads, for a total of $150. During the late lunch, 14 turkey sandwiches and 25 chef salads were sold, for a total of $78. How much does each item cost? A turkey sandwich costs $ , and a chef salad costs $ .
Answers
Answer:
Equation 1: 14t + 61s = 150
Equation 2: 14t + 25s = 78
Use Elimination (x)
(-1) (14t + 25s) = (78) (-1)
-14t - 25s = -78
14t + 61s = 150
+ -14t - 25s = -78
--------------------------
36s = 72
s = 2
Salad costs $2
Then find t
14t + 61(2) = 150
14t + 122 = 150
14t = 28
t = 2
Sandwich costs $2
Please help!
Whoever answers right gets brainliest!!!!
Answers
Answer:
\(y - 4 = - 3(x - 2)\)
lled a 12:3:112:3:1 ratio. Such a model can provide the basis for the null hypothesis in a significance test. A cross of white and green summer squash plants gives the number of squash in the second generation F2:131F2:131 white squash, 3434 yellow squash, and 1010 green squash. Are these data consistent with a 12:3:112:3:1 dominant epistatic model of genetic inheritance( white being dominant)? The null hypothesis for the chi‑square goodness‑of‑fit test is
Answers
Here is the full question:
When a species has several variants of a phenotype passed on from generation to generation, we can form a hypothesis about the genetics of the trait based on Mendelian theories of genetic inheritance. For example, in a two-gene dominant epistatic model, the first gene masks the effect of the second gene, leading to the expression of three phenotype variants. Crossing the dominant and recessive homozygote lines would result in a second generation represented by a mix of dominant, intermediate, and recessive phenotype variants in the expected proportions: and respectively, also called a 12:3: 1 ratio.
Such a model can provide the basis for the null hypothesis in a significance test. A cross of white and green summer squash plants gives the number of squash in the second generation F2: 131 white squash, 34 yellow squash, and 10 green squash. Are these data consistent with a 12: 3: 1 dominant epistatic model of genetic inheritance( white being dominant)?
The null hypothesis for the chi-square goodness-of-fit test is
Answer:
The null hypothesis for the chi-square goodness-of-fit test is :
\(\mathbf{H_o:p_{white} = \frac{12}{16}, p_{yellow} = \frac{3}{16}; p_{green} = \frac{1}{16} }\)
Step-by-step explanation:
The objective of this question is to state the null hypothesis for the chi-square goodness-of-fit test.
Given that:
There are three colors associated with this model . i,e White , yellow and green and they are in the ratio of 12:3:1
The total number of these color traits associated with this model = 12 + 3 + 1 = 16
Thus ;
The null hypothesis for the chi-square goodness-of-fit test is :
\(\mathbf{H_o:p_{white} = \frac{12}{16}, p_{yellow} = \frac{3}{16}; p_{green} = \frac{1}{16} }\)
My salary next year will be at least $22,000.translate?
Answers
Somebody please help me ITS URGENT
Answers
According to the computation, each ticket is $37.5 is t = ($175 - $25)/4.
What is equation?An equation is a formula that uses the equals symbol (=) to denote the equality of two expressions. Multiple languages may have somewhat distinct meanings for the term equation and its cognates. For instance, in English, an equation is any properly constructed formula that consists of two expressions joined by the equals sign, whereas in French, an equation is any well-formed formula that contains one or more
variables 5.
Given the overall cost of parking and four tickets for a baseball game = $175.00
cost of parking = $25
The price of 4 tickets = $175 - $25
let cost of each ticket is t
t =($175 - $25)/4
cost of each ticket is $37.5
Therefore, the formula for a ticket is
t = ($175 -$25)/4, cost of ticket is $37.5.
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(-2)^p+7 * (-2)^p+8 = (-2)^9
please explain properly
Answers
\( {( - 2)}^{p + 7} \times {( - 2)}^{p + 8} = {( - 2)}^{9} \\ = > {( - 2)}^{p + 7 + p + 8} = {( - 2)}^{9} \\ = > {( - 2)}^{2p + 15} = {( - 2)}^{9} \\ = > 2p + 15 = 9 \\ = > 2p = 9 - 15 \\ = > 2p = - 6 \\ = > p = \frac{ - 6}{2} \\ = > p = - 3\)
The answer is -3.the length of one side of a parallelogram is two over three times the length of its adjacent side if perimeter of the parallelogram is 20 cm find the sides of the parallelogram
Answers
Answer:
\(A = 4\)
\(B = 6\)
Step-by-step explanation:
Let the two sides be A and B, such that:
\(A = \frac{2}{3} * B\)
\(Perimeter = 20cm\)
Required
Find A and B
The perimeter is calculated as:
\(Perimeter = 2 * (A + B)\)
Substitute \(\frac{2}{3} * B\) for A and 20 for Perimeter
\(20 = 2 * (\frac{2}{3} * B + B)\)
\(20 = 2 * (\frac{2B}{3} + B)\)
Divide both sides by 2
\(10 = \frac{2B}{3} + B\)
Multiply both sides by 3
\(3 * 10 = 3 * (\frac{2B}{3} + B)\)
\(30 = 2B + 3B\)
\(30 = 5B\)
Solve for B
\(B = \frac{30}{5}\)
\(B = 6\)
Recall that:
\(A = \frac{2}{3} * B\)
\(A = \frac{2}{3} * 6\)
\(A = 2 * 2\)
\(A = 4\)
Hence, the lengths of the sides are 4 cm and 6 cm
Select the correct answer.
Which statement describes the end behavior of the function f(x) = |x + 9| − 8?
A.
As x approaches negative infinity, f(x) is no longer continuous.
B.
As x approaches negative infinity, f(x) approaches negative infinity.
C.
As x approaches positive infinity, f(x) approaches negative infinity.
D.
As x approaches positive infinity, f(x) approaches positive infinity.
Answers
As x approaches negative infinity, f(x) approaches positive infinity. The statement that explains the final behaviour of the function f(x) is discovered to be using limitations.
It is given by the limit of f(x) as x approaches both positive infinity and negative infinity.
In this problem, the function is:
f(x) = |x + 9| − 8
Hence, the limits are:
\(\lim_{x \to \infty} f(x)\) = \(\lim_{x \to \infty}\) |x + 9| − 8 = |∞ + 9| − 8 = ∞
\(\lim_{x \to -\infty}f(x)\) = \(\lim_{x \to \infty}\) |x + 9| − 8 = |-∞ + 9| − 8 = ∞
Approaches positive infinity in both cases.
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The Correct question is below
Select the correct answer.
Which statement describes the end behaviour of the function f(x) = |x + 9| − 8?
A. As x approaches negative infinity, f(x) is no longer continuous.
B. As x approaches negative infinity, f(x) approaches positive infinity
C. As x approaches positive infinity, f(x) approaches negative infinity.
D. As x approaches positive infinity, f(x) approaches positive infinity.
What is the value of the expression when x = 3, y = 5, and z = -4?
Answers
Answer:
7 x ^2 y - 3 z
= 7 * (3)^2 * 5 - 3 * - 4
= 7 * 9 * 5 + 12
= 315 + 12
= 327
it's answer is D 327
hope it helps you
explanation:
just plug in the numbers for their corresponding letter!
7(3²)(5) - (3)(-4)
= 7(9)(5) - (3)(-4)
= 315 - (-12) = 315 +12
= 327
Which equations have the same value of x as Three-fifths (30 x minus 15) = 72? Select three options. 18 x minus 15 = 72 50 x minus 25 = 72 18 x minus 9 = 72 3 (6 x minus 3) = 72 x = 4.5
Answers
The equations which have the same value of x as "three-fifth(30x minus 15 ) 72 are "18 x minus 9 = 72", "3 (6 x minus 3) = 72", and "x = 4.5".
What is an equation?Two or more expressions with an equal sign are defined as an equation.
The given equation is Three-fifths(30x - 15) = 72.
Simplify the equation as follows:
Three-fifths(30x - 15) = 72
3/5(30x - 15) = 72
18x - 9 = 72
Which is equivalent to "18x minus 9 = 72".
Solve for the value of x:
18x -9 = 72
18x = 72 + 9
18x = 81
x = 81/18
x = 27/6
x = 4.5
Now, solve the equation in the first option:
18x - 15 = 72
18x = 87
x = 4.83
Solve the equation in the second option:
50x - 25 = 72
50x = 97
x = 1.94
The third equation is already shown to be equivalent to the given equation.
The solution to the fourth equation is:
3(6x - 3) = 72
18x -9 =72
Which is the same as the given equation.
The last equation is x = 4.5
Hence, the equations which have the same value of x as "three-fifth(30x minus 15 ) 72 are "18 x minus 9 = 72", "3 (6 x minus 3) = 72", and "x = 4.5".
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two person A and B spent a total of pkr 486 .Person A spent twice as much money as person B. How much money did person A spend
Answers
9514 1404 393
Answer:
pkr 324
Step-by-step explanation:
Person A spent 2/3 of the total money spent, so ...
(2/3)(pkr 486) = pkr 324 . . . spent by person A
7,587 divide by 8 I need helpb
Answers
3.2 The line drawn from the midpoint of the one side of a triangle, parallel to the second side, ... ACS is a triangle. P is a point on AS and R is a point on AC such that PSRQ is a parallelogram. PQ intersects AC at B such that B is the midpoint of AR. QC is joined. Also, CR-PS, C, -50° and BP- 60 mm. C 2 R 3 2 B/3 2 3.2.1 Calculate the size of A 3.2.2 Determine the length of QP. 2 1 P 2 (5) (3) [9]
Answers
The coordinates of midpoint P are P(-1/2, 3/2) and coordinates of midpoint Q are Q(-3/2, -4).
To find the coordinates of the midpoints P and Q of sides AB and AC, we can use the midpoint formula.
The midpoint formula states that the coordinates of the midpoint of a line segment between two points (x1, y1) and (x2, y2) are given by:
Midpoint = ((x1 + x2) / 2, (y1 + y2) / 2)
Using this formula, we can find the coordinates of P and Q as follows:
Coordinates of midpoint P:
P = ((2 + (-3)) / 2, (-1 + 4) / 2)
= (-1/2, 3/2)
Therefore, the coordinates of midpoint P are P(-1/2, 3/2).
Coordinates of midpoint Q:
Q = ((2 + (-5)) / 2, (-1 + (-7)) / 2)
= (-3/2, -4)
Therefore, the coordinates of midpoint Q are Q(-3/2, -4).
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Let the points A(2,-1), B(-3,4), and C(-5,-7) be the vertices of triangle A B C. Let P and Q be the midpoints of the sides AB and AC respectively. Find the coordinates of P and Q. (2 marks)
Someone help
A)17/15
B)15/17
C)17
D)8/17
E)17/8
Answers
Answer:
B) 15/17
Step-by-step explanation:
You want the sine of acute angle A in the right triangle shown.
SineThe sine of the angle is the ratio ...
Sin = Opposite/Hypotenuse
We can go to the trouble to figure the hypotenuse, or we can choose the only suitable answer from the list provided. (It is the one marked already.)
The leg lengths of the triangle shown are 8 and 15, with leg 15 being opposite angle A. This is the first clue that the ratio will have 15 in the numerator. Only answer choice B matches.
CheckThe value of the sine function is never greater than 1, eliminating answer choices A, C, and E, leaving choices B and D.
Since the side opposite angle A is the longest of the two legs, we know that angle A is more than 45°, and its sine is more than √2/2. That means choice D can be eliminated, since it is less than 1/2.
The sine of angle A is 15/17.
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Patel is solving 8x2 + 16x + 3 = 0. Which steps could he use to solve the quadratic equation? Select three options. 8(x2 + 2x + 1) = –3 + 8 x = –1 Plus or minus StartRoot StartFraction 5 Over 8 EndFraction EndRoot x = –1 Plus or minus StartRoot StartFraction 4 Over 8 EndFraction EndRoot 8(x2 + 2x + 1) = 3 + 1 8(x2 + 2x) = –3
Answers
The steps that Patel could he use to solve the quadratic equation include:
8(x² + 2x) = –3
8(x² + 2x + 1) = –3 + 8
x = –1 Plus or minus StartRoot StartFraction 5 Over 8 EndFraction EndRoot
How to illustrate tye information?It is preferred to solve quadratic equations without the use of the known quadratic formula solver. This can be completing squares and solving for x.
The equation given is:
8x² + 16x + 3 = 0
8(x² + 2x) = -3
Completing squares in the brackets and balancing the equation:
8(x² + 2x + 1) = -3 + 8
Factoring the perfect square will give 8(x + 1)² = 5.
This is illustrated in the options picked for the step.
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Which term describes the distribution of this graph?
A. Uniform
B. Skewed Right
C. Normal
D. Skewed Left
(Reward, 50 Points.)
Answers
Explanation: The reason I say A is because it is evenly distributed throughout the graph.
In the figure below, what is the value of xº?
68
100°
A. 800
B. 689
C. 32°
D. 180°
Answers
Answer:
x = 32
Step-by-step explanation:
The exterior angle of a triangle is equal to the sum of the opposite interior angles
100 = 68+x
Subtract 68 from each side
100 -68 = x
32 =x
\(\huge\bold{Given :}\)
Angle AOB = 100°
Angle OBC = 68°
Angle BCO = \(x°\)
\(\huge\bold{To\:find :}\)
The value of \(x°\).
\(\large\mathfrak{{\pmb{\underline{\orange{Solution}}{\orange{:}}}}}\)
\(\implies {\blue {\boxed {\boxed {\purple {\sf {C.\:x°\:=\:32°}}}}}}\)
\(\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\red{:}}}}}\)
An exterior angle of a triangle is equal to sum of two opposite interior angles.
And so we have,
➪ ∠ AOB = ∠ OBC + ∠ BCO
➪ 100° = 68° + \(x°\)
➪ \(x°\) = 100° - 68°
➪ \(x°\) = 32°
Therefore, the value of \(x°\) is 32°.
\(\large\mathfrak{{\pmb{\underline{\blue{To\:verify}}{\blue{:}}}}}\)
∠ AOB = ∠ OBC + ∠ BCO
✒ 100° = 68° + 32°
✒ 180° = 100°
✒ L. H. S. = R. H. S.
\(\boxed{Hence\:verified.}\)
(Note: Kindly refer to the attached file.)
\(\huge{\textbf{\textsf{{\orange{My}}{\blue{st}}{\pink{iq}}{\purple{ue}}{\red{35}}{\green{ヅ}}}}}\)
if you take away 25 from a number you will be left with two and halftimes 30. what is the number?
Answers
If you take away 25 from (100) you get 75.
70 also equals 2.5*30
The perimeter of the TCL 3-Series Roku Smart TV is 112 inches. The width of the TV is 16 inches greater than its height. Find the width and the height of the TV.
Answers
Answer: Height = 20 inches, Width = 36 inches
Step-by-step explanation:
Let the height be \(h\) and the width be \(h+16\).
Using the formula for the perimeter of a triangle,
\(2(h+h+16)=112\\\\2(2h+16)=112\\\\2h+16=56\\\\2h=40\\\\h=20 \implies h+16=36\)
Two different students decide to compare their businesses. Scooter makes his own t-shirts,
while Karissa does computer repairs. For both models, x represents the number of sales made
each month and f(x) represents total money for each individual. The two functions below model
their respective businesses:
Scooter: f(x) = 200 + 15x
Karissa: f(x) = 80 + 35x
a. Describe what the slope and y intercept represent for both models based on the context.
Compare the two functions. What is one statement you could say about each?
b.
C.
In one month, Scooter sells 20 shirts. That same month, Karissa does 12 repairs. Who had
the better month?
Answers
a) Comparing the two functions, Scooter's business has a lower slope of 15 compared to Karissa's business with a slope of 35. b) Both Scooter and Karissa earned a total of $500 in that month. Therefore, they had an equal month in terms of total money earned.
How to Describe what the slope and y intercept represent for both models based on the contexta) In the context of Scooter's business, the slope of the function f(x) = 200 + 15x represents the rate at which the total money earned increases with each additional sale. Each unit increase in x (number of sales) results in an increase of $15 in total money earned. The y-intercept of 200 represents the initial amount of money Scooter already had before making any sales.
In the context of Karissa's business, the slope of the function f(x) = 80 + 35x represents the rate at which the total money earned increases with each additional repair job. Each unit increase in x (number of repairs) results in an increase of $35 in total money earned. The y-intercept of 80 represents the initial amount of money Karissa already had before doing any repair jobs.
Comparing the two functions, Scooter's business has a lower slope of 15 compared to Karissa's business with a slope of 35. This means that Karissa's business earns more money per repair job compared to Scooter's business per t-shirt sale.
b) To determine who had the better month, we need to calculate the total money earned by each individual based on the given sales/repairs.
For Scooter, with x = 20 (number of shirts sold):
f(x) = 200 + 15x
f(20) = 200 + 15 * 20
f(20) = 200 + 300
f(20) = 500
For Karissa, with x = 12 (number of repairs):
f(x) = 80 + 35x
f(12) = 80 + 35 * 12
f(12) = 80 + 420
f(12) = 500
Both Scooter and Karissa earned a total of $500 in that month. Therefore, they had an equal month in terms of total money earned.
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how to solve 10-[p+3] when p=7
Answers
Answer:
0
Step-by-step explanation:
plug in 7 for "P"
so 10 - [7+3]
solve the inside first, which is 10, therefore 10-[10] leaving you with no solution or 0 as answer
Sketch the graphs of the absolute value functions y = - |x + 6|
Answers
The Absolute value function takes the same value for positive and negative values of its argument.
The graph of the absolute value function y = -|x + 6|, we first need to understand the properties of an absolute value function.
The absolute value of a number is its distance from 0 on the number line. Thus, the absolute value function |x| will always return a non-negative value, regardless of the sign of x. When the absolute value function is multiplied by -1, as in -|x|, the function reflects the graph over the x-axis and makes it negative.
Applying these principles to the given function y = -|x + 6|, we can start by identifying the vertex, which is the point where the absolute value term inside the function equals 0. In this case, the vertex is at x = -6.
Next, we can plot some points to get a sense of the shape of the graph. We can choose values of x that are greater than or less than -6, and use the fact that the function is negative to find the corresponding y-values. For example:
- When x = -7, y = -|(-7) + 6| = -1
- When x = -5, y = -|(-5) + 6| = -1
We can see that the graph has a "V" shape, with the vertex at (-6,0). The line of symmetry is the vertical line passing through the vertex, which is the equation x = -6. The graph approaches the x-axis on either side of the vertex, but never touches it. The negative sign in front of the absolute value term causes the graph to be reflected over the x-axis.
since the absolute value function takes the same value for positive and negative values of its argument.
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I need help with number 1
Answers
Answer:
3,418.32yd³
Step-by-step explanation:
For volume you do the area (8)² multiplied by the height (17). 8 x 8 = 64. 64 x 17 = 1,088. you then multiply 1,088 by 3.14, the π, which is 3,416.32. We are using yards so the end result is 3,418.32yd³.
Don't understand? Yeah, I didn't at first either, I had to refresh my memory. If you don't understand, https://youtu.be/fGVlL47TKAw helped me. Have a wonderful day!
how do i solve this Please give me a advise
Answers
The probability of spinning an even number, flipping tails, then spinning an odd number is:
1/9 (as fraction) or 11.11% (as percent)
How to find the probability of spinning an even number, flipping tails, then spinning an odd number?
To find the probability of spinning an even number, flipping tails, then spinning an odd number. We need to consider the individual probabilities. That is:
We have only one even number in the spinner, and that is 2. Thus,
P(even number) = 1/3
For a coin, the probability of head or tail is 1/2. Thus,
P(tail) = 1/2
We have two odd number in the spinner, and that is 1 and 3. Thus,
P(odd number) = 2/3
Therefore, the probability of spinning an even number, flipping tails, then spinning an odd number will be:
P(even, tail, odd) = 1/3 * 1/2 * 2/3
= 2/18
= 1/9 (as fraction)
In percent:
P(even, tail, odd) = 1/9 * 100
= 11.11%
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