See explanation below
Explanation:Proportion simply means two ratios or two fractions are equal.
For example:
1/5 is proportional to 2/10
\(\frac{1}{5}=\frac{2}{10}\)This is because when we break down 2/10 to the simplest term, we would have 1/5
In proportion, the difference between the two fractions that are equal to each other is that one fraction was multiplied by a constant number in both the nummerator and denominator.
using the example above:
\(\begin{gathered} \frac{2}{10}=\frac{2(1)}{2(5)} \\ =\text{ }\frac{2}{2}\times\frac{1}{5} \\ =\text{ }\frac{1}{5} \end{gathered}\)Another example of proportion:
3/4 = 9/12
9/12 = 3(3)/3(4) = 3/4
The number of points that Shira scored each basketball game so far this season is shown on the dot plot. A number line going from 1 to 13. 2 dots are above 2. 1 dot is above 3. 1 dot is above 5. 2 dots are above 7. 3 dots are above 9. 6 dots are above 11. 1 dot is above 12. Which statement must be true according to the dot plot?
The according to the dot plot, the true statement is: the data is left-skewed and shows Shira never scored fewer than 2 points or more than 12 points in a game
What is Left-Skewed Data Distribution?A data distribution that is left-skewed is negatively skewed. This means that the long tail goes in the negative direction of the number line, with most of the values being concentrated on the right side.
The dot plot given is left-skewed, which means it is negatively-skewed.
Therefore, the according to the dot plot, the true statement is:
The data is left-skewed and shows Shira never scored fewer than 2 points or more than 12 points in a game
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Answer:
c
The data is skewed to the left and shows that she never scored fewer than 2 points or more than 12 points in a game.
Step-by-step explanation:
swag
The table below shows the number of grams of fat contained in a pizza according to the number of meat toppings on the pizza.
Which equation best models this set of data?
Answer:
Plot the points on the graphing calculator, and then generate the best regression model. That model is:
F = 16.65x + 15.7
The closest equation is D.
Determine the volume of the following spheres with the given dimensions. To break the code find the mean of all your answers. Round your answers to the hundredth place. Use 3.14 for an approximation for pi.
Question 1
Answer:
You have to make an equation. The equation for sphere is V=4/3 π r^3
radius is half of diameter. Radius is 3 cm
Step-by-step explanation:
4/3 x3.14 x 3^3
= 113.04 cm
than you have to do the cubic root of 113.04.
= 4.83515851269 cmBy doing it like that, you can answer the rest of the 3 questions.
Thank you, I hope this is helpful!
A) Function 1
B) Function 2
C) The functions have the same slope
Answer:
A) Function 1
Step-by-step explanation:
Function 1:
the slope in y=mx+b is m
the slope is 1/3
Function 2:
(4,1) (8,2)
(2-1) / (8-4) = 1/4
In a certain country, approximately 22 out of 100 people over the age of 12 smoke. How many smokers would you expect in a group of 850 people over the age of 12?
Answer:
I would guess about 187 people out of the 850. I'm not really sure though.
Step-by-step explanation:
Answer:
People smoking= 187
Step-by-step explanation:
Take ratio of 22 people smoking out of 100,
\(\frac{22}{100}\)
now take ratio of unknown people smoking to 850 that is,
\(\frac{x}{850}\)
Compare them[i.e. take into proportion]
\(\frac{22}{100} = \frac{x}{850}\)
\(\frac{22}{100} . 850 = x\)
\(x= 187\)
please help me please i really need help please
Answer:
y = 1/6x
Step-by-step explanation:
linear equations don't have exponents
HELPPPP PLEASEEEEEEEEE
So, the length of WZ is 24 in kite WXYZ with diagonals WY and XZ.
What is triangle?A triangle is a closed, two-dimensional geometric shape that is formed by three line segments, called sides, that intersect at three points, called vertices. Triangles are one of the most basic shapes in geometry and are studied extensively in mathematics. The properties of triangles depend on the length of their sides and the size of their angles. Triangles can be classified based on the length of their sides as equilateral, isosceles, or scalene, and based on the size of their angles as acute, right, or obtuse. In an equilateral triangle, all three sides are of equal length. In an isosceles triangle, two sides are of equal length, while the third side is of a different length. In a scalene triangle, all three sides are of different lengths.
Here,
Since WXYZ is a kite, we know that its diagonals, WY and XZ, intersect at a right angle and bisect each other. Let M be the point of intersection of the diagonals, so that MW = MY and MX = MZ.
We can use the Pythagorean theorem to find MW and MX, and then use the fact that they are equal to find WZ.
Using the Pythagorean theorem in right triangles WMX and WMY, we have:
MW² = WX² - MX²
= 17² - 5²
= 264
MY² = WY² - MW²
= 13² - 264
= 25
MX² = XZ² - MZ²
= 17² - 13²
= 144
Since MW = MY, we have MW = √(25)
= 5
Therefore, WZ = 2MX
= 2√(144)
= 2*12
= 24
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A June 2009 Harris Interactive poll asked people their opinions about the influence of advertising on the products they buy. Among the people aged 18 to 34 years, 45% view advertisements as being influential, whereas among the people aged 35 to 44 years, 37% view advertisements as being influential. Suppose that this survey included 655 people in the 18- to 34-year age group and 420 in the 35- to 44- year age group. At the 1% significance level, can you conclude that the proportion of all people aged 18 to 34 years who view advertisements as being influential in their purchases is greater than the proportion of all people aged 35 to 44 years who hold the same opinion
Answer:
We accept with 99 % of confidence that p₁ ( the proportion in the group aged 18 - 34 ) is bigger than p₂ (the proportion in the group aged 35-44)
Step-by-step explanation:
Group aged 18 - 34
Sample size n₁ = 655 sample size enough to apply a normal distribution aproximation for the test
p₁ = 0,45 and q₁ = 1 - p₁ q₁ = 0,55
p₁*n₁ = 0,45*655 = 294 q₁*n₁ = 0,55*655 = 360
both bigger than 5
p₁ = 45 % or p₁ = 0,45 then q₁ = 1 - 0,45 q₁ = 0,55
Group aged 35 - 44
Sample size n₂ = 420 sample size enough to apply a normal distribution aproximation for the test
p₂ = 37% p₂ = 0,37 and q₂ = 0,63
p₂*n₂ = 0, 37*420 = 155 q₁*n₁ = 0,63*420 = 264
Test Hypothesis
Null Hypothesis H₀ p₁ = p₂
Alternative Hypothesis Hₐ p₁ > p₂
Significance level α = 1% α = 0,01
Confidence Interval CI = 99 %
Then from z table we find critical z z (c ) = 3,1
Calculating z(s)
z(s) = ( p₁ - p₂ )/ √[ ( p₁*q₁)/n₁ ] + [ (p₂*q₂)/n₂ ]
z(s ) = (0,45 - 0,37 ) / √ 0,45*0,55)/655 + 0,37*0,63 /420
z(s) = 0,08 /0,03
z(s) = 2,66
Comparing z(s) and z(c)
z(s) < z(c)
Then z (s) is inside the acceptance region for H₀
Solve for b b+4.22=7.08
Steps to solve:
b + 4.22 = 7.08
~Subtract 4.22 to both sides
b = 2.86
Best of Luck!
In the following image, segment BD bisects segment AC, and three triangles are similar: AABC~ AADB~ ABDC. Complete the two-column
proof of the Pythagorean theorem.
3: A. (AC)DC) + (AC)(CD) = (AC)AC) + (BC)BC)
B. (AC)(CD) + (AC)(AD) = (BC)BC) + (AB)AB)
C. (AB)(CB) + (AD)CD) = (AC)AC) + (BC)BC)
D. (AC)BC) = (AC)(AC) + (BC)BC)
5: A.angle bisector postulate
B. triangles
C. common line segment
D. segment addition postulate
1. The Fill ups are as follow:
AB² + BC² = AC. AD + AC. CD
2. Segment addition postulate
What is Pythagorean theorem?The relationship between the three sides of a right-angled triangle is explained by the Pythagoras theorem, commonly known as the Pythagorean theorem. The Pythagoras theorem states that the square of a triangle's hypotenuse is equal to the sum of its other two sides' squares.
Given:
BC/ AC = CD/ BC and AB/ AC = AD/ AB
Now, BC² = AC. CD and AB² = AC. AD
Using, Addition Property of Equality
AB² + BC² = AC. AD + AC. CD
and, AB² + BC² = AC (AD + CD) [factor]
AD + CD = AD (segment addition postulate)
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PLATO
i got it correct :)
. Cell Phone Models A particular cell phone company
offers 4 models of phones, each in 6 different colors and
each available with any one of 5 calling plans. Howy
many combinations are possible?
:C
120 many combinations are possible.
What is combination formula?The number of possible ways to choose items from a collection when the order of choice is irrelevant is determined using the combination formula. Combination, to put it simply, is the process of choosing items or things from a bigger group where order is irrelevant.
Consider a collection of three integers P, Q, and R. The number of ways that we may choose two numbers from each group is thus determined by combination.
It is represented as: \(^nC_r\)
where, n = total number of objects in the set
r = number of choosing objects from the set
Given that,
Cell Phone Models A particular cell phone company offers:
4 models of phones
each in 6 different colors
each available with any one of 5 calling plans
Thus, possible combination numbers are:
= (No. of models) × (No. of colors) × (No. of calling plans)
= (4)× (6)× (5)
= 120 possibilities
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please help me please help me please help me please help me please help me please help me please
Answer:
q5 is 4
q6 is 72
Step-by-step explanation:
yan na po ..sana maktulong sau
2x - y=17 and x-y=10
Solve with substitution, show work?
Answer:
x = 7 y = -3
Step-by-step explanation:
x - y = 10 ⇒ x = 10 + y
Substitute x = 10 + y into 2x - y = 17:
2(10 + y) - y = 17
20 + 2y - y = 17
y = -3
Substitute the found value of y into x = 10 + y to find x:
x = 10 - 3 = 7
A carpentry tool has replaceable hexagonal heads. The diagram below shows the replaceable head. *Picture not drawn to scale What is the area of the replaceable head? Round to the nearest hundredth, if necessary. A. 13.59 square inches B. 12 square inches C. 15 square inches D. 17.81 square inches
Answer:
Step-by-step explanation:c 15
solve the following two equation X+Y=5
X-2Y=2
Step-by-step explanation:
x=4 and y= 1 because of 4+1=5 and add 2y to both sides
x-2y+2y=2+ 2y
x=2y+2
4-2=2
\(\left \{ {{x+y=5} \atop {x-2y=2}} \right.\)
Here we have 2 equations in one system.
System of Equations/Simultaneous Equations are for finding the intercepts of both graphs.
We can solve these Simultaneous Equations in many ways. However, I'll be solving by substitution.
To solve by using substitution, we need to move either x or y to the another side. I'll move x term to another side for the first equation. (We'll substitute the first equation in the second.)
\(\left \{ {{y=-x+5} \atop {x-2y=2}} \right.\)
Now we substitute y = -x+5 in x-2y = 2
\(x-2(-x+5)=2\\\)
Then distribute -2 in (-x+5) | Note that multiplying the negative will get positive. |
\(x-2(-x+5)=2\\x+2x-10=2\\3x=2+10\\3x=12\)
We should get this. When we get this, we move 3 to divide 12 (Opposite when moving to another side so from plus to minus and from multiply to divide.)
\(x=4\)
But we are not done yet. We have to find the y-value. After all they are two variables equations.
If we want to find the y-value then we have to substitute x = 4 in any given equations. I'd suggest to substitute in the equation that doesn't have a coefficient with high value.
So I'll be substituting in x + y = 5 instead.
Substitute x = 4 in x + y = 5
\(4+y=5\\y=5-4\\y=1\)
Thus, we get both x and y value. Answer in either coordinate point or writing form.
Therefore, the answer is
x = 4 when y = 1 or (4,1)
Both works. Hope this helps.
Find the values of x in the figure below. Express your answer in simplest radical form.
Answer:
Step-by-step explanation:I don't say u must have to mark my ans as brainliest but if it has really helped u plz don't forget to thank me...
Need help urgently. This is a simple but difficult math equation
Answer:
The last one looks like its not true
Answer:
Step-by-step explanation:
4) looks wrong , or untrue.
Using Additive Inverse to Factor by Grouping
Factor the polynomial 4x4-20x²-3x² + 15 by grouping. What is the resulting expression?
O (4x²+3)(x2²-5)
O (4x²-3)(x²-5)
O (4x² - 5)(x²+3)
O (4x²+5)(x²-3)
Let a=\(4x^{4} -20x^{2} -3x^{2} +15\) . So the resulting polynomial after factorization is a= \((4x^{2} -3)(x^{2} -5)\).
What is polynomial?A polynomial is an expression that only uses the operations of addition, subtraction, multiplication, and non-negative integer exponentiation of variables. Variables are also known as indeterminates.
How do you identify a polynomial?In an equation such as the quadratic equation, cubic equation, etc., a polynomial function is a function that only uses non-negative integer powers or only positive integer exponents of a variable. For instance, the polynomial 2x+5 has an exponent of 1.
Let
\(a=4x^{4}-20x^{2} -3x^{2} +15\\=4x^{4} -3x^{2} -20x^{2} +15\\=x^{2} (4x^{2} -3)-5(4x^{2} -3)\\=(4x^{2} -3)(x^{2} -5)\)
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Two hundred eighty-two people attended a recent performance of Cinderella. Adult tickets sold for $5 and children’s tickets sold for $3 each. Find the number of adults and the number of children that attended the play if the total revenue was $1046.
Part A: Write a system of equations in standard form (Ax + By = C) that can be solved to find the number of adults and children who attended the performance. Define the variables used in the equations. (4 points)
Part B: How many adults attended the performance? How many children attended the performance? Show your work and steps of how you found your answer using elimination.
A. A system of equations in standard form that can be solved to find the number of adults and children who attended the performance is:
x + y = 282
3x + 5y = 1046
B. The number of adults who attended the performance is 182 adults.
The number of children who attended the performance is 100 children.
How to determine the number of each type of tickets sold?In order to write a system of linear equations to describe this situation, we would assign variables to the number of adult tickets sold and number of children tickets sold, and then translate the word problem into an algebraic equation as follows:
Let the variable x represent the number of adult tickets sold.Let the variable y represent the number of children tickets sold.Since 282 people attended the recent performance by Cinderella, a linear equation that models the situation is given by:
x + y = 282 ....equation 1.
Additionally, adult tickets sold for $5 while children tickets sold for $3 each with a total revenue was $1046, a linear equation that models the situation is given by:
3x + 5y = 1046 .......equation 2.
Part B.
By multiplying equation 1 by 3, we have:
3x + 3y = 846 .......equation 3.
By subtracting equation 3 from equation 2, we have:
2y = 200
y = 100 children.
For the x-value, we have:
x = 282 - y
x = 282 - 100
x = 182 adults.
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x - 2y = 14
x + 3y = 9
Answer:
x = 12, y = -1
Step-by-step explanation:
x - 2y = 14 (call this equation '1.')
x + 3y = 9 (call this '2')
'2' - '1' :
0x + (3 - -2)y = 9 -14
(3 + 2)y = -5
5y = -5
y = -1.
substitute than into '1':
x - 2(-1) = 14
x + 2 = 14
x = 12.
check we are correct by subbing into '2'.
x + 3y = 9
12 + 3(-1) = 12 - 3 =9
so, x= 12 and y = -1
Answer:
X=14+2y
14+2y+3y=9
14+5y=9
5y=9-14
5y=–5
Y=–1
A fair die has 12 sides and they are labeled 1, 2, 3, …, 12. All answers should be in fraction form.
What is the probability of rolling the die and it lands with the 3 face on top?
What is the probability of rolling the die and it lands with the 3 or a 7 face on top?
What is the probability of rolling the die and it lands with a 15 face on top?
The probability of rolling the dice and having the three faces land on top is 1/4.
What is probability?The probability of an occurrence is a number used in science to describe how likely it is that the event will take place.
In terms of percentage notation, it is expressed as a number between 0 and 1, or between 0% and 100%.
The higher the likelihood, the more likely it is that the event will take place.
The probability of an event can be calculated using the following formula.
Probability(Event) = Positive Results/Total Results = x/n. In order to better grasp probability, let's look at a straightforward application.
So, we are aware of the formula:
P(E) = Favourable events/Total events
Now, substitute the values and calculate as follows:
P(E) = Favourable events/Total events
P(E) = 3/12
P(E) = 1/4
Therefore, the probability of rolling the dice and having the three faces land on top is 1/4.
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Complete question:
A fair die has 12 sides and they are labeled 1, 2, 3, …, 12. What is the probability of rolling the die and it lands with the 3 faces on top?
x = 13, ¿cuál ecuación es verdadera?
3(18 - x) = 67
4(9x) = 23
2(x-3)=7
5(x-9) = 20
When x = 13, the equation that is true is option D) 5(x - 9) = 20.
To determine which equation is true when x = 13, we can substitute the value of x into each equation and see which equation holds true. Let's go through each option:
A) 3(18 - x) = 67
Substituting x = 13:
3(18 - 13) = 67
3(5) = 67
15 = 67
The equation is not true when x = 13. Therefore, option A is false.
B) 4(9x) = 23
Substituting x = 13:
4(9*13) = 23
4(117) = 23
468 = 23
Again, the equation is not true when x = 13. Therefore, option B is also false.
C) 2(x - 3) = 7
Substituting x = 13:
2(13 - 3) = 7
2(10) = 7
20 = 7
Once again, the equation is not true when x = 13. Therefore, option C is false as well.
D) 5(x - 9) = 20
Substituting x = 13:
5(13 - 9) = 20
5(4) = 20
20 = 20
Finally, the equation is true when x = 13. Therefore, option D is true.
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Note: the translated questions is
X = 13, which equation is true?
how to solve this question
For the trigonometric identity
11. If cos 27° = x, then the value of tan 63° interims of "x" is x/√1 - x²
12. If Θ be an acute angle and 7sin²Θ + 3 cos²Θ= 4, then tan Θ is 1/√3
13. The value of tan 80° × tan 10° + sin² 70° + sin² 20° is 2
14. The value of (sin 47°/cos 43°)² + (cos 43°/sin 47°) - 4 cos²45° is 0
15. If 2 (cos²Θ - sin²Θ) = 1, Θ is a positive acute angle them the value of Θ is 30°
16. If 5 tan Θ = 4, then (5 sin Θ - 3 cos Θ)/(5 sin Θ + 2 cos Θ) is equal to 1/6
17. If sin(x + 20)° = cos (x + 10)° then the value of "x" is 30°
18. The value of (sin 65°)/ (cos 25°) is 1
How do we find the various trigonometric identity?To solve the various trigonometric identity;
11. Given: cos 27° = x
We know that cos (90 - θ) = sin θ
So, cos 63° = sin 27°
And sin 63° = √1 - cos²27°
Substituting cos 27° = x, we get
sin 63° = √1 - x²
Therefore, Therefore, tan 63° = sin 63° / cos 63° = cos 27° / cos 63° = x / cos 63°.
= x/√1 - x²
12. Given: Θ is an acute angle and 7sin²Θ + 3 cos²Θ= 4
Since Θ is an acute angle, sin²Θ + cos²Θ = 1
Substituting sin²Θ + cos²Θ = 1 into the equation 7sin²Θ + 3 cos²Θ= 4, we get
7 (sin²Θ/ cos²Θ) + 3 = 4/cos²Θ - 4 sec²Θ
⇒ 7tan²Θ + 3 = 4(1 + tan²Θ)
⇒ 7tan²Θ + 3 = 4 + 4 tan²Θ
⇒3 tan²Θ = 1
⇒ tan²Θ = 1/3
⇒ tanΘ = 1/√3
13. For tan 80° × tan 10° + sin² 70° + sin² 20°
⇒ tan 80° = cot (90 - 80)° = cot 10°
⇒ sin 70° = cos (90 - 70) = cos 20°
⇒ cot 10° × tan 10° + cos 20° + sin² 20°
= 1 + 1 = 2
14. (sin 47°/cos 43°)² + (cos 43°/sin 47°) - 4 cos²45°
= (sin 47°/cos43°)² + (cos 43°/sin 47°)² - 4(1/√2)²
= (sin (90° - 43°)/cos43°)² + (cos (90° - 47°)/sin)² = 4(1/2)
= (cos 43°/cos 43°)² + (sin 47°/ sin 47°)² - 2
= 1 + 1 - 2 = 0
15. 2 (cos²Θ - sin²Θ) = 1
cos²Θ - sin²Θ = 1/2
Since Θ is an acute angle, sin²Θ + cos²Θ = 1
Substituting sin²Θ + cos²Θ = 1 into the equation cos²Θ - sin²Θ = 1/2, we get
cos²Θ - (1 - cos²Θ) = 1/2
2cos²Θ = 3/2
cos Θ = √3/2(cos 30° = (√3)/2
= 30°
16. Given: 5 tan Θ = 4
We know that tan Θ = sin Θ / cos Θ
So, 5 sin Θ / cos Θ = 4
5 sin Θ = 4 cos Θ
Dividing both sides of the equation by 5, we get
sin Θ / cos Θ = 4/5
∴ sin Θ = 4/5 cos Θ
given that the expression is (5 sin Θ - 3 cos Θ)/(5 sin Θ + 2 cos Θ)
we substitute sin Θ = 4/5 cos Θ into the equation
⇒(5 × 4/5 cos Θ - 3 cos Θ)/(5 × 4/5 cos Θ + 2 cos Θ)
= (4-3)/(4 + 2) = 1/6
17. Given: sin(x + 20)° = cos (x + 10)°
We know that sin(90 - θ) = cos θ
So, sin(x - 20)° = sin(90 - (3x + 10))°
⇒ (x - 20)° = (90 - (3x + 10))°
⇒ x - 20° = 90° - 3x + 10
⇒ 4 x = 120°
⇒ x = 120°/4
⇒ x = 30°
18. To find the value of (sin 65°) / (cos 25°), we can use the trigonometric identity:
To solve this, we can use the following trigonometric identities:
sin(90 - θ) = cos θ
cos(90 - θ) = sin θ
We can also use the fact that sin²θ + cos²θ = 1.
Rewrite sin (65°) / cos (25°)
⇒ sin (65°) = cos (25°)
∴ cos (25°)/ cos (25°) = 1
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Someone please help!! I am horrible at trig!!!!!
Find the third side in simplest radical form:
33
56
Answer:
65
Step-by-step explanation:
I hope it helps
A^2 + B^2 = C^2
If possible factor. Find LCD. Multiply both sides by LCD. Solve show all work.
The lowest common denominator of the fraction is 6
What is LCDThe lowest common denominator (LCD) is the smallest common multiple of the denominators of a set of fractions. It is used to add or subtract fractions with different denominators.
The LCD of a set of fractions is the smallest number that is divisible by all the denominators in the set. When all the denominators are divided into the LCD, each fraction has an equivalent fraction with the same value and a denominator equal to the LCD.
In the fraction given;
x / 3 + x / 2 = 20
The lowest common denominator is 6
Using 6, we can divide through each of the fraction.
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4.02>4.1 TRUE OR FALSE
Answer: true
Step-by-step explanation: cuz
Answer:
False
Step-by-step explanation:
Which variable will you choose to eliminate? How? -3x -8y=-24 and
3x - 5y= 45
Answer:
Lets choose y
-8y=3x-24y=-3/8x+3Plug in
3x+15/8x-15=45 39/8x= 60 x=480/39Answer:
I'll choose 'x' variable first to eliminate because -
-3 (coefficient of 'x' in Eqn.1) & 3 (coefficient of 'x' in Eqn.2) are additive inverses of each other , so they can be easily eliminated by simply adding those equations. It can be also solved by using elimination method but you'll need to multiply -1 with either Eqn.1 or Eqn.2 because in elimination method , a variable can be eliminated only when their coefficients are numerically equal (along with their sign).Step-by-step explanation:
Eqn.1 → -3x - 8y = -24
Eqn.2 → 3x - 5y = 45
If we'll add both the equations , then '3x' would be getting cancelled first.
⇒ \((-3x - 8y) + (3x - 5y) = (-24) + (45)\)
⇒ \(3x - 3x - 8y - 5y = 45 - 24\)
⇒ \(-13y = 21\)
⇒ \(y = \frac{-21}{13}\)
Putting the value of y in eqn.2 ,
⇒ \(3x - 5(\frac{-21}{13}) = 45\)
⇒ \(3x + \frac{105}{13} = 45\)
⇒ \(3x = 45 - \frac{105}{13}\)
⇒ \(3x = \frac{585 - 105}{13} = \frac{480}{13}\)
⇒ \(x = \frac{480}{13 \times 3} = \frac{480}{39}\)
Reducing the fraction gives ,
⇒ \(x = \frac{160}{13}\)
Enter the coordinates of a point that is 5 units from (-2, -1). The coordinates of a point 5 units away is (-2, ).
Answer:
22
Step-by-step explanation:
Error Analysis:
Describe and correct the error made in the reasoning:
If a/5 = b/3, then 5/a = b/3 * x
The correct expression is 5/a = 1. There is no need to introduce an additional variable "x".
What is a fraction?In such a fraction, the value that appears above the horizontal line is referred to as the numerator.
It represents the number of pieces removed from the whole. The denominator of a fraction is the numerical value that comes before the brings together various.
The error in the reasoning is that it assumes that multiplying the second fraction by "x" will result in an equivalent expression to 5/a. However, this is not necessarily true.
To correct the error, we can use the property of reciprocals, which states that if a/b = c/d, then b/a = d/c. Using this property, we can rewrite the given equation as:
a/5 = b/3
5/a = 3/b (multiplying both sides by 5/a)
5/a = (b/3) * (3/b) (multiplying both sides by the reciprocal of b/3)
5/a = 1
Therefore, the correct expression is 5/a = 1. There is no need to introduce an additional variable "x".
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A bag of numbered lottery balls contains the numbers 1 through 50. What is the probability that a randomly selected ball will be a number that is not a multiple of 8? Give your answer as a simplified fraction.
A bag of numbered lottery balls contains he numbers 1 through 50.
One ball is selected at random.
From 50 balls, one ball can be selected in 50 different ways.
So, the total number of points in sample space is 50.
Let us consider the event that the number is a multiple of 8 be A.
There are six numbers between 1 o 50 which are multiple of 8.
Therefore, one ball can be selected from 6 balls in 6 different ways.
So, the number of points in sample space in favour of the event A is 6.
Therefore, by the classical definition of probability,
\(\begin{gathered} P(A)=\frac{6}{50} \\ =\frac{3}{25} \end{gathered}\)Then, the probability that the selected number is not a multiple of 8 is
\(\begin{gathered} P(A^C)=1-P(A) \\ =1-\frac{3}{25} \\ =\frac{22}{25} \end{gathered}\)So, the required probability is 22/25.