It is a independent event. The probability is 6/25.
What is an independent event?An independent event is an event whose occurrence are random event. There is no relationship between picking a yellow highlighter and then a green highlighter.
What is the probability?
Probability determines the chances that a random event would happen. The probability the event occurs is 1 and the probability that the event does not occur is 0.
Probability of picking a yellow highlighter and then a green highlighter = (number of yellow highlighters / total number of highlighters) x = (number of green highlighters / total number of highlighters)
(12 / 20) x (8 /20) = 6/25
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Consider the expression 4a + (-3b), where bis a negative number and a < b. Is the sum positive or negative?
The sum will be negative.
The product of two negative numbers is always positive and if we add two numbers, the sign of the greater number is used in the result.
Here, we are given an expression 4a + (-3b)
Also we are told that a < b and b is a negative number
Mow, since b is a negative number, (-3b) will always be positive. This is because the product of two negative numbers, here -3 and b, will always be positive.
Now, a can be positive or negative. If a is positive, the sum will always be positive. However, if it is negative, the sum can be either positive or negative.
Here, in fact, since a < b, a will always be negative only
Let us take an example, say a = -3 and b = -2
Then the sum becomes 4(-3) + (-3)(-2)
= -12 + 6
= -6
If we observe closely since a and be are both negative and a < b, in absolute terms a will always be greater than b since for negative numbers higher the value, smaller is the number.
Thus, we can conclude that 4a > (-3b) for all values of a and b
and since 4a will always be negative, the sum will also be negative.
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3. What is an equation of the line in slope intercept form? (1 point)
A.y=2x-2
B.y=-2x-2
C.y=-2x+2
D.y=2x+2
Answer:
C. y = 2x + 2
Step-by-step explanation:
There are 2 points on the line (0,2) and (-3,-4)
from (-3,-4) to (0,2), rise over run is 6/3 so slope is 2
You can calculate it too
m = (y2-y1)/(x2-x1)
m = (-4 - 2)/(-3 - 0) = -6/-3 = 2
Using m = 2, x = 0, y = 2
y = mx + b
2 = 2(0) + b
b = 2
therefore
y = 2x + 2
hi please help me ii need this one right now
Answer:the graph is not linear
Step-by-step explanation:
For Exercises 23 and 24, find the value of x and the measure of each interior angle
If the interior angles in the octagon is (4x-80)°, (4x-80)°,(2x+50)°,(2x+50)°,(4x-80)°,(4x-80)°,(2x+50)°,(2x+50)° then the value of x is equal to 50.
Given that the interior angles in the octagon is (4x-80)°, (4x-80)°,(2x+50)°,(2x+50)°,(4x-80)°,(4x-80)°,(2x+50)°,(2x+50)°,(4x-80)°.
We are required to find the value of x that are used in the angles of the given octagon.
Octagon is the shape that has eight sides,eight vertices,eight angles. Sum of all the interior angles of octagon is equal to 1080°.
(4x-80)°+ (4x-80)°+(2x+50)°+(2x+50)°+(4x-80)°+(4x-80)°+(2x+50)°+(2x+50)°=1080
24x-120=1080
24x=1080+120
24x=1200
x=1200/24
x=50
Hence if the interior angles in the octagon is (4x-80)°, (4x-80)°,(2x+50)°,(2x+50)°,(4x-80)°,(4x-80)°,(2x+50)°,(2x+50)° then the value of x is equal to 50.
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The velocity (v metres per second) of a body is known to be proportional to the square root of its kinetic energy (e joules). When the velocity of a body is 120 m/s, its kinetic energy is 1600 J.
a) Write down a relationship between v and e, using k as the constant of proportionality.
b) Calculate the value of k.
c) If v = 21, calculate the kinetic energy of the body in joules.
Answer: Find step-by-step Probability solutions and your answer to the following textbook question: The velocity (v metres per second) of a body is known to be proportional to the square root of its kinetic energy (e j.) I don't know if this will help
Step-by-step explanation:
A right triangle has side lengths 8, 15, and 17 as shown below.
Use these lengths to find sin.X, tanX, and cos.X.
Answer:
please demonstrate how tha triangle looks like
I need help right now!
Which expression is equivalent to 5(−2.3b − 4.1) − (7b + 0.7)?
−18.5b − 21.2
18.5b − 21.2
−18.5b − 3.4
18.5b + 3.4
Answer: B (18.5b-21.2)
The required expression −18.5b − 21.2 is equivalent to the given expression which is the correct answer that would be option (A).
What is the algebraic expression?Algebraic expressions are mathematical statements with a minimum of two terms containing variables or numbers.
We have been given the expression below as
5(−2.3b − 4.1) − (7b + 0.7)
Open the parentheses and apply the distributive property of multiplication,
⇒ −2.3b × 5 − 4.1 × 5 − 7b - 0.7
⇒ -11.5 - 20.5 − 7b - 0.7
Rearrange the likewise terms and apply the arithmetic operation,
⇒ −18.5b − 21.2
Hence, the required expression −18.5b − 21.2 is equivalent to the given expression.
Thus, the correct answer would be an option (A).
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What is 166.44 divided by 4 equal using long division. Please answer this is due in 10 minutes. The person with THE RIGHT ANSWER get brainiest and 30 points.
is anybody good at maths
15times15 divide by 20 takeway 5 add100
[tex]111.2[/tex]
Step-by-step explanation:
As per the question, 15 times 15 i.e. 225
[tex]15 \times 15 = 225[/tex]
225 divide by 20 i.e. 11.25
[tex] \frac{225}{20} = 11.25[/tex]
take away five from the 11.25 then it will be 11.2
Add 100 to 11.2 i.e
[tex]11.2 + 100 = 111.2[/tex]
Answer: 115
Step-by-step explanation:
[tex]\displaystyle\\\frac{15*15}{20-5} +100=\\\\\frac{15*15}{15} +100=\\\\15+100=\\\\115[/tex]
John runs the same number of kilometres each day.write an expression to represent the number of kilometre john ran in june last year
An algebraic expression to represent the number of kilometres John ran in June month last year is 30a.
Given that, John runs the same number of kilometres each day.
We need to find an algebraic expression to represent the number of kilometres John ran in June month last year
What is an algebraic expression?An algebraic expression (or) a variable expression is a combination of terms by the operations such as addition, subtraction, multiplication, division, etc.
Let us assume that john is running 'a' kilometres per day.
We know that June month composed of total 30 days
So the algebraic expression for the number of kilometres John ran in June last year = Number of kilometres running per day × Number of days in the month of June
=a × 30=30a
Therefore, an algebraic expression to represent the number of kilometres John ran in June month last year is 30a.
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Elsa opens an account to save money for a family vacation. the account earns an annual interest rate of 4% 4 % . she earns $37 $ 37 in simple interest after 6 6 months.
Amount while opening account at rate of 4% for 6 months and earn simple interest $37 is $1850.
As given,
Simple interest amount earned by Elsa = $37
Annual interest rate R= 4%
Time T =6 months
Let P be the principal amount she put while opening account
Simple interest = (P × R × T) / 100
⇒37 ={P × 4 × (6/12)}/100
⇒P =(37 × 100) / 2
= $1850
Therefore, amount while opening account at rate of 4% for 6 months and earn simple interest $37 is $1850.
The complete question is:
Elsa opens an account to save money for a family vacation. The account earns an annual interest rate of 4%. She earns $37 in simple interest after 6 months. How much money did she put in the account when she opened it?
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solve the equation for the given variable. justify each step.
9x + 2y = 5; y
1/15s - 2/3t = -2; s
Answer: y=[tex]\frac{5-9x}{2}[/tex]
s=-30+10t
Step-by-step explanation:
9x + 2y = 5; y
9x-9x+2y = 5-9x
2y=5-9x
y=[tex]\frac{5-9x}{2}[/tex]
1/15s - 2/3t = -2; s
(1/15s - 2/3t = -2)*15 ==> Get rid of fraction by multiplying both sides by 15
s - 30/3 t=-30
s-10t=-30
s=-30+10t
work out the area of the shape
Answer:
88 [tex]cm^{2}[/tex]
Step-by-step explanation:
We need to find the area of the rectangle and the triangle.
Area of the rectangle:
a = length x width
a = 11 x 6 = 66
Area of the triangle:
a = [tex]\frac{ b x h}{2}[/tex] We need to find the base and height of the triangle. The base is the same length as the length of the rectangle: 11 and the height is 10 - 6 or 4
a = [tex]\frac{11 x 4}{2}[/tex]
a = [tex]\frac{44}{2}[/tex]
a = 22
Add the area of the rectangle and the triangle together. 66 + 22 = 88
A new yo-yo factory is operating at 80 percent
of capacity and produces 4,000 yo-yos daily.
when the factory reaches 100 percent of
capacity, how many yo-yos should be
produced each day?
a.
800
b. 3,200
c. 4,800
d. 5,000
e. 7,200
PLEASE HELP ME ILL RATE U 5 STARS PLEASEE
Ali and Leila are analyzing the following points. Ali thinks that most of the points are in
quadrant 2 because there are many x-values that are negative. Leila disagrees. Who is
correct?
(−3, 6), (−2, 4), (−3, −1), (−1, −6), (−4, −5), (−2, −7), (−5, −9), (−8, −9), (−12, −3), (2, 4),
(3, 2) and (4, 1).
Answer: Ali is correct because all of the negatives are mostly in quadrant 2.
Step-by-step explanation:
Express in simplest radical form.
Square root of 160
Answer:
4 [tex]\sqrt{10}[/tex]
Step-by-step explanation:
Simplify
[tex]\sqrt{160}[/tex]
We can rewrite this as
[tex]\sqrt{16 * 10}[/tex]
Breaking this up
[tex]\sqrt{16} \sqrt{10}[/tex]
We know the square root of 16 is 4
4 [tex]\sqrt{10}[/tex]
sqrt(10) cannot be simplified so
Answer:
[tex]4\sqrt{10}[/tex]
Step-by-step explanation:
160 = 16 * 10
[tex]\sqrt{160} = \sqrt{16 \cdot 10} = \sqrt{16} \cdot \sqrt{10} = 4\sqrt{10}[/tex]
we cannot simplify further as 10 is 2*5, there are no more squares to simplify.
“ – 9(11 – 18) – 5.5”
please help thank youuu
Answer:
f(6) = - 10 and g(- 4) = 125
Step-by-step explanation:
substitute x = 6 into f(x) , that is
f(6) = - 2(6) + 2 = - 12 + 2 = - 10
substitute x = - 4 into g(x) , that is
g(- 4) = - 2(- 4)³ - 3 = - 2(- 64) - 3 = 128 - 3 = 125
Fritz can build a bookcase in 8 hours and Holly can build the same bookcase in 10 hours. After working together for 3 hours, Fritz leaves how long will it take holly to finish the bookcase by herself?
Holy will take 13/5 or 2.6 hours to finish the bookcase.
What is relation between time and work?The relation between time and work is
Work Done = Time Taken × Rate of Work ·
or, Rate of Work = 1 / Time Taken ·
or, Time Taken = 1 / Rate of Work ·
Now it is given that,
Time taken by Fritz to build a bookcase = 8 hours
So, Bookcase build by Fritz in 1 hour = 1/8
Similarly,
Time taken by Holly to build a bookcase = 10 hours
So, Bookcase build by Holly in 1 hour = 1/10
So, bookcase build in 3 hours
Fritz = 3/8
Holly = 3/10
Total bookcase build in 3 hours = 3/8 + 3/10 = 27/40
So. remaining work = 1 - 27/40 = 13/40
Thus, Time taken by Fritz to complete the bookcase = 8 * (13/40) hours
= 13/5 or 2.6 hours
Thus, Holy will take 13/5 or 2.6 hours to finish the bookcase.
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Find the value of sin c
Check the picture below.
[tex]\textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2\implies c=\sqrt{a^2 + b^2} \qquad \begin{cases} c=hypotenuse\\ a=\stackrel{adjacent}{7}\\ b=\stackrel{opposite}{\sqrt{95}}\\ \end{cases} \\\\\\ c=\sqrt{7^2~~ + ~~(\sqrt{95})^2}\implies c=\sqrt{49+95}\implies c=\sqrt{144}\implies c=12 \\\\[-0.35em] ~\dotfill\\\\ sin(C )=\cfrac{\stackrel{opposite}{\sqrt{95}}}{\underset{hypotenuse}{12}}\implies sin(C)\approx \text{\LARGE 0.81}[/tex]
vertical shrink by a factor of 1/4 of the graph of g(x)=|x|
The equation of the function after translation: [tex]$y=\frac{|x|}{4}$[/tex]
The y values advance toward the x-axis as they are multiplied by a value between 0 and 1. This is known as a vertical shrink and tends to flatten the graph.
When a base graph is multiplied by a particular factor larger than 1, vertical stretch happens. As a consequence, the graph is stretched outward while keeping the input values (or x). We anticipate that the y values in a function's graph will be further away from the x-axis when it is vertically extended.
The y-values are multiplied by a value between 0 and 1, which causes them to travel in the direction of the x-axis. This is known as a vertical shrink and tends to flatten the graph. A point (a,b) on the graph of y=f(x) y = f (x) shifts to a point (a,kb) (a, k b) on the graph of y=kf(x) y = k f (x) in both scenarios.
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graph g(x) = -3|x+5|-1. Describe the transformations of the parent function f (x) =|x| that produce the graph g(x).
Answer:
horizontal shift 5 units left
Vertical shift 1 unit down
reflection on the x-axis: Reflected
Vertical stretch: stretched
Step-by-step explanation:
i need help with plotting and answering bottom questions please
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Question 2 of 3
Question 2
Select the sentence(s) that represent(s)
the equation.
7(p +23) = 102
Save and Exit
A) Seven times the sum
of p and twenty-three
is the same as one
hundred two.
B) Seven times p plus
twenty-three equals
one hundred two.
C) Seven times the quan-
tity p plus twenty-three
equals one hundred
two.
D) The quantity seven
Submit Assignment
The sentence that represents the equation (7p + 23) = 102 is Seven times the sum of p and twenty-three is the same as one hundred two.
It is given that (7p + 23) = 102
Now, we have to write this equation in a sentence or to translate it in words.
As we can see in the given equation that seven is multiplied by p and then twenty three is added in the multiplication of seven and three, after that their addition is equal to one hundred two.
So, the Option A will be the correct answer which is Seven times the sum of p and twenty-three is the same as one hundred two.
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Money is borrowed at 18% simple interest. after one year, $610.06 pays off the loan. how much was originally borrowed?
The original amount borrowed was $517.
Simple Interest is the method to calculate the interest charged for a given number of years and given rate , in simple interest the principle remains same for each year.
Simple interest =[tex]\frac{P*R*T}{100}[/tex]
where P= principle, R=rate in % , T= time
We know that Amount= Principle+ Simple Interest........(1)
According to the question
Amount=$610.06
Rate=18%
time = 1yr
Substituting the value in equation (1) we get
[tex]610.06=P+\frac{P*18*1}{100}[/tex]
[tex]610.06=\frac{100P+18P}{100}[/tex]
[tex]610.06=\frac{118P}{100}[/tex]
[tex]61006=118P[/tex]
[tex]P=\frac{61006}{118}[/tex]
[tex]P=517[/tex]
Therefore , The original amount borrowed was $517.
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Find the missing Endpoint
Solve the equation
3x/3x-1 + 2/x = 1
Answer:
x= 2/7
Step-by-step explanation:
Multiply both sides by the common denominator
3x^2 +6x−2=3x^2 −x
Move everything to the left side.
3x^2+6x-2-3x^2+x=0
Simply.
7x-2=0
Separate the cosntants and variables.
7x=0+2
Add or subtract zero
7x=2
Then divide both sides by 7.
7x/7=2/7
Cancel out common factors in the numerator and denominator
x=2/7
Answer:
x = 2/7
Step-by-step explanation:
You want to solve the equation 3x/(3x-1) + 2/x = 1.
SolutionIt works nicely to subtract 1 from both sides, then simplify.
[tex]\dfrac{3x}{3x-1}+\dfrac{2}{x}=1\\\\\dfrac{3x}{3x-1}\cdot\dfrac{x}{x}+\dfrac{2}{x}\cdot\dfrac{3x-1}{3x-1}-\dfrac{x(3x-1)}{x(3x-1)}=0\\\\\dfrac{3x^2+6x-2-3x^2+x}{x(3x-1)}=0\qquad\text{combine terms}\\\\\dfrac{7x-2}{x(3x-1)}=0\qquad\text{simplify}\\\\7x-2=0\qquad\text{expression is 0 when numerator is 0}\\\\\boxed{x=\dfrac{2}{7}}\qquad\text{add 2, divide by 7}[/tex]
__
Additional comment
The values x=0 and x=1/3 would make the denominator zero, so are excluded from the domain of the equation. By working the problem this way, we ensure that extraneous solutions do not present themselves.
solve the simultaneous equation
-4x+3y=1
6x-y=2
Answer:
x = 1/2, y = 1
Step-by-step explanation:
Let's change the equation,
→ 6x - y = 2
→ y = 6x - 2
Then the value of x will be,
→ -4x + 3y = 1
→ -4x + 3(6x - 2) = 1
→ -4x + 18x - 6 = 1
→ 14x = 1 + 6
→ x = 7/14
→ [ x = 1/2 ]
Hence, the value of x is 1/2 (or) 0.5.
Now the value of y will be,
→ y = 6x - 2
→ y = 6(1/2) - 2
→ y = 3 - 2
→ [ y = 1 ]
Hence, the value of y is 1.
Answer:
x = ¹/₂
y = 1
Step-by-step explanation:
Given system of equations:
[tex]\begin{cases}-4x+3y=1\\\:\:\:\:\:\:6x-y=2 \end{cases}[/tex]
Multiply the second equation by 3:
[tex]\implies 3 \cdot 6x-3 \cdot y = 3 \cdot 2[/tex]
[tex]\implies 18x-3y=6[/tex]
Add this to the first equation to eliminate the term in y:
[tex]\begin{array}{lrr}&-4x+3y & = 1\\+ & 18x-3y& = 6\\\cline{2-3} & 14x \phantom{-3x)} & = 7\end{array}[/tex]
Solve for x:
[tex]\begin{aligned}\implies 14x & = 7\\\\\dfrac{14x}{14} & = \dfrac{7}{14}\\\\\implies x & = \dfrac{1}{2}\end{aligned}[/tex]
Substitute the found value of x into the first equation and solve for y:
[tex]\begin{aligned}-4x+3y & =1\\x=\dfrac{1}{2}\implies -4\left(\dfrac{1}{2}\right)+3y & =1\\-\dfrac{4}{2}+3y & =1\\-2+3y & =1\\-2+3y+2 & =1+2\\ 3y & =3\\\dfrac{3y}{3} & =\dfrac{3}{3}\\\implies y & =1\end{aligned}[/tex]
Therefore, the solution to the given system of equations is:
x = ¹/₂ and y = 1
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Help please I will mark you as a brainliest.
Answer:
(5² - 8) x 2 doesn't belong
Step-by-step explanation:
this is because this answer is the only one with parintisies around the 5²
Solve the following:
1. even integers between 1 and 101
2. first 25 terms of the arithmetic sequence 4, 9, 14, 19, 24 ...
Answer:
1. 2550
2. 1600
Step-by-step explanation:
Question 1Even Integer: A whole number that can be positive, negative, or zero, and that can be divided exactly by 2.
Even integers between 1 and 101:
2, 4, 6, 8, 10, ... , 100This forms an arithmetic sequence with:
first term (a) = 2common difference (r) = 2Sum of the first n terms of an arithmetic series:
[tex]\boxed{S_n=\dfrac12n[2a+(n-1)d]}[/tex]
There are 50 even integers between 1 and 101.
Therefore, to find the sum of the even integers between 1 and 101, substitute n = 50 and the found values of a and r into the formula:
[tex]\begin{aligned}\implies S_{50} & =\dfrac{1}{2}(50)[2(2)+(50-1)2]\\\\& =25[4+(49)2]\\\\& =25[4+98]\\\\& =25[102]\\\\& = 2550\end{aligned}[/tex]
Therefore, the sum of the even integers between 1 and 100 is 2550.
Question 2Given arithmetic sequence:
4, 9, 14, 19, 24, ...From inspection of the given arithmetic sequence:
first term (a) = 4common difference (r) = 9 - 4 = 5Sum of the first n terms of an arithmetic series:
[tex]\boxed{S_n=\dfrac12n[2a+(n-1)d]}[/tex]
To find the sum of the first 25 terms of the given arithmetic sequence, substitute n = 25 and the found values of a and r into the formula:
[tex]\begin{aligned}\implies S_{25} & =\dfrac{1}{2}(25)[2(4)+(25-1)5]\\\\& =\dfrac{25}{2}[8+(24)5]\\\\& =\dfrac{25}{2}[8+120]\\\\& =\dfrac{25}{2}[128]\\\\& = \dfrac{3200}{2}\\\\& = 1600\end{aligned}[/tex]
Therefore, the sum of the first 25 terms of the given arithmetic sequence is 1600.
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