Answer:
15/70 is the answer
Step-by-step explanation:
3/10 x 5/7
3x5=15 and 10x7=70
As a result, the answer to the question is 15/70
Thank you for reading! It is my hope that you will find it helpful in some way!
You have a bag which contains only red and green marbles. In this bag with $x^{2} 5$ marbles total, $x 1$ are red. Also, $x-3$ marbles have a scratch on them. The probability of drawing a red marble from the original bag is equal to that of drawing a marble with a scratch from the marbles left in the bag after twenty scratch-free marbles are taken out of the full bag. How many marbles were originally in the bag?
The original number of marbles in the bag is 30.
The given parameters are:
[tex]Red = x + 1[/tex]
[tex]Total = x^2 + 5[/tex]
The probability of red is:
[tex]P(Red) = \frac{Red}{Total}[/tex]
[tex]P(Red) = \frac{x+1}{x^2 + 5}[/tex]
When 20 marbles were removed, the marbles left are:
[tex]Marbles =Total - 20[/tex]
This gives:
[tex]Marbles =x^2 + 5 - 20[/tex]
[tex]Marbles =x^2 -15[/tex]
The probability of selecting a scratched marble at this point is:
[tex]P(Scratch) = \frac{Scratch}{Marbles}[/tex]
[tex]P(Scratch) = \frac{x -3}{x^2 - 15}[/tex]
This probability equals the probability of red.
i.e.
[tex]P(Red) = P(Scratch)[/tex]
So, we have:
[tex]\frac{x +1}{x^2 + 5} = \frac{x -3}{x^2 - 15}[/tex]
Cross multiply
[tex](x + 1)(x^2 - 15) = (x - 3)(x^2 + 5)[/tex]
Expand
[tex]x^3 - 15x + x^2 - 15 = x^3 + 5x - 3x^2 - 15[/tex]
Subtract [tex]x^3[/tex] from both sides
[tex]- 15x + x^2 - 15 = 5x - 3x^2 - 15[/tex]
Add 15 to both sides
[tex]- 15x + x^2 = 5x - 3x^2[/tex]
Collect like terms
[tex]3x^2 + x^2 - 15x - 5x = 0[/tex]
[tex]4x^2 - 20x = 0[/tex]
Divide through by 4
[tex]x^2 - 5x = 0[/tex]
Expand
[tex]x(x - 5) = 0[/tex]
Split
[tex]x = 0[/tex] or [tex]x - 5 = 0[/tex]
[tex]x = 0[/tex] or [tex]x = 5[/tex]
x can't be 0.
So: [tex]x = 5[/tex]
The number of marbles initially is:
[tex]Total = x^2 + 5[/tex]
[tex]Total = 5^2 + 5[/tex]
[tex]Total = 30[/tex]
Hence, the original number of marbles in the bag is 30.
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5. PLEASE HELP ME
Write the equation in standard form. Then factor the left side of the equation.
2x2 + 7x = 15
A. (2x – 3)(x + 5) = 0
B. (2x + 3)(x + 5) = 0
C. (2x + 5)(x – 3) = 0
D. (2x – 5)(x + 3) = 0
Answer:
7x=11
Step-by-step explanation:
do it
Consider triangle GHJ in the figure below.
please help :)
Answer:
The picture isnt really showing for me
Step-by-step explanation:
It's either me or the picture.
PLEASE HELP! I'LL GIVE BRAINLIEST:)
The center of the circle whose equation is (x + 2)² + (y - 3)² = 25 is (2, -3) (2, 3) (-2, 3)
Step-by-step explanation:
We know that if (h,k) is the center of any circle and whose radius is = r then its equation is :
[tex] {(x - h)}^{2} + {(y - k)}^{2} = {r}^{2} [/tex]
Given, the equation of circle
[tex] {(x + 2)}^{2} + (y - 3) ^{2} = 25 = {5}^{2} [/tex]
By comparing, we will get,
h = -2
k = 3
So, center of the circle is ( -2,3)
[tex]\large \green{ \: \: \: \: \boxed{\boxed{\begin{array}{cc} \bf\:Mark\\\bf\:me\:as\\\bf brainliest \end{array}}}} \\ [/tex]
Answer:
-2;3
Step-by-step explanation:
we have a formular
(x-a)^2 +(y-b)^2=c
the center of the cirlce is (a;b)
so in this case it's (-2;3)
can the area of a square be expressed as a prime number if its side length is expressed as a natural number?
not possible because the area of a square is always a square of it's length and a square cannot be a prime number
Answer:
No
Step-by-step explanation:
Because the area of a square is always a square of its length and a square can't be prime.
The sum of 2 consecutive integers 117 what are the integers
Answer:
58,59
Step-by-step explanation:
Let x be the first integer
x+1 be the next consecutive integer
x + x+1 = 117
2x+1 = 117
2x +1-1 =117-1
2x = 116
2x/2 = 116/2
x = 58
x+1 = 59
Janice's age was two-third of her elder sister's age now. If Janice's elder sister was x years old three years ago, determine Janice's age three years later in terms of x.
Answer: Her sister's age 3 years ago = x
so, her age now = x+3
so Janice's present age = 2/3 of (x+3) {as Janice's present age is two-third of her sister's age now}
Therefore, Janice's age determining the value of x is 2/3 of (x+3).
5. Find the measure of x and and the angle measure.
(3x - 15)
(2x + 7)
Answer:
here's the answer to your question
What is the midpoint of the segment shown below?
10
O A. (-1,-1)
(-11, 0)
O B. (-2, -3)
O C. (-1, -3)
- 10
10
(9,-1)
- 10
D. (-2, -1)
Answer:
(-1,-0.5)
Step-by-step explanation:
Find the solution to this problem by using the midpoint formula which is (x1+x2/2,y1+y2/2) plug in the values of y and x to get -11+9/2+0-1/2. simplify to get the solution of (-1,-0.5)
It is known that seventy percent (70%) of married couples paid for their honeymoon themselves. You randomly select 9 independent married couples and ask each if they paid for their honeymoon themselves. Let our random variable be X = the number of married couples that paid for their honeymoon themselves. What is the probability that all married coupled asked stated they paid for their honeymoon themselves? (Round your answer to four decimal places).
Answer:
0.0404 = 4.04% probability that all married coupled asked stated they paid for their honeymoon themselves.
Step-by-step explanation:
For each couple, there are only two possible outcomes. Either they paid for their honeymoon, or they did not. The probability of a couple having paid for their honeymoon is independent of any other couple, which means that the binomial probability distribution is used to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
It is known that seventy percent (70%) of married couples paid for their honeymoon themselves.
This means that [tex]p = 0.7[/tex]
You randomly select 9 independent married couples.
This means that [tex]n = 9[/tex]
What is the probability that all married coupled asked stated they paid for their honeymoon themselves?
This is P(X = 9). So
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 9) = C_{9,9}.(0.7)^{9}.(0.3)^{0} = 0.0404[/tex]
0.0404 = 4.04% probability that all married coupled asked stated they paid for their honeymoon themselves.
to use the Pythagorean theorem, we need
a. right triangle with 2 known angles and 1 side
b. right triangle with 2 known angles
c. right triangle with 1 known side and 1 known angle
d. right triangle with 2 known sides
Answer:
sfygyisfislsiyitiyjhjs hjgks6skyk
Step-by-step explanation:
jzsisfyisyistoisisoootsFind the measure of the indicated angle to the nearest degree
Plssssss help!!! On the first day of travel, a driver was going at a speed of 40 mph. The next day, he increased the speed to 60 mph. If he drove 2 more hours on the first day and traveled 20 more miles, find the total distance traveled in the two days.
The total distance traveled in two days would be 380 miles.
Let's see how we calculate the distance.
Distance is calculated by multiplying speed with time. So,D = S * TS = D ÷ TGiven that,
Speed on first day = 40 mph
Since,
Speed = Distance/Time
∵ 40 = [tex]d_{1}[/tex]/[tex]T_{1}[/tex] ...(i)
Speed on the second day = 60 mph
Distance traveled = [tex]d_{1}[/tex] - 20
Time taken = [tex]T_{1}[/tex] - 2
Since,
Speed = Distance/Time
∵ 60 = ([tex]d_{1}[/tex] - 20)/ ([tex]T_{1}[/tex] - 2) ...(ii)
As we know,
Total distance = [tex]d_{1} + d_{2}[/tex]
= [tex]d_{1}[/tex] + [tex](d_{1} - 20)[/tex]
= 2[tex]d_{1}[/tex] - 20 ...(iii)
From (i), we can deduce that,
[tex]d_{1}[/tex] = 40[tex]T_{1}[/tex]
[tex]T_{1}[/tex] = [tex]d_{1}[/tex]/40
Now, by putting the values of [tex]d_{1}[/tex] and [tex]T_{1}[/tex] in equation (ii), we get
60 = ([tex]d_{1}[/tex] - 20)/ ([tex]T_{1}[/tex] - 2)
⇒ [tex]d_{1}[/tex] - 20 = 60([tex]T_{1}[/tex] - 2)
⇒ [tex]d_{1}[/tex] - 20 = 60[tex]T_{1}[/tex] - 120
⇒ [tex]d_{1}[/tex] - 20 = 60 * (
⇒ [tex]d_{1}[/tex] = 3
⇒ [tex]d_{1}[/tex] - 3
⇒ - [tex]d_{1}[/tex]/2 = -100
∵ [tex]d_{1}[/tex] = 200
By substituting the value of [tex]d_{1}[/tex] in equation (iii),
Total distance = 2[tex]d_{1}[/tex] - 20
= 2(200) - 20
= 400 - 20
= 380 miles
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lvan earned $8 each time he walks his neighbor's dog. he already walked the dog 5 times.
How many more times does her need to walk the dog to earn enough money to buy a game that costs $88
__? more times
what is value of y and x if 3x+2y=2 and 2x+3y=4
We need to form a system of equations:
3x + 2y = 2
2x + 3y = 4
Now, we can multiply the first equation by 2, and the second equation by 3, to even out the coefficients by the variables (to make them the same thing).
6x + 4y = 4
6x + 9y = 12
Next, we can subtract the second equation from the first. We get:
0x - 5y = -8
Then this becomes:
-5y = -8
÷-1 ÷-1
5y = 8
÷5 ÷5
y = 1.6
Substitute 1.6 for y in one of the equations:
2x + 3(1.6) = 4
2x + 4.6 = 4
2x = -0.6
÷2 ÷2
x = -0.3
Answer: [tex]\Large \boldsymbol{(-0,4 \ \ ; \ \ 1,6)}[/tex]
Step-by-step explanation:
[tex]\displaystyle \Large \boldsymbol{} - \left \{ {{3x+2y=2} \ \ |\times3\atop {2x+3y=4}\ \ |\times2} \right. => \\\\\\\ 9x-4x+6y\!\!\!\!\!\!\diagup-6y\!\!\!\!\!\!\diagup=6-8 \\\\5x=-2 \\\\x=-0,4 \ \ ; \ \ y=(2+1,2):2 =1,6[/tex]
Solve: 3w + 2 = 20 Write a real world problem that this equation represents.
Step-by-step explanation:
3w + 2 = 20
-2 -2
------------------
3w = 18
---- ----
3 3
w = 6
You and your 2 friends have 20 fruits in total and your friend's mother gave you and your friends two more.
Hope this helped.
Equation – 3w + 2 = 20
Solution :3w + 2 = 20Transpose 2 to the right hand side of the given equation
3w = 20 - 2Now, simplify the right hand side
3w = 18Cross multiply
w = 18/3 w = 6Hence, the solution of the equation is 6
Find the perimeter of the following figure.
Answer:
10 meters
Step-by-step explanation:
Perimeter= 3+3+2+2
=10
Have a nice day:)
If you can show the work please its due in 1 hour 15 points and marking brainliest.
Answer:
[tex]a) \: \: 7x[/tex]
[tex]b) \: \: 12 {x}^{2} - 5x[/tex]
[tex]c) \: \: - 3x + 4[/tex]
Step-by-step explanation:
[tex]a) \: \: 4x+7x−3x−x \\ 11x−3x−x \\ 8x−x \\ 7x[/tex]
[tex]b) \: \: 7 {x}^{2} −6x+5 {x}^{2} +x \\ 12 {x}^{2} −6x+x \\ 12 {x}^{2} - 5x[/tex]
[tex]c) \: \: 9−4x−5+x \\ −4x+4+x \\ −3x+4[/tex]
Hope it is helpful....If MN = 5, NO = 13, then LM = (Blank 1). (Round your answer to one decimal place, as necessary.)
Answer:
8.1 = LM
Step-by-step explanation:
(whole secant) x (external part) = (tangent)^2
13 * 5 = LM^2
65 = LM^2
sqrt(65) = LM
8.06225 = LM
To one decimal place
8.1 = LM
What is the domain of the function graphed below?
Answer:
(-2,4] and [7,α)
Step-by-step explanation:
the domain is open at -2 but closed at 4 and also closed at 7 but open till infinity..
The domain of the given function is (-2,4] U [7, ∞), which is the correct option (B).
What is a piecewise function?A piecewise-defined function (also known as a piecewise function or a hybrid function) is a function defined by multiple sub-functions, each of which applies to a different interval of the main function's domain (a sub-domain).
The graph is given in the question, as shown
f(x) = x²+1 if (-2,0]
This the sub-function define between the interval (-2,0].
f(x) = -1 if (0, 4]
This the sub-function define between the interval (0, 4].
f(x) = -(x-7)² if [7, ∞)
This the sub-function define between the interval [7, ∞).
Thus, the domain of the given function is (-2,4] U [7, ∞).
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Help with this question
Step-by-step explanation:
Hey there!
Given;
-6(2x-9) + (7-6x) = 0
Simplify it.
-12x + 54 + 7 - 6x = 0
-18x +61 = 0
Therefore, answer is option B.
Hope it helps!
The domain for f(x) and g(x) is the set of all real numbers.
Let f(x) = x2 + 1 and g(x) = 3x.
Find f − g.
A.
x2 + 3x + 1
B.
x2 + 3x
C.
3x3 + 3x + 1
D.
x2 − 3x + 1
Answer:
D
Step-by-step explanation:
(f-g)(x) = x^2+1-3x= x^2-3x+1
Which number is rational?
A. -3 1/2
B. sqrt 5
C. Pi
D. 9.23157 ...
Answer:D
Step-by-step explanation:
At a summer camp the campers can choose one of three programmes: camp craft, water sports or hiking. During the first week of camp the campers chose the programmes in the ratio 7:5:8. During the second week of camp the same number of campers chose the programmes in the ratio 7:6:4. Did more campers choose the camp craft programme in the first or second week? How many more?
Answer: Second week
Step-by-step explanation:
Given
In first week, campers choose programmes in the ratio of [tex]7:5:8[/tex]
In second week, this ratio becomes [tex]7:6:4[/tex]
Suppose 100 campers Joined the camp
Number of hikers who choose camp craft in first week are
[tex]\Rightarrow \dfrac{7}{7+5+8}\times 100=\dfrac{7}{20}\times 100\\\\\Rightarrow 35[/tex]
Number of hikers who choose camp craft in second week are
[tex]\Rightarrow \dfrac{7}{7+6+4}\times 100=\dfrac{7}{17}\times 100\\\\\Rightarrow 41.17\approx 41[/tex]
Therefore, in second week more campers take part in camp craft.
If 100 campers take part then, 6 more campers takes part in camp craft.
quadratics formula 4x^2+3x-1=0
Answer: X = 1/4 or X = -1
Step-by-step explanation:
4x2+3x−1=0
(4x−1)(x+1)=0
4x−1=0 or x+1=0
4x=1 or x=-1
Now divide 4 from both sides
like this 4x/4=1/4
now cancel out two 4's so the answer will be x=1/4
2. Given the function f : x -> |x+8|, find the possible values of x when the image is 3.
Answer:
f (x)=11
Step-by-step explanation:
f (x)= x + 8
f (3)= (3 +8)
=f(x) =11
**replace the x with a variable which is 3
The height of a right cylinder is 3 times the radius of the base. The volume of the cylinder is 247 cubic units.
What is the height of the cylinder?
O 2 units
O 4 units
O 6 units
O 8 units
The height of the cylinder is 6 units.
What is cylinder?A cylinder has traditionally been a three-dimensional solid, one of the most basic of curvilinear geometric shapes. In elementary geometry, it is considered a prism with a circle as its base.
Given that, the height of a right cylinder is 3 times the radius of the base. The volume of the cylinder is 24π cubic units.
Volume = π × radius² × height
Let the height of 3x then the radius will be x,
24π = π × x² × 3x
24 = 3x³
x = ∛8
x = 2
Therefore, height = 6
Hence, the height of the cylinder is 6 units.
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Find the value of x in the figure.
X= _
Answer:
x=35
Step-by-step explanation:
For a polygon with n sides, the sum of its interior angles is equal to
(n-2) * 180
Here, there are 6 sides, so the sum of this polygon's interior angles is equal to (6-2)* 180 = 720
Therefore, the sum of the interior angles is 720. We can add them up to get
(4x-5) + 117 + (3x-3) + (3x+6) + 118 + 4x-3
= 14x +230 = 720
subtract 230 from both sides to isolate the x and its coefficint
14x = 490
divide both sides by 14 to get x
x=35
pls help i need to finish this !!
Answer:
a
Step-by-step explanation:
it's non-linear
Step-by-step explanation:
the functions linear because as x increases by 4, y is increasing by 12 at a constant rate
A translation is shown on the grid below in which triangle A is the pre-image and triangle B is the image.
x+0
x+6
x-6
x+4
Answer: x+6
Step-by-step explanation:
