[tex]\huge\tt\pink{Answer}[/tex]
A≈852.83cm²
Radius
7cm
Height
31cm
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.
Read more about probabilities at:
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The scale on a map of Virginia shows that 1 centimeter represents 30 miles. The actual distance from Richmond, VA to Washington, DC is 110 miles. On the map, how many centimeters are between the two cities? Plz someone answer
Answer:
3.667
Step-by-step explanation:
30 miles per cm means divide distance by 30 or
110/30 = 3.667
The temperature falls from 0 degrees to - 123 degrees in 3 hours. Which expression finds the change in
temperature per hour? ?
7 49
024
-
7 49
0 -24
49 7
0 -1
0
49 7
4 -
Answer:
D
Step-by-step explanation:
Change=Temperature/Time
Change=(-49/4)/(7/2)
I neeeddddd helppppp it’s urgenttttttt!!!!!!!!
Answer:
x=7
Step-by-step explanation:
The sum of the arc of a circle is 360 degrees
85+5x+5+10x+5+-7+6x+6+17x = 360
Combine like terms
38x+94=360
Subtract 94 from each side
38x+94-94 = 360-94
38x = 266
Divide each side by 38
38x/28 = 266/38
x = 7
if n(p(a)) = 256. find n(a)
n(p(a)) = 256
256 = 2^8
n(a) = 8
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I’m giving out brainlist!!!
Answer:
$0.60
Step-by-step explanation:
Find the unit rate.
[tex]\frac{Dollars}{Cookies}=\frac{9}{15}[/tex] ÷ [tex]\frac{15}{15}=\frac{0.6}{1}[/tex]
Therefore, the cost for one cookie is $0.60.
Answer:
$0.60
You need to find the unit rate. Unit rate is a ratio of 1 to another number, written like 1 : ?.
If a box of 15 cookies costs $9, and you want to find the price of one cookie, then you will need to use unit rate.
Start with the ratio of cookies to dollars.
15:9
Now, you need to find out the cost of one cookie. To do this, you will need to divide 9 by 15 (9/15) because you're trying to split 9 into 15 cookies.
9÷15= .6But, you can't have .6 dollars, so the answer will be $0.60, or 60 cents.
Brainliest is very much appreciated! I work very hard to write lengthy answers.find the value of x give reasons to justify your solutions b ∈ ac, d ∈
help asap please!! will award brainliest
Answer:
x = 27°
Step-by-step explanation:
180° - 72° = 108°
108° / 4 = 27°
72° + (27° * 4) = 180°
Hope it helps!
The graph represents the system of inequalities shown below. Determine whether the statement that follows the graph is true or false.
Answer:
false
Step-by-step explanation:
there is no graph...
solve for x. Round to the nearesr tenth of a degree if necessary.
Answer:
im not sure but i got 30.1
Step-by-step explanation:
[tex] \cos(x) = \frac{45}{52} \\ x = 30.1[/tex]
Write an equation in point-slope form for the line through the given point with the given slope.
3
(4, -6); m =
Answer:
y+6 = 3(x-4)
Step-by-step explanation:
Point slope form is
y-y1 = m(x-x1) where m is the slope and (x1,y1) is a point on the line
y - -6= 3(x - 4)
y+6 = 3(x-4)
Round the number 553 to the tens place.
is it 550? because 3 is less than 5 so I replace it with a 0
Answer:
550
Step-by-step explanation:
To round 553 to the tens place, we would need to identify the value of the digit in the ones place.
If the digit in the ones place is greater than 5, we increase the tens place by 1 & convert the ones place into a 0.
If not, we leave the tens place as is & convert the ones place into a 0.
Since 3 is less than 5, we round 553 to 550 so you are correct.
Answer:
Yes
550 has 2 sig figs
553 has 3
Step-by-step explanation:
plsssssssssssssss help meeee
Answer:
64 vs. 4 so 60 extra people
Step-by-step explanation:
Answer:
I think 60 more people
Step-by-step explanation:
You just plug in p for period 4 and period 2 then solve for N. Then it's asking for how many more in pd 4 then 2 which is 60, I think..
Someone exchanged a dollar bill for change and received 7 coins, none of which were half-dollars. How many of these coins were dimes? a. 0 b. 1 c. 4 d. 5 e. Cannot be determined from the information given
There is only 1 dime because there are 3 quarters, 3nickels, and 1 dime which makes 7 coins
A ladder is resting against a wall. The top of the ladder touches the wall at a height of 6
feet. Find the length of the ladder if the length is 2 feet more than its distance from the
wall.
Answer:
10 feet
Step-by-step explanation:
let the ladder be x feet in length
Using the Pythagoras theorem,
6^2+(x-2)^2=x^2
if you solve this you'll get, x = 10
Answered by GAUTHMATH
Find the equation of the axis of symmetry and the coordinates of the vertex of the graph of y = 2x2 – 12x + 6.
Step-by-step explanation:
The real part (red) and imaginary part (blue) of the Riemann zeta function along the critical line Re(s) = 1/2. The first non-trivial zeros can be seen at Im(s) = ±14.135, ±21.022 and ±25.011. The Riemann hypothesis, a famous conjecture, says that all non-trivial zeros of the zeta function lie along the critical line.
s
SO, LAST IS CORRECT
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5[tex]5^{56} x 5^{22} x 5^{-96}[/tex]
Answer:
[tex] \frac{ {11}^{56} }{ {5}^{18} } [/tex]
Step-by-step explanation:
[tex] {55}^{56} \times {5}^{22} \times {5}^{ - 96} [/tex]
[tex] = {55}^{56} \times {5}^{ - 74} [/tex]
[tex] = {11}^{56} \times {5}^{56} \times \frac{1}{ {5}^{74} } [/tex]
[tex] = {11}^{56} \times \frac{1}{ {5}^{18} } [/tex]
[tex] = \frac{ {11}^{56} }{ {5}^{18} } [/tex]
Expand and simply
(5x + 4)²
Answer:
25x^2 +40x+16
Step-by-step explanation:
(5x + 4)²
(5x+4)(5x+4)
FOIL
first 5x*5x = 25x^2
outer 5x*4 = 20x
inner 4*5x = 20x
last = 4*4 = 16
Add them together
25x^2 +20x+20x+16
Combine like terms
25x^2 +40x+16
Answer:
[tex] {(5x + 4)}^{2} \\ = {(5x)}^{2} + 2 \times 4 \times 5x + {4}^{2} \\ = 25 {x}^{2} + 40x + 16 \\ thank \: you[/tex]
The equation a[tex]x^{2}[/tex]+b[tex]x[/tex]+c=0 has roots α, β. Express (α+1)(β+1) in terms of a, b and c.
Answer:
[tex]\displaystyle \left(\alpha+1\right)\left(\beta + 1\right) = \frac{a+c-b}{a}\:\: \left(\text{ or } 1+\frac{c-b}{a}\right)[/tex]
Step-by-step explanation:
We are given the equation:
[tex]ax^2+bx+c=0[/tex]
Which has roots α and β.
And we want to express (α + 1)(β + 1) in terms of a, b, and c.
From the quadratic formula, we know that the two solutions to our equation are:
[tex]\displaystyle x_1 = \frac{-b+\sqrt{b^2-4ac}}{2a}\text{ and } x_2=\frac{-b-\sqrt{b^2-4ac}}{2a}[/tex]
Let x₁ = α and x₂ = β. Substitute:
[tex]\displaystyle \left(\frac{-b+\sqrt{b^2-4ac}}{2a} + 1\right) \left(\frac{-b-\sqrt{b^2-4ac}}{2a}+1\right)[/tex]
Combine fractions:
[tex]\displaystyle =\left(\frac{-b+2a+\sqrt{b^2-4ac}}{2a} \right) \left(\frac{-b+2a-\sqrt{b^2-4ac}}{2a}\right)[/tex]
Rewrite:
[tex]\displaystyle = \frac{\left(-b+2a+\sqrt{b^2-4ac}\right)\left(-b+2a-\sqrt{b^2-4ac}\right)}{(2a)(2a)}[/tex]
Multiply and group:
[tex]\displaystyle = \frac{((-b+2a)+\sqrt{b^2-4ac})((-b+2a)-\sqrt{b^2-4ac})}{4a^2}[/tex]
Difference of two squares:
[tex]\displaystyle = \frac{\overbrace{(-b+2a)^2 - (\sqrt{b^2-4ac})^2}^{(x+y)(x-y)=x^2-y^2}}{4a^2}[/tex]
Expand and simplify:
[tex]\displaystyle = \frac{(b^2-4ab+4a^2)-(b^2-4ac)}{4a^2}[/tex]
Distribute:
[tex]\displaystyle = \frac{(b^2-4ab+4a^2)+(-b^2+4ac)}{4a^2}[/tex]
Cancel like terms:
[tex]\displaystyle = \frac{4a^2+4ac-4ab}{4a^2}[/tex]
Factor:
[tex]\displaystyle =\frac{4a(a+c-b)}{4a(a)}[/tex]
Cancel. Hence:
[tex]\displaystyle = \frac{a+c-b}{a}\:\: \left(\text{ or } 1+\frac{c-b}{a}\right)[/tex]
Therefore:
[tex]\displaystyle \left(\alpha+1\right)\left(\beta + 1\right) = \frac{a+c-b}{a}[/tex]
In an arithmetic sequence, the first term is 5 and the third term is -5. What is the 20th term?
Answer:
-115
Step-by-step explanation:
Thus with the sequence /question numbers are reducing by 5 .
Which value for the constant d makes x = -2 an extraneous solution in the following equation?
[tex]\sqrt{6-15x} =5x+d[/tex]
Answer:
Solution given:
[tex]\sqrt{6-15x} =5x+d[/tex]......(1)
d=?
and
x=-2
Substituting value of x in equation 1.
[tex]\sqrt{6-15*-2} =5*-2+d[/tex].
Solve the like terms
[tex]\sqrt{6+30} =-10+d[/tex].
solve the like terms
[tex]\sqrt{36} =-10+d[/tex].
we have square root of 36 is 6.
6=-10+d
d=16
the value of constant term is 16.
The value of d for the expression [tex]\sqrt{6-15x} = 5x+d[/tex] is 16.
What is an expression?Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication and division.
The value of 'd' is calculated as,
[tex]\sqrt{6-15x} = 5x+d[/tex]
Put the value of x =-2,
[tex]\sqrt{6-(15\times -2)}=(5\times -2)+d[/tex]
√36 = -10 + d
6 = -10 + d
d = 16
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Someone plz help me I’m stuck with this one T^T
Answer:
SID WILL FINISH FIRST
Step-by-step explanation:
[tex]\frac{2}{3}[/tex] ÷ [tex]\frac{1}{6} =[/tex]
[tex]\frac{2}{3}[/tex] * [tex]\frac{6}{1} =[/tex] = 12/3 = 4
~~~~~~~~~~~~~~~~~~~
[tex]\frac{1}{3}[/tex] ÷ [tex]\frac{1}{9} =[/tex]
[tex]\frac{1}{3}[/tex] * [tex]\frac{9}{1} =[/tex] = 9/3 = 3
Your monthly finance charge is based on your interest rate and your balance, the higher your interest rate, the higher your finance charge will be.
True
False
Answer:
True
Step-by-step explanation:
If you don't pay by the deadline, interest rate will contribute to your finance charge.
please answer this!!
Answer:
b
Step-by-step explanation:
tan equal to (opposite side) /(adjacent side)
am not able to write root 3 on phone but its something like this
(a¤3)/a
in which¤3 is root 3
PLEASE HELP ME!. I will give thanks, 5 star rating, and brainly to the most helpful answer, and I will report unrelated answers, so don't try me.
Three vertices of a parallelogram are (0,1), (2,0), and (2,5). Label all the possible location(s) of a fourth vertex.
Answer:
(0, 6), (4, 4), and (0, -4)
Step-by-step explanation:
basically you pick 2 sides (each with endpoints at two of the three verticies) to be the adjacent sides, and then you can easily find the fourth vertex for each case.
the study of the organization and collection of data is know as?
Answer:
investigation isanswer
URGENT HELP I REALY NEED AN EXPERT HERE
Hi
P and Q only intersect for 2 as 2 is common for P and Q . So P U Q = 2
For the diagram :
One big circle name U with 1 on the
Far corner left and 9 on the far right corner.
Then on the left, a circle within circle U with the number Of P
Same with Q on the right.
But P and Q must intersect on number 2 as 2 is in both circles.
ps : nothing oblidge you to set the number on mathematical order. Of it'esasier to do the circles, do it whatever you like as long as you respect what is said.
Chọn bốn ví dụ sau Ví dụ nào không phải là phân số
A.3/-5 B.1,7/3 C.0/2 D.-13/-4
Answer:
a
Step-by-step explanation:
vì số âm không nằm ở dưới
What do the sides in a triangle add up to? I know that the inner angles of a triangle add up to 180°, but what do the sides of a triangle add up to?
Answer:
The most basic fact about triangles is that all the angles add up to a total of 180 degrees. The angle between the sides can be anything from greater than 0 to less than 180 degrees. The angles can't be 0 or 180 degrees, because the triangles would become straight lines.
Step-by-step explanation:
basic only
There are 6 wooden cubes, each of side 5 centimeters there total mass is 525 grams find the mass per cube. b)find the mass per cubic centimeter of a cube.
Answer:
(a) 87.5 g
(b) 0.7 g per cubic cm
Step-by-step explanation:
side of each cube, s = 5 cm
total mass, M = 525 g
(a) mass of each cube, m = M/6 = 525/6 = 87.5 g
(b) Volume of each cube = s x s s = 5 x 5 x 5 = 125 cubic cm
mass per cubic cm = 87.5/125 =0.7 g per cubic cm
SOMEBOBY HELP ME OUT !!!
Answer:
Dilation of 1/2 means we have to multiply the number by 1/2
V' (-2,1)
U' (1,3)
E' (0,1)
Hope it helps :)
