Answer: 6 or -6
hello,
Step-by-step explanation:
Let say n the number
[tex]\dfrac{2}{3} *n^2-7=17\\\Longrightarrow\ \dfrac{2}{3} *n^2=24\\\Longrightarrow\ n^2=\dfrac{3*24}{2}\\\Longrightarrow\ n^2=36\\\Longrightarrow\ (n-6)(n+6)=0\\\\n=6\ or\ n=-6\\[/tex]
A sphere with surface area of 154cm² is fit exactly in cubical box, Use π 22/7
what is the volume of the box A.147
B.154
C.216
D.343
Answer:
Answer :-Surface area of sphere = 4 π r²
154 = 4 × 22/7 × r²
154 = 88/7 × r²
154 × 7/88 = r²
12.25 = r²
3.5 = r
Now
Volume of sphere = 4/3 × π r³
Volume = 4/3 × 22/7 × (3.5)³
Volume = 88/21 × 42.875
Volume = 154 cm³
Volume of sphere = Volume of cube
Volume of cube = 154 cm³
If a fair coin is tossed 6 times, what is the probability, rounded to the nearest thousandth, of getting at most 2 heads?
Answer:
[tex] \displaystyle 0.344[/tex]
Step-by-step explanation:
we are given that a coin is tossed 6 times and we want to find the probability of getting at most 2 heads.
To solve this problem,we can consider binomial distribution, which is given by
[tex] \displaystyle P(X = r) = \binom{n}{r} {p}^{r} {q}^{n - r} [/tex]
where:
P = binomial probabilityr = number of times for a specific outcome within n trials[tex]{n \choose r}[/tex] = number of combinationsp = probability of success on a single trialq = probability of failure on a single trialn = number of trialswe want to figure out the probability of getting at most 2 heads out of 6 trials , The probability can therefore be found by adding up all the binomial distributions including X=2 and less than it, Thus
[tex] \displaystyle P(X \leq 2) = P(X=0)+P(X=1)+P(X=2) [/tex]
[tex] \displaystyle P(X \leq 2) = \binom{6}{0} {p}^{0} {q}^{6 - 0} + \binom{6}{1} {p}^{1} {q}^{6- 1} + \binom{6}{2} {p}^{2} {q}^{6 - 2} [/tex]
when a coin is tossed, the probability of getting both head (success) and tail (failure) are ½ which is why ,the variables, p and q are assigned to ½. therefore substitute
[tex] \rm\displaystyle P(X \leq 2) = \binom{6}{0} { \left( \frac{1}{2} \right) }^{0} { \bigg( \frac{1}{2} \bigg) }^{ 6- 0} + \binom{6}{1} { \bigg( \frac{1}{2} \bigg) }^{1} { \bigg( \frac{1}{2} \bigg) }^{6 - 1} + \binom{6}{2} { \bigg( \frac{1}{2} \bigg)}^{2} { \bigg( \frac{1}{2} \bigg) }^{6- 2} [/tex]
since p and q are the same. it won't make any difference to write all the product of p and q as (½)⁶:
[tex]\rm\displaystyle P(X \leq 2) = \binom{6}{0} { \bigg( \frac{1}{2} \bigg) }^{ 6} + \binom{6}{1} { \bigg( \frac{1}{2} \bigg) }^{6} + \binom{6}{2} { \bigg( \frac{1}{2} \bigg) }^{6}[/tex]
In the expression the term (½)⁶ is common thus factor it out:
[tex]\rm\displaystyle P(X \leq 2) = { \bigg(\frac{1}{2}\bigg) }^{ 6} \left( \binom{6}{0} + \binom{6}{1} + \binom{6}{2} \right) [/tex]
calculate the combinations:
[tex]\rm\displaystyle P(X \leq 2) = { \bigg(\frac{1}{2}\bigg) }^{ 6} \left(1+6+15\right) [/tex]
simplify addition:
[tex]\rm\displaystyle P(X \leq 2) = { \bigg(\frac{1}{2}\bigg) }^{ 6} \left(22\right) [/tex]
simplify exponent:
[tex]\rm\displaystyle P(X \leq 2) = { \bigg(\frac{1}{64}\bigg) } \left(22\right) [/tex]
simplify multiplication:
[tex]\rm\displaystyle P(X \leq 2) = \frac{22}{64} [/tex]
dividing yields:
[tex]\rm\displaystyle P(X \leq 2) = 0.34375 [/tex]
[tex]\rm\displaystyle P(X \leq 2) \approx 0.344 [/tex]
In conclusion
The answer is 0.344
What is the slope of the graph shown below?
A. 1/2
B. -2
C. 2
D. 1
What is (f - g)(x)? f(x) = 3x g(x) = -3x² + 3x Write your answer as a polynomial or a rational function in simplest form.
Answer:
3x²
Step-by-step explanation:
(f - g)(x)
= f(x) - g(x)
= 3x - (- 3x² + 3x) ← distribute parenthesis by - 1
= 3x + 3x² - 3x ← collect like terms
= 3x²
algebra 2 help please????
Answer:
Sqrt(-108)=6i*sqrt(3)
Step-by-step explanation:
-108=3*6*6*(-1). Sqrt(-108)=6i*sqrt(3) where i is iota
Solve - 3 [ ( x + 2 ) ( x - 1 ) - x ^ { 2 } + 1 ] + 3 ( x - 1 ) (and could you please explain it to me?? I really don't get it. Thanks!)
Answer:
Step-by-step explanation:
[tex](x+2)(x-1)= x^2+2x-x-2= x^2 +x -2\\\\( x + 2 ) ( x - 1 ) - x ^ { 2 } + 1 =x^2+x-2-x^2+1=x-1\\\\- 3 [ ( x + 2 ) ( x - 1 ) - x ^ { 2 } + 1 ] =-3(x-1)=-3x+3\\\\- 3 [ ( x + 2 ) ( x - 1 ) - x ^ { 2 } + 1 ] + 3 ( x - 1 ) =-3x+3+3x-3=6x\\[/tex]
another easy question pls answer
Answer:
22.5 degrees and 67.5 degrees
Step-by-step explanation:
complementary angles add up to 90°
x + 3x = 90°
4x = 90
90/4 = x
x = 22.5
The first angle is 22.5
The second angle is 3 times as much
22.5 x 3 = 67.5
If my answer is incorrect, pls correct me!
If you like my answer and explanation, mark me as brainliest!
-Chetan K
15=a/3-2
please help !!
Here is your answer. Hope this helps you.
Answer:
51
Step-by-step explanation:
15= a/3 -2
17= a/3
51=a
What is (f + g)(x)? f(x) = -3x² + 6x g(x) = -X Write your answer as a polynomial or a rational in simplest form
Answer:
- 3x² + 5x
Step-by-step explanation:
(f + g)(x)
= f(x) + g(x)
= - 3x² + 6x - x ← collect like terms
= - 3x² + 5x
PLZ HELP QUICKLY!!!!!!!!!!!!
No LINKS PLEASE!!!!!!!!!
Answer:
Uhh i dont rly know sry
Step-by-step explanation:
sq root 30
A whole number, natural number, integer
B rational
C irrational
D whole number, integer, rational
Answer:
good luck
Step-by-step explanation:
Answer:
C
Step-by-step explanation:
this is the answer
it is irrational because it cannot be expressed in a ratio of two integers
please give me brainliest .
Need awnsers please
Answer:
1_ 129 , 51
2_ b
3_ 40
Step-by-step explanation:
1_ we can represent the bigger angle with x and smaller one with y
and as given, y is smaller than x by 78
so y = x - 78 (1)
as x + y = 180
we put y as we did in (1)
x + x - 78 = 180
so 2x = 258
so x = 129
and y will be 51
2_ from the figure we find the two angles form one angle = 90 degree
3_ from the defenition of complementary angles
m(c) + m(d) = 90
7r + 5 + 8r + 10 = 90
15r + 15 = 90
r = 5
so m(c) will be equal 7*5 + 5 = 40
Which is the graph of the equation y- 1= 5(x-3)?
Answer:
linked below
Step-by-step explanation:
If you use desmos, it show this which is the correct graph :)
A point is plotted on the number line at 225 . A second point is plotted at −434 .
What is the length of a line segment joining these points?
Enter your answer as a simplified mixed number in the box.
ANSWER:_____ units?
Answer:
659 units
Step-by-step explanation:
The length of the segment is the distance between the points.
The distance between two points on the number line is the absolute value of the difference between their coordinates. It does not matter in which order you subtract the numbers.
One point has coordinate 225.
Another point has coordinate -434.
Subtract one coordinate from the other and take the absolute value of the difference.
distance = |-434 - 225| = |-659| = 659
Answer: 659 units
Length of given line segment is 659 units
Step-by-step explanation:
Given:
First point plotted on number line = 225
Second point plotted on number line = - 434
Find:
Length of line segment
Computation:
Length of line segment = Distance between two point
(Distance between two point will be added as absolute value)
So,
Length of line segment = |-434| + |225|
Length of line segment = 434 + 225
Length of line segment = 659 units
Learn more:
https://brainly.com/question/23782800?referrer=searchResults
s= zh - 2zt^3 solve for z
Hi ;-)
[tex]s=zh-2zt^3\\\\z(h-2t^3)=s \ \ /:(h-2t^3)\\\\z=\dfrac{s}{h-2t^3}[/tex]
Answer:
z = [tex]\frac{s}{h-2t^3}[/tex]
Step-by-step explanation:
Given
s = zh - 2zt³ ← factor out z from each term
s = z(h - 2t³ ) ← divide both sides by h - 2t³
[tex]\frac{s}{h-2t^3}[/tex] = z
Alex had $29 in a bank account. He withdrew $13 for pizza and then $18 for a movie. How much money does Alex have left in his account?
Answer:
-12
Step-by-step explanation:
18 plus 13 is 41 29 subtracted from 41 is -12
Answer:
- $2
Step-by-step explanation:
Alex withdrew money twice, or he subtracted those amounts from the total that he had.
In this case, he withdrew $13 first, and then $18, or:
13 + 18 = 31
$31 dollars in all.
Alex had $29. Subtract the total that he withdrew from the amount he had:
29 - 31 = -2
Alex has - $2, or he owes the bank $2 with interest.
~
The length of each side of an equilateral triangle having an area of 9√3 cm² is
Answer:
6 cm
Step-by-step explanation:
Let each side of the equilateral triangle be a.
Given, area of an equilateral triangle = 9√3 cm2
Area of an equilateral triangle = (√3)/4 × (Side)²
=> (√3)/4 × a² = 9√3
[tex] {a}^{2} = \frac{9 \sqrt{3} }{ \frac{ \sqrt{3} }{4} } = \frac{9 \sqrt{3} }{ \sqrt{3} } \times 4 = 9 \times 4[/tex]
=> a² = 36
[tex] \sqrt{ {a}^{2} } = \sqrt{36} \\ a = (+ - )6[/tex]
∴ Side = 6 cm [taking positive square root because side is always positive]
simplify:
3/2 x 5/3 ÷ (-2+7)
Answer:
-1/2
Step-by-step explanation:
3/2 x 5/3 ÷ (-2+7)
=> 3/2 x 5/3 ÷ (-5)
=> 3/2 x 5/3 x (-1/5)
=> -1/2
Given: F(x) = 2x - 1; G(x) = 3x + 2; H(x) = x 2
Find F[G(x)] - F(x).
4x + 4
4x
4x + 2
Step-by-step explanation:
F[G(x)]=2(3x+2)-1= 6x+4-1= 6x +3
F[x]=2x-1
F[G(x)] - F(x)=6x+3-(2x-1)=6x+3-2x-1
=4x+2
answer=4x+2
Answer: A
Step-by-step explanation:
[tex]F(x)=2x-1\\G(x)=3x+2\\\\F(G(x))-F(x)=F(3x+2)-(2x-1)\\\\=2*(3x+2)-1-2x+1\\\\=6x+4-2x\\\\=4x+4\\\\\\Answer\ A[/tex]
the distance between the points (-1,3) and (2,-1) is?
Answer:
It is 5.83 units
Step-by-step explanation:
[tex]{ \bf{length = \sqrt{ {(x_{1} - x _{2} ) }^{2} + {(y _{1} - y_{2})}^{2} } }}[/tex]
x1 is -1
x2 is 2
y1 is 3
y2 is -1
[tex] = \sqrt{ {( - 1 - 2)}^{2} + { \{3 - ( - 2) \}}^{2} } \\ \\ = \sqrt{9 + 25} \\ = \sqrt{34} [/tex]
please help!!! the question is in the picture above— this is geometry
Use the co‐interior rule, corresponding angle rule, alternate angle rule and vertical opposite angle rule to solve the question above.
angle G5 = angle K1 reason : corresponding angles
angle J1 = angle H3 reason: vertical opposite angles
angle J2 = angle K4 reason: vertical opposite angles
angle G5 = angle K4 reason: co‐ interior angles
angle F6 = angle K4 reason: alternate angle
Answer this question and turn it in HERE or on paper in the TURN-IN BOX by Friday for +2 Practice points. 0, 1, 1, 2, 3, 5, 8,... What are the next three numbers? Explain!
Answer:
13, 24, and 34
Step-by-step explanation:
0, 1, 1, 2, 3, 5, 8, 13, 24, 34, . . .
0+ 1 = 1
1+ 1 = 2
2+ 1 = 3
3+ 2 = 5
5+ 3 = 8
8+ 5 = 13
13+ 8 = 24
24+ 13 = 34
start at 1, then add the number behind it to move forward one space. repeat process.
what is the answer to 90π + 2π(7.5)2
Answer:
635.75
Step-by-step explanation:
90π + 2π(7.5)²
~Simplify
90π + 2π(56.25)
~Multiply
282.5 + 2(176.625)
~Simplify
282.5 + 353.25
635.75
All this was simplified using PEMDAS.
Best of Luck!
..... + ..... x ..... = 1452
Answer:
452 + 100 × 10 = 1452
Step-by-step explanation:
There are many possible solutions. This is one of them.
Bacteria of species A and species B are kept in a single environment, where they are fed two nutrients. Each day the environment is supplied with 19,660 units of the first nutrient and 31,890 units of the second nutrient. Each bacterium of species A requires 4 units of the first nutrient and 5 units of the second, and each bacterium of species B requires 1 unit of the first nutrient and 6 units of the second. What populations of each species can coexist in the environment so that all the nutrients are consumed each day?
Answer:
4570 species of the type A and 1540 species of the type B.
Step-by-step explanation:
A:
1st: 4 units
2nd: 5 units
B:
1st: 1 unit
2nd: 6 units
A=x, B=y
4x + 1y = 19820 units of the first nutrient
5x + 6y = 32090 units of the second nutrient
5x + 6*(19820-4x) = 32090.
32090 - 6(19820-4x)
x= ------------------------------------- = 4570
5-24
y = 19820 - 4*4570 = 19820 - 18280 = 1540.
ANSWER: 4570 species of the type A and 1540 species of the type B.
Hopes this solves it.
The populations of each species can coexist in the environment so that all the nutrients are consumed each day are 4530 and 10600
What are simultaneous equation?In mathematics, a set of simultaneous equations, also known as a system of equations or an equation system, is a finite set of equations for which common solutions are sought.
Given;
Each day the environment is supplied with 19,660 units of the first nutrient and 31,890 units of the second nutrient
2 Nutrient Requirements of both species of Bacteria A and B , Total Nutrients available
Now,
Let the number of bacteria of Specie A and Specie B be x and y respectively;
To find : Number of Bacteria 1 and Bacteria 2
Nutrient 1 Constraint Equation : 4x + y = 19660
Nutrient 2 Constraint Equation : 5x + 6y = 31890
Putting the value of y from 1st equation in 2nd equation;
5x + 6 (19660 - 4x) = 31890
5x + 117960 - 24x = 31890
117960 - 31890 = 19x
19x = 86070
x = 86070 / 19 = 4530 { Bacteria A}
Putting the value of x in 1st equation;
2 (4530) + y = 19660
9060 + y = 19660
y = 19660 - 9060= 10600{Bacteria B}
Therefore, the solution of equations will be 4530 and 10600
To learn more about simultaneous equations :
brainly.com/question/16763389
#SPJ2
log(12), round to the nearest thousandths?
Answer:
1.079.
Step-by-step explanation:
Use ur calculator.
Simplify the expression
by combining like terms.
3y2+2y-y2+y
Answer:
= 3y2-y2+2y+y
= 2y+3y
= 5y
PLEASE HELP YOU WILL GET A BRAINLY AND A LOT OF POINTS
Four coins are tossed. What is the probability of at least one tail?
Step-by-step explanation:
I can't understand it so plz don't mind or else I will mind
Answer:
93.75%
This type of problem you have to REVERSE the question...
"at least one tail" is all possibilities EXCEPT "all heads"...
so your answer is 100% - P(4 heads)
P(4 heads) = (1/2)^4 = .0625
1 - .0625 = .9375
Step-by-step explanation:
Help solve pls fast
it's a maths question
Answer:
Step-by-step explanation:
[tex][(\sqrt[4]{x^{\dfrac{3}{4}}})^{\dfrac{-4}{3}} ]^{4}[/tex]
[tex]= [(x^{\frac{3}{4}*\frac{1}{4}})^{\frac{-4}{3}}]^{4}\\\\\\= [(x^{\frac{3}{16} ) ^{\frac{-4}{3}}}]^{4}\\\\=[ x^{\frac{3}{16}*\frac{-4}{3}}]^{4}\\\\=[x^{\frac{-1}{4}}]^{4}\\\\=x^{\frac{-1}{4}*4}\\\\=x^{-1}\\\\=\dfrac{1}{x}[/tex]
Hint:
[tex](a^{m})^{n}=a^{m*n}[/tex]
Answer:
[tex]1/x[/tex]
Step-by-step explanation:
To simplify, work from the inside out.
We start with
[tex]\sqrt[4]{x^{3/4}}[/tex]
on the inside. And we can change the fourth root into a fractional exponent -- 1/4:
[tex](x^{\frac{3}{4})^{1/4}[/tex]
A power of a power means multiply the exponents, giving
[tex]x^{\frac{3}{4} * \frac{1}{4}} = x^{3/16}[/tex]
So now we have
[tex][(x^{3/16})^{-4/3}]^4[/tex]
From here, apply the "power of a power rule" again, working from the inside out.
[tex](x^{-12/48})^4[/tex]
[tex]x^{-48/48}[/tex]
[tex]x^{-1}[/tex]
or
[tex]1/x[/tex]
