Answer:
x=16/81
Step-by-step explanation:
3^4x-1=15
81x-1=15
81x=15+1
81x+16
divide both sides by 81
x=16/81
The weights of the fish in a certain lake are normally distributed with a mean of 20 lb and a standard deviation of 9. If 9 fish are randomly selected, what is the probability that the mean weight will be between 17.6 and 23.6 lb
Step-by-step explanation:
mean of 20 lb and a standard deviation of 9. If 9 fish are randomly selected,
what is the probability that the mean weight will be between 17.6 and 23.6
Ib? Write your answer as a decimal rounded to 4 places
Find the derivative of the function y = ln(3t+4)
Answer:
3 / (3t+4) is the answer
3 bombas de agua llenan una piscina en 10 días trabajando 5 horas diarias.
Si hay 5 bombas de agua, ¿cuántos días demoran en llenar la misma piscina, si trabajan 8 horas diarias?
5 bombas deben trabajar durante 4 dias para llenar la piscina.
¿cuántos días demoran en llenar la misma piscina, si trabajan 8 horas diarias?Cada bomba trabaja a un rate (razon de trabajo) R.
Sabemos que 3 bombas, trabajando 5 horas diarias por 10 días (un total de 50 horas), llena una piscina, entonces:
(3R)*50 horas= 1 piscina.
R = (1 piscina)/(150 horas).
Es decir, una sola bomba tarda 150 horas en llenar una piscina.
En el caso de que 5 bombas trabajen, tenemos que para llenar una piscina tienen que trabajar un tiempo T.
5*((1 piscina)/(150 horas))*T = 1 piscina.
(1 piscina)/(30 horas)
Resolviendo para T, obtenemos:
T = 1 piscina*(30 horas)/(1 piscina) = 30 horas.
Y sabemos que trabajan 8 horas diarias, es decir, las bombas deben trabajar durante:
30/8 = 3.75 ≈ 4 días.
5 bombas deben trabajar durante 4 dias para llenar la piscina.
Sí quieres aprender más sobre razones de trabajo.
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Lyra is designing a model of a solar system with a planet and a comet. The planet has a circular orbit, centered at the origin with a diameter of 100. The comet follows a parabolic path with directrix x = 70 and vertex at (60, 0).
Part A: Write the equation of the planet's orbit in standard form. Show your work. (2 points)
Part B: Write the equation of the comet's path in standard form. Show your work. (4 points)
Part C: Identify all points where the planet's orbit intersects the path of the comet. Show your work and round answers to the hundredth place. (4 points)
The equation of the circular orbit and the parabolic path of the comet are
given by the center, diameter, vertex, and directrix.
Part A: The equation of the planet's orbit is; x² + y² = 50²
Part B: The equation of the comet's orbit is; [tex]\underline{x = -\dfrac{y^2}{280} + 60}[/tex]
Part C: The planet's orbit and the comet's path do not intersect.
Reasons:
Part A: The center of the orbit = The origin (0, 0)
The diameter of the orbit = 100
Therefore;
[tex]Radius \ of \ orbit = \dfrac{100}{2} = 50[/tex]
The radius of the planet's orbit, r = 50
The equation of a circle with center (h, k) is; (x - h)² + (y - k)² = r²
Therefore, the equation of the circle is (x - 0)² + (y - 0)² = r²
Which gives;
x² + y² = 50²
Part B: The directrix of the parabolic path is x = 70
The vertex = (60, 0)
Therefore, -p = 70
[tex]The \ equation \ is \ x = \dfrac{1}{4\cdot p} \cdot (y - k)^2 + h[/tex]
Which gives;
[tex]The \ equation \ is \ x = \dfrac{1}{4\times (-70)} \times (y - 0)^2 + 60 = -\dfrac{y^2}{280} + 60[/tex]
[tex]x = \mathbf{ -\dfrac{y^2}{280} + 60}[/tex]
The equation of the comet's path in standard form is [tex]\underline{x = -\dfrac{y^2}{280} + 60}[/tex]
Part C: At the point where the path intersect, we have;
[tex]x^2 = \left( -\dfrac{y^2}{280} + 60 \right)^2[/tex]
Therefore;
[tex]\mathbf{\left( -\dfrac{y^2}{280} + 60 \right)^2} = 50^2 - y^2[/tex]
Let y² = a, we get;
[tex]\left( -\dfrac{a}{280} + 60 \right)^2 = 50^2 -a[/tex]
a ≈ -2015.693 and a ≈ -42784.31
y ≈ √(-2015.693) or y ≈ √-42784.31) (imaginary numbers)
The planet's orbit does not intersect the path of the comet.
Learn more here:
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The function c(h)= (20h)/(h^2+2) models the concentration of a medication in the bloodstream h hours after it’s injection into the muscle tissue.
-Does the graph have a vertical asymptote? If so, give the equation of the vertical asymptote and explain why this would be a concern or not. If the function does not have a vertical asymptote, explain why.
-Find the horizontal asymptote, what does it mean in the context of this problem?
-Does the function cross the horizontal asymptote? Does it make sense in the relation to this problem?
I have the answers, I just don’t understand how to explain them in the context of the problem.
Answer:
Step-by-step explanation:
What’s it’s answer I am wonder
list all counting numbers which leave a remainder of 4 when divided by 22.
Answer:
0.1818
i hope it helped you :)
mark brainliest
What is 3.59 rounded to the nearest whole number?
Answer:
its 4 ezy
Step-by-step explanation:
please mark as brainlists
What are the equivalent ratios to 6:5
Ratio of 6 to 5
A ratio of 6 to 5 can be written as 6 to 5, 6:5, or 6/5. Furthermore, 6 and 5 can be the quantity or measurement of anything, such as students, fruit, weights, heights, speed and so on.
A ratio of 6 to 5 simply means that for every 6 of something, there are 5 of something else, with a total of 11
Below is a list of equivalent ratios of 6:5 that we created using our 6:5 ratio calculator above.
6:5
12:10
18:15
24:20
30:25
36:30
42:35
48:40
54:45
60:50
66:55
72:60
geometry B: fill in the blank
Answer:
The circumference of a circle is the distance around the entire circle, while arc length, s, is the distance between two points on the circle.
C = 2πr = 2π( 5 ) = 10π ≈ 31.4 units
3.14 is an approximation for π.
s = θ/360° (C)
mAB = 60°/360° ( 31.4)
= 1/6(31.4) ≈5.2 units
If a line l is perpendicular to a segment AB at point E and AE = EB how many points on line l are the same distance from point A as from point B
Answer:
101
Step-by-step explanation:
Translate and solve using proportions: What number is 30% of 60
Answer: 18
Step-by-step explanation:
The question is asked to know 30% of 60, we get
60 x 30% = 60 x 0.3 = 18
Answer:
18
Step-by-step explanation:
We know that 30% means 30/100
30/100 multiplied by 60
hence, the answer is 18
pls find prism if you find it your littearly a pro hacker
Answer:
24 cubic unitsStep-by-step explanation:
Given, in picture,It is a rectangular prism.
It's length in units = 4
It's breadth in units = 2
It's height in units = 3
Therefore,Volume of the given rectangular prism
= length × breadth × height
= 4 units × 2 units × 3 units
= 24 cubic units (Ans)
see image above ^^^^
Triangle ABC was rotated 90 degrees counter clockwise to become triangle STU
do atoms have potential and kinetic energy
Answer: Kinetic and potential energy of atoms result from the motion of electrons. ... The further the orbital is from the nucleus, the higher the potential energy of an electron at that energy level. When the electron returns to a low energy state, it releases the potential energy in the form of kinetic energy.
(i searched it and found this. If it helped, pls mark me brainliest! tysm)
Balamma
Model with Math How many things are
used to make a guitars like the ones in the
picture Draw a bar diagram to show how
you found your answer
Answer:
Where is the questions picture so I know what I am about to answer
Step-by-step explanation:
I need a pic.
Shape l and ll are what?
Answer:
a trapezoid:ll and a dented triangle:l
Evaluate each expression.
12
N
3
(2511)
-
DONE
Answer:
1/5Step-by-step explanation:
[tex](25^{-3/2})^{1/3} = 25^{-3/2*1/3} = 25^{-1/2}=5^{-1/2*2}=5^{-1}=1/5[/tex]Let's evaluate the expression,
→ (25^-3/2)^1/3
→ 25^-3/2×1/3
→ 25^-3/6
→ 5^-1/2×2
→ 5^-1 {or} 1/5
Hence, the answer is 1/5.
Please help! Thanks!: If a 95% confidence interval was being calculated using the following expression:
3.2 ± 1.96 ⋅ 1.1
What would be the margin of error for this confidence interval?
If you can please give an explanation on how to solve?
The confidence interval can be calculated from the margin of error, and vice versa,
The margin of error of the confidence interval is 2.156
The confidence interval is given as:
[tex]\mathbf{CI = 3.2 \pm 1.96 \cdot 1.1}[/tex]
The formula of confidence interval is:
[tex]\mathbf{CI = \bar x\pm E}[/tex]
Where E represents the margin of error.
So, by comparison:
[tex]\mathbf{E = 1.96 \cdot 1.1}[/tex]
Multiply
[tex]\mathbf{E = 2.156}[/tex]
Hence, the margin of error of the confidence interval is 2.156
Read more about margin of errors at:
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what is the slope will mark brainlist
The equation of slope is y2 - y1/x2 - x1
0 - 4/0 - 5
-4/5
Another method in image added.
Alexander is a car salesman. He earns 7% in commission each week. Last week, he sold $164,000 worth of cars. How much did he make last week in commission?
Answer:
$11,480
Step-by-step explanation:
Solve: 2x^2 -x >15 Show your work.
Answer:
x>3
Step-by-step explanation:
Work:
2x^2-x>15
Subtract 15 on both sides:
2x&2-x-15>0
Factor the left side of equation to cancel out the ^2.
(2x+5)(x−3)>0
2x+5=0 or x−3>0
Then to make it easier we will do the x-3>0 one, add 3 to both sides = x>3
Find x.
Multiple choice.
8, 9, 10, 11
Answer:
Step-by-step explanation:
As RS is a straight line sin ∠RUT = sin ∠SUT
line UT bisects ∠RTS
Let θ be ∠UTR and ∠UTS
Law of sines
Left side triangle
3x/sinθ = 40/sinRUT
sinRUT = 40sinθ / 3x
Right side triangle
(x + 2) / sinθ = 16 / sinSUT
(x + 2) / sinθ = 16 / (40sinθ / 3x)
(x + 2)(40sinθ / 3x) = 16sinθ
(x + 2)(40sinθ) = 48xsinθ
40xsinθ + 80sinθ = 48xsinθ
40x + 80 = 48x
80 = 8x
x = 10
Find the exact valueFind sin theta:/2
See picture. Show steps
Answer:
Step-by-step explanation:
Use the half angle formulas
sin(θ/2) = ±√((1 - cosθ)/2)
sin(θ/2) = ±√((1 - (3/5))/2)
sin(θ/2) = ±√((2/5)/2)
sin(θ/2) = ±√(1/5)
knowing θ is in the 4th quadrant, θ/2 will be in the second quadrant where sines are positive.
sin(θ/2) = +√(1/5) = √0.2
Work out the area of this semicircle.
Take a to be 3. 142 and write down all of the digits given by your calculator.
11 cm
Answer:
Step-by-step explanation:
A = πr²/2 = 3.142(11²)/2 = 190.091 cm²
You are traveling in a car. Your speed is 40 miles per hour. What is your speed in feet per minute?
You are traveling in a car. Your speed is 40 miles per hour. What is your speed in feet per minute?
You are traveling in a car. Your speed is 40 miles per hour. What is your speed in feet per minute?
You are traveling in a car. Your speed is 40 miles per hour. What is your speed in feet per minute?
You are traveling in a car. Your speed is 40 miles per hour. What is your speed in feet per minute?
You are traveling in a car. Your speed is 40 miles per hour. What is your speed in feet per minute?
You are traveling in a car. Your speed is 40 miles per hour. What is your speed in feet per minute?
You are traveling in a car. Your speed is 40 miles per hour. What is your speed in feet per minute?
You are traveling in a car. Your speed is 40 miles per hour. What is your speed in feet per minute?
You are traveling in a car. Your speed is 40 miles per hour. What is your speed in feet per minute?
Answer:
58 2/3 fps
Step-by-step explanation:
To convert a speed value from miles per hour to feet per second, multiply it by 5280, then divide by 3600.
40 * 5280 = 211200
211200 / 3600 = 58.6666..... [58 2/3]
2/3 of a cup of batter can make 5/6 of a batch of pancakes. How many cups of water are needed to make one batch of pancakes?
Answer:
1 11/12 cups of water
What are the solutions of x2 - 2x + 10 = 0 ?
Answer:
Step-by-step explanation:
=
−
±
2
−
4
√
2
x
=
−
b
±
b
2
−
4
a
c
2
a
x=2a−b±b2−4ac
Once in standard form, identify a, b, and c from the original equation and plug them into the quadratic formula.
2
−
2
+
1
0
=
0
x
2
−
2
x
+
10
=
0
x2−2x+10=0
=
1
a
=
1
a=1
=
−
2
b
=
−
2
b=−2
=
1
0
c
=
10
c=10
=
−
(
−
2
)
±
(
−
2
)
2
−
4
⋅
1
⋅
1
0
√
2
⋅
1
x
Answer:
C. x=1+3i, x=1-3iStep-by-step explanation:
[tex]\frac{-\left(-2\right)\pm \sqrt{\left(-2\right)^2-4\cdot \:1\cdot \:10}}{2\cdot \:1} \\=\frac{-\left(-2\right)\pm \:6i}{2\cdot \:1}\\x_1=\frac{-\left(-2\right)+6i}{2\cdot \:1},\:x_2=\frac{-\left(-2\right)-6i}{2\cdot \:1}\\\frac{-\left(-2\right)+6i}{2\cdot \:1}\\ =\frac{2+6i}{2\cdot \:1}\\=\frac{2+6i}{2}\\=\frac{2\left(1+3i\right)}{2}\\1+3i\\\\\\frac{-\left(-2\right)-6i}{2\cdot \:1}\\=\frac{2-6i}{2\cdot \:1}\\=\frac{2-6i}{2}\\=\frac{2\left(1-3i\right)}{2}\\1-3i\\x=1+3i,\:x=1-3i[/tex]
PLS HELP ASAP
x^2 - 4x-1=0
Solve using formula
2x ( x - 2x) = 1
2x= 1
x = 0.5
x-2x = 1
-x = 1
x = -1
Find the domain of the function
Answer:
Here you go :)
Step-by-step explanation:
A store pays $85 for a picnic table and marks the price up by 25%. What is the new price