Through setting up and solving the equation 1/3 * x + 2 = 8, where x represents the number of Saturn's moons, it was determined that Saturn is known to have 18 moons.
Explanation:The student's question pertains to a comparison of the moons of Neptune and Saturn, using mathematical operations to deduce the number of known moons of Saturn. First, we're told that Neptune has 8 known moons, which is said to be 2 more than 1/3 of the number of known moons on Saturn. We are seeking to solve for the number of moons that Saturn has.
To find out, we set up an equation where 1/3 of the number of moons of Saturn plus 2 equals the number of Neptune's moons: 1/3 * x + 2 = 8, where x represents the number of Saturn's moons. Solving for x, we subtract 2 from both sides to get 1/3 * x = 6. We then multiply both sides by 3 to isolate x and find that x = 18.
Therefore, Saturn is known to have 18 moons according to the given information.
Eight people enter a race. If there are no ties, in how many ways can the first two places come out
The number of ways the first two places can come out is 56.
Permutation and CombinationPermutation helps us to know the number of ways an object can be arranged in a particular manner. A permutation is denoted by 'P'.
The combination helps us to know the number of ways an object can be arranged without a particular manner. A combination is denoted by 'C'.
[tex]^nP_r = \dfrac{n!}{(n-r)!},\ \ ^nC_r = \dfrac{n!}{(n-r)!\times r!}[/tex]
where,
n is the number of choices available,
r is the choices to be made.
Given to us,Eight people enter a race, n = 8,
There are no ties, r = 2,
As there is an equal chance of everyone being first and second, but also there will be cases where the first and second positions can be exchanged between the same two people. therefore, there is a particular order in which these 8 people can win. Thus, we will use permutation.
Permutation[tex]^8P_2 = \dfrac{8!}{(8-2)!}=\dfrac{8!}{(6)!} = \dfrac{8\times 7\times 6!}{6!} = 8\times 7 = 56[/tex]
Hence, the number of ways the first two places can come out is 56.
Learn more about Permutation and Combination:
https://brainly.com/question/11732255
Which should come next at the end of this row of letters: a b d g?
Answer:
Next letter will be k.
Step-by-step explanation:
we have to find the letter which will come next at the end of the row of letters
a b d g.
First we will write the alphabets as below to understand the sequence
a b c d e f g h i j k
Between a and b alphabet skipped = 0
Between b and d alphabets skipped = 1 (c)
Between d and g skipped alphabets = 2 (e and f)
Therefore after g number of alphabets skipped will be = 3 (h i j)
Next alphabet will be k.
Provide the reasons for the proof:
Given: Trapezoid RIAG with RI = RG = GA
m angle I = m angle NAG
Prove: angle T ≈ angle N
The safety inspector notes that Ray also needs to plan for a vertical ladder through the center of the coaster's parabolic shape for access to the coaster to perform safety repairs. Find the vertex and the equation for the axis of symmetry of the parabola, showing your work, so Ray can include it in his coaster plan.
f(x)= 3x^2+9x+12
Answer with explanation:
Equation of the Parabola is
[tex]f(x)= y=3x^2+9x+12\\\\y=3[x^2+3 x+4]\\\\y=3[(x+\frac{3}{2})^2+4-(\frac{3}{2})^2]\\\\y=3[(x+\frac{3}{2})^2+(\frac{\sqrt 7}{2})^2]\\\\y-\frac{21}{4}=3[(x+\frac{3}{2})^2][/tex]
Vertex of the parabola can be obtained by
[tex]x+\frac{3}{2}=0\\\\ x=\frac{-3}{2}\\\\ y-\frac{21}{4}=0\\\\y=\frac{21}{4}\\\\ Vertex(\frac{-3}{2},\frac{21}{4})[/tex]
Axis is that line of parabola which divides the parabola into two equal halves.
[tex]x+\frac{3}{2}=0\\\\x=-\frac{3}{2}[/tex]
Which equation would best help solve the following problem? Rennie kicks a field goal with an initial vertical velocity of 31 m/s. How long will it take the football to hit the ground?
–4.9t2 + 31t = 0
–4.9t2 – 31t = 0
16t2 + 31t = 0
–16t2+ 31t = 0
The equation =+y3115
is solved in several steps below.
For each step, choose the reason that best justifies it.
A mouse spots an owl flying 10.1 feet over a nearby bush. The mouse is 30 feet away from the bush, and it sees the owl at a certain angle of elevation.
Which trigonometric equation can be used to solve for x, the angle of elevation from the mouse to the owl?
A survey was taken of students in math classes to find out how many hours per day students spend on social media. The survey results for the first-, second-, and third-period classes are as follows: First period: 2, 4, 3, 1, 0, 2, 1, 3, 1, 4, 9, 2, 4, 3, 0 Second period: 3, 2, 3, 1, 3, 4, 2, 4, 3, 1, 0, 2, 3, 1, 2 Third period: 4, 5, 3, 4, 2, 3, 4, 1, 8, 2, 3, 1, 0, 2, 1, 3 Which is the best measure of center for second period and why?
A) Mean, because there are no outliers that affect the center.
B) Median, because there is 1 outlier that affects the center.
C) Interquartile range, because there is 1 outlier that affects the center.
D) Standard deviation, because there are no outliers that affect the center
I believe the answer is D.
Answer:
B) Median, because there is one outlier that affects the center
A boat makes a 120-mile trip downstream in 3 hours but makes the return trip in 4 hours. If b = the rate of the boat in still water and c = the rate of the current, which of the following equations represents the trip downstream?
3(b - c) = 120
3(b + c) = 120
4(b + c) = 120
Find the center, vertices, and foci of the ellipse with equation x squared divided by one hundred plus y squared divided by thirty six = 1.
A man paid the bank $4,080 at the end of three years. This was the amount borrowed plus 12% interest for three years. How much money had he borrowed?
If the ratio between the radii of the two spheres is 5:8, what is the ratio of their volumes?
Answer: The required ratio of the volumes of two spheres is 125 : 512.
Step-by-step explanation: Given that the ratio between the radii of the two spheres is 5 : 8.
We are to find the ratio of the volumes of the two spheres.
Let, 'r' and 'R' represents the radii of the two spheres, so
r : R = 5 : 8.
The volume of a sphere with radius 'r' units is given by the formula:
[tex]V=\dfrac{4}{3}\pi r^3.[/tex]
Let, V and V' be the volumes of the spheres with radius r and R units respectively.
Then, the ratio of the volumes of the two spheres will be
[tex]\dfrac{V}{V'}=\dfrac{\frac{4}{3}\pi r^3}{\frac{4}{3}\pi R^3}=\dfrac{r^3}{R^3}=\left(\dfrac{r}{R}\right)^3=\left(\dfrac{5}{8}\right)^3=\dfrac{125}{512}\\\\\\\Rightarrow V:V'=125:512.[/tex]
Thus, the required ratio of the volumes of two spheres is 125 : 512.
Answer: 125:512
Step-by-step explanation:
a p e x
What are radians, how do I solve for the measurement of radians in the angle of BAC
If y varies inversely as the square of x and y=4 when x=5, find y when x is 2
need to kind K
Y=k x 1/x^2 = k/x^2
Find K when y=4 & x=5
Y=k/x^2 =
4=k/5^2=
4=k/25
K=4*25 =100
When x = 2
Y=100/2^2
Y=100/4
Y=25
Which table represents the second piece of the function f(x)
Answer:
Third table represents the second piece of the function f(x)
Step-by-step explanation:
The second piece of the function f(x) is [tex]f(x)=8-2x[/tex]
Now, we substitute some values of x and find the corresponding function values and check which table satisfy the points.
For x = 1
[tex]f(1)=8-2(1)\\f(1)=6[/tex]
For x = 2
[tex]f(2)=8-2(2)\\f(2)=4[/tex]
For x = 3
[tex]f(3)=8-2(3)\\f(3)=6[/tex]
Among the given tables, third tables contains these values.
Third table represents the second piece of the function f(x)
A local university accepted 2300 students out of 4500 applicants for admission. What was the acceptance rate expressed as a percent
Find the value of x. Express your answer in simplest radical form
An 800 gallon swimming pool is being drained. After five hours, 500 gallons have been drained. If the rate of drainage continues, how long will it take to drain the pool?
A) 0.125 hours
B) 5 hours
C) 8 hours
D) 9 hours
Write the converse of the statement. If the converse is true, write true; if not true, provide a counterexample.
If x = 4, then x2 = 16
how do you solve this system of linear equation by substitution
x-3y=-12
y=2x+9
Help!!!!ASAP PLEASE
Question 1(Multiple Choice Worth 5 points) (07.05 HC)
The work of a student to solve the equation 3(2x − 4) = 8 + 2x + 6 is shown below: Step 1: 3(2x − 4) = 8 + 2x + 6 Step 2: 5x − 7 = 14 + 2x Step 3: 5x − 2x = 14 + 7 Step 4: 3x = 21 Step 5: x = 7 In which step did the student first make an error and what is the correct step?
Step 2; 6x − 12 = 14 + 2x
Step 2; 6x − 7 = 2(6 + x + 4)
Step 3; 5x − 2x = 14 − 7
Step 3; 5x + 2x = 14 + 7
The length of the rectangle is 4 times the height. the area of the triangle is 63 cm2. Find the width. Round to the nearest tenth of an inch
area = l x h
l=4h
area = 4h x h = 4h^2
4h^2 =63
63/4 = 15.75
h^2 = 15.75
sqrt(15.75)=h
h = 3.968cm
rounded to nearest tenth would be 4.0cm
check L=4(4) = 16 x 4 = 64 ( since it was round 64 is pretty close to 63)
A ball is dropped from the top of a 550 ft. building. The function h(t) = - 16t2 + 50 models the height of the ball, h(t) (in feet), at any given time, t (in seconds).
What is the maximum height of the ball?
550 ft
423 ft
What are the difference between polynomial long division and arithmetic long division?
Answer:
The purpose of long division with polynomials is similar to long division with integers; to find whether the divisor is a factor of the dividend and, if not, the remainder after the divisor is factored into the dividend. The primary difference here is that you are now dividing with variables.
Solve the following system by any method. 8x + 9y = –5 –8x – 9y = 5 A. (–10, 3) B. (–3, 10) C. (0,0) D. Infinitely many solutions
Ryan flew from Wiley Post to Ponca City and back. Ryan maintained an average rate of 450 mph going to Ponca City and an average rate of 400 mph returning to Wiley Post. If the actual flying time for the round trip was one hour, about how far is it from Wiley Post to Ponca City? Round to nearest mile.
A.
0.47 miles
B.
212 miles
C.
239 miles
D.
3,600 miles
what are the discontinuities of the function f(x) =x<2-36/4x-24 ?
When 0.3(4x – 8) – 0.5(–2.4x + 4) is simplified, what is the resulting expression?
The resulting expression for x when the algebraic expression is simplified is 2.4x - 4.4
What is the simplification of an algebraic expression?The simplification of algebraic expressions follows an approach where we aim to solve for the unknown variables of the algebraic expression.
From the given algebraic expression, we have:
0.3(4x – 8) – 0.5(–2.4x + 4)
Open brackets1.2x - 2.4 + 1.2x - 2
Collect like terms1.2x + 1.2x = 2.4 + 2
2.4x = 4.4
2.4x - 4.4
Learn more about algebraic expression here:
https://brainly.com/question/2164351
Answer:
simply d
Step-by-step explanation:
ANSWER PLEASE
In the figure, sin ∠MQP =
a. cos N and sin R
b. sin R and sin N
c. cos N and sin M
d. cos R and sin N