Answer:-27
Step-by-step explanation:
-3 x -3 = 9
9 x -3 =27
a guitar string 61 cm long vibrates with a standing wave that has three antinodes. Which harmonic is this and what is the wavelength of this wave?
This is the fourth harmonic and the wavelength of the wave is 40.67 cm.
How to the harmonic of standing wave?For a standing wave on a guitar string, the length of the string (L) and the number of antinodes (n) determine the wavelength (λ) of the wave according to the formula:
λ = 2L/n
In this case, the length of the guitar string is 61 cm and the number of antinodes is 3. Therefore, the wavelength of the standing wave is:
λ = 2(61 cm)/3 = 40.67 cm
The harmonic number (i.e., the number of half-wavelengths that fit onto the string) for this standing wave can be determined by the formula:
n = (2L/λ) + 1
Plugging in the values of L and λ, we get:
n = (2(61 cm)/(40.67 cm)) + 1 = 4
Therefore, this standing wave has the fourth harmonic.
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How much does a customer pay for an article marked at $50 if a sales tax of 6% is charged? (A) (B) © ថ្មី > $44 547 553 556 (D)
Answer:
53
Step-by-step explanation:
Find the sales tax
50 * 6%
50 * .06
3
Add this to the original price
50 +3
53
What is the solution set for 9x2-25=0
Answer: i hope i helped if not im truly sorry
Solving for 9x^2 - 25 = 0
Standard form:
9x2 − 25 = 0
Solutions based on quadratic formula:
x1
= −0 − √ 02 − 4×9×(−25)
2×9
= 0 − 30 × √ 1
18
≈ −1.667
x2
= −0 + √ 02 − 4×9×(−25)
2×9
= 0 + 30 × √ 1
18
≈ 1.667
Extrema:
Min = (0, −25)
Step-by-step explanation: im not dumb and im not smart
Please help me with this question!!!!!
h = 11.9 cm
cos = adjacent/ hypotenuse
therefore:
cos(24) = h/ 13
rearrange:
h = 13cos(24)
put into calculator:
h = 11.8760...
rounded to one decimal point:
h = 11.9cm
Evaluate: Question(2): Z+8-6(z-2a)+5z
Answer:
Z+12a−z+8+12−+8
Step-by-step explanation:
Z+8−6(z−2a)+5z
+8−6(−2)+5
Z+8−6(−2a+z)+5z
+8−6(−2+)+5
Z+8−6(−2a+z)+5z
+8−6(−2+)+5
Z+8+12a−z+8+12−
Answer:
Z + 8 + 12a − z
12a + 8
Step-by-step explanation:
What is the domain of the function f(x) = square root 3x + 1 for the range 4 <= f(x) <= 5?
The domain of a functio f(x) is the set of vlues for which the function is defined (all the values of x for which the function is defined).
Range: the values that f(x) takes.
\(4\leq f(x)\leq5\)Find the values of x when f(x) is greather than or equal to 4 and less than or equal to 5
When f(x)≥4
\(\begin{gathered} 4\leq\sqrt[]{3x+1} \\ 4^2\leq(\sqrt[]{3x+1})^2 \\ 16\leq3x+1 \\ 16-1\leq3x \\ 15\leq3x \\ \frac{15}{3}\leq x \\ \\ 5\leq x \end{gathered}\)When f(x)≤5
\(\begin{gathered} 5\ge\sqrt[]{3x+1} \\ 5^2\ge(\sqrt[]{3x+1})^2 \\ 25\ge3x+1 \\ 25-1\ge3x \\ 24\ge3x \\ \frac{24}{3}\ge x \\ \\ 8\ge x \end{gathered}\)Then. the domain in that interval of range is:
\(5\leq x\leq8\)how do you find the height of a cone
Answer:Write down the radius and volume.
Input them in the height of a cone formula for volume: h = 3 × V/(π × r²) where: V is the cone's volume; r is the radius; and. h is the resulting height.
It's as simple as that!
Step-by-step explanation: i took the test!
For practical answer; If we open a cone its a semi circle and the distance from center to a edge is radius so the height of the cone is the radius of that semi circle.
need help with this please..
Answer:
.1/2
Step-by-step explanation:
is the same as 20÷40
which gives you 1/2
The quadrilateral below is a rhombus. Find the missing measures. Any decimal answers should be rounded to the nearest tenth.
NK =
m
NL =
m
ML =
m
JM =
m
m
A rhombus with MK = 24 m, JL = 20, ∠MJL = 50°. So, NK = 24 m, NL = 24.8 m, ML = 24.8 m, and JM = 20 m.
We need the information about the measurements or a description of the missing measures in the rhombus. We can make it MK = 24 m, JL = 20, ∠MJL = 50° for example. Since it's a rhombus, all sides are equal in length. Therefore, NK = MK = 24 m, JM = JL = 20 m, and ML = NL.
To find ML (or NL), we can use the Law of Cosines on the triangle MJL. In this case,
ML² = JM² + JL² - 2(JM)(JL)cos(∠MJL):
ML² = 20² + 20² - 2(20)(20)cos(50°)
ML² = 400 + 400 - 800cos(50°)
ML² ≈ 617.4
Taking the square root of both sides, we get ML ≈ √617.4 ≈ 24.8 m.
So, NK = 24 m, NL = 24.8 m, ML = 24.8 m, and JM = 20 m.
The complete question is The quadrilateral below is a rhombus. Given MK = 24 m, JL = 20, ∠MJL = 50°. Find NK, NL, ML, and JM. Any decimal answers should be rounded to the nearest tenth.
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Please help I have a lot of work to do :(
Answer:
Distributive
Step-by-step explanation:
The equation just distributes the 0.5 to the numbers in the parenthesis.
Juan bought 15 pounds of flour for $8.
How many pounds of flour did he get per dollar?
plz help simplify 8/10
\(\frac{8}{10}\) → \(\frac{4}{5}\)
8 and 10 can both be divided by 2. So, 8 ÷ 2 is 4 and 10 ÷ 2 is 5.
Hope this helps :)
Answer:
4/5
Step-by-step explanation:
okay so to simplify, we first need to find the GCF of 8 and 10. The GCF of 8 and 10 would be 2. We now divide both 8 and 10 by 2. That will give us 4/5.
\(\frac{8}{10}\)÷\(\frac{2}{2}\)=\(\frac{4}{5}\)
Question 3 The Schwarzschild metric is given by 2M 2M ds² -(₁-²M) di² + (1-²¹)- 1- dr² +r² (d0² + sin² 0 dó²). There are Killing vectors associated with time invariance and angular momen- tum invariance in the direction in this geometry leading to the conserved quantities e = (1-2) and l= r² sin² 0 dr From this one can derive an analog to the radial energy equation in Newtonian mechanics by orienting the coordinates so that the orbits are confined to the equatorial plane where 0 = π/2 and u = 0. One finds 2 1 dr + Veff (r) = E 2 dr (e²_ -1) where E = and Veft(r) = - + 2/²/²2 - Mp³². Further, for circular orbits one can show that M | [₁ + √/₁−12 (+1)]. r+= | 2M Finally, for circular orbits of radius R do 1/2 M dt R³ (a) Which value of r corresponds to the Schwarzschild radius of stable circular orbits: r or r? Justify your answer. [3 marks] (b) Show that for circular orbits of radius R do 1/2 M -1/2 3M (²) ¹² (1-³) dT R³ R where is the proper time. [6 marks] (c) A free particle is moving in a circular orbit around a spherical source of curvature of mass M. The Schwarzschild radius of the orbit is 8M. Use the equivalence principle to argue that the period as measured at infinity should be larger than that measured by the particle. [4 marks] (d) Find the period of the orbit as measured by an observer at infinity. Find the period of the orbit as measured by the particle. [7 marks] M
(A) Circular orbits of stable particles are possible at radii greater than three times the Schwarzschild radius for the non-rotating spherically symmetric mass.
This represents the radius of a black hole's event horizon, within which nothing can escape. The Schwarzschild radius is the event horizon radius of a black hole with mass M.
M can be calculated using the formula: r+ = 2Mwhere r+ is the radius of the event horizon.
(B) 1/2 M -1/2 3M (²) ¹² (1-³) dT = R³ R. This is the required expression.
Tau is the proper time of the particle moving around a circular orbit. Hence, by making use of the formula given above:1/2 M -1/2 3M (²) ¹² (1-³) dT = R³ dt.
(C) Time passes differently in different gravitational fields, and it follows that the period as measured at infinity should be larger than that measured by the particle.
The principle of equivalence can be defined as the connection between gravitational forces and the forces we observe in non-inertial frames of reference. It's basically the idea that an accelerating reference frame feels identical to a gravitational force.
(D) The period of the orbit as measured by an observer at infinity is 16π M^(1/2) and the period of the orbit as measured by the particle is 16π M^(1/2)(1 + 9/64 M²).
The period of orbit as measured by an observer at infinity can be calculated using the formula: T = 2π R³/2/√(M). Substitute the given values in the above formula: T = 2π (8M)³/2/√(M)= 16π M^(1/2).The period of the orbit as measured by the particle can be calculated using the formula: T = 2π R/√(1-3M/R).
Substitute the given values in the above formula: T = 2π (8M)/√(1-3M/(8M))= 16π M^(1/2)(1 + 9/64 M²).
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find the specified probability. round your answer to four decimal places, if necessary.p(0
Given information:The random variable X has a binomial distribution with n = 5 and p = 0.3.Want to find: The probability that X is less than or equal to 1 i.e. P(X ≤ 1).
Solution:Given, the random variable X has a binomial distribution with n = 5 and p = 0.3.The probability mass function (pmf) of the binomial distribution is given by\(;P(X = x) = nCx * p^x * (1-p)^(n-x),\) where;n = 5, the number of trials.p = 0.3, the probability of success.x = 0, 1, 2, 3, 4 and 5.
The required probability is to find P(X ≤ 1).P(X ≤ 1) = P(X = 0) + P(X = 1)Putting the values;\(P(X = 0) = 5C0 * 0.3^0 * 0.7^5= 0.16807 P(X = 1) = 5C1 * 0.3^1 * 0.7^4= 0.36015 Therefore, P(X ≤ 1) = P(X = 0) + P(X = 1)= 0.16807 + 0.36015= 0.52822\)Therefore, the probability that X is less than or equal to 1 i.e. P(X ≤ 1) is 0.52822 (approx) when n = 5 and p = 0.3.
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Alex works as a health insurance agent for Medical Benefits Fund. The probability that he succeeds in selling an insurance policy to a given customer aged 25 years or older is 0.45. On a given day he interacts with 8 customers in this age range. Find the probability that he will sell exactly 2 insurance policies on this day.
a)0.157
b)0.0632
c)0.220
d)0.780
e)0.999
The probability of Alex selling exactly 2 insurance policies to customers aged 25 years or older on a given day is 0.311.
Alex works as a health insurance agent for Medical Benefits Fund. The probability that he succeeds in selling an insurance policy to a given customer aged 25 years or older is 0.45. On a given day, he interacts with 8 customers in this age range. We are to find the probability that he will sell exactly 2 insurance policies on this day. This is a binomial experiment as the following conditions are met: There are only two possible outcomes. Alex can either sell an insurance policy or not. The number of trials is fixed. He interacts with 8 customers, so this is the number of trials. The trials are independent. Selling insurance to one customer does not affect selling insurance to the next customer. The probability of success is constant for each trial. It is given as 0.45.The formula for finding the probability of exactly x successes is:
\(P(x) = nCx * p^x * q^(n-x)\)
where n = number of trials, p = probability of success, q = probability of failure = 1 - p, and x = number of successes. We want to find P(2). So,
n = 8, p = 0.45, q = 0.55, and x = 2.
\(P(2) = 8C2 * 0.45^2 * 0.55^6\)
P(2) = 28 * 0.2025 * 0.0988
P(2) = 0.311
The probability of Alex selling exactly 2 insurance policies to customers aged 25 years or older on a given day is 0.311, which is closest to option a) 0.157.
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Rearrange x = 3g + 2 to make g the subject.
Answer:
g = ( x - 2 ) / 3
Step-by-step explanation:
x = 3g + 2
subtract 2 from each side
x - 2 = 3g + 2 - 2
simplify
x - 2 = 3g
Divide each side by 3
(x - 2)/3 = 3g/3
Simplify
( x - 2 ) / 3 = g
Flip equation
g = ( x - 2 ) / 3
And we are done!
Mr. Perez gave his students a biology test last week.
Here are the test scores for each of the twelve students.
Complete the grouped frequency distribution for the data.
In the distribution, the frequency of a class is the number of test scores in that class.
(Note that we are using a class width of 5.)
Answer: To create a grouped frequency distribution for the given data, we need to group the test scores into classes and count the frequency of each class.
The smallest test score is 62, and the largest test score is 98, so the range is 98 - 62 = 36. To create classes with a width of 5, we can start with the class containing the smallest test score, which is 60 to 64.
The complete grouped frequency distribution is:
Class Frequency
60 to 64 1
65 to 69 1
70 to 74 2
75 to 79 2
80 to 84 3
85 to 89 2
90 to 94 0
95 to 99 1
In the above table, the class represents the range of test scores, and the frequency represents the number of students who scored in that range.
Step-by-step explanation:
The area of an animal pen is 30 square feet. what are the legnths of the pen's sides if the pen has each given shape?
L = 1.3245 is the legnths of the pen's sides .
What is area and perimeter?
Perimeter is the distance around the outside of a shape. Area measures the space inside a shape.
The equation for perimeter is 2L + W = 30 ( I'm assuming that the shed takes up one of the Widths, but you can use the Length if you want, it doesn't matter.)
So W = 30 - 2L.
Area = L x W = L (30 - 2L) = 30L - 2L^2.
This is a quadratic equation, easily graphed as a parabola, with a maximum point at L = 1.3245 .
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Which set of numbers contains only solutions to the inequality 2-3x > 17 ?
Ox=-5, -3, 0, 1
Ox=-12, 9, 8, 5
Ox=-9, -8, -7, -6
Ox= -2, 1, 0, 1
An inequality is a relation that makes a non-equal comparison between two numbers. Hence, option third is the correct answer i.e., \(x=-9,-8,-7,-6\)
What is inequality?
An inequality is a relation that makes a non-equal comparison between two numbers or other mathematical expressions.
Here given that,
\(2-3x > 17\\-3x > 17-2\\3x < -15\\x < -3\)
Hence, option third is the correct answer i.e., \(x=-9,-8,-7,-6\)
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It takes three minutes to
make four paper
valentines
How long will
it take to make eight?
Answer: six minutes
Step-by-step explanation: 8 / 4 = 2 , 3 x 2 = 6
If two events are mutually exclusive, they cannot be independent. True False 2. Suppose a class of 120 students took their statistics final and their grades are shown in the table below. (Enter your answers in three decimal places) (a) Choose one student at random. What is the probability that he/she received a B or a C? (Enter your answers in three decimal places) (b) What is the probability that a student selected at random passed the final (where a D is considered to be a not passing grade) (Enter your answers in three decimal places) (c) What is the probability that a student selected at random not passed the final (where a D is considered to be a not passing grade)? (d) D is considered to be a not passing grade. Assuming all students took exam independently. If random select three students, what is the probability that at least one of them passed the class? (e) D is considered to be a not passing grade. Assuming all students took exam independently. If random select three students, what is the probability that at least one of them failed the class? (f) What is the probability that two students selected at random both received A?
The statement that If two events are mutually exclusive, they cannot be independent is false. The probability are a) 0.49167 b) 0.8 c) 0.2 and
d) 0.674.
Let there be 2 mutually exclusive events A and B.
If the events are independent then,
P(A ∩ B) = P(A) X P(B)
Any set of events is called mutually exclusive if their intersection is 0
Hence,
P(A) X P(B) = 0
Therefore, two mutually exclusive events can be independent if the probability of one of them happening is 0.
Hence it's True.
2.
The total number of students is 120. The number of students to receive the grade:
A is 27
B is 32
C is 37
D is 15
F is 9
We can clearly say that if a student receives a grade A then they cannot receive a grade B, hence the events are mutually exclusive
a)
The probability that the students recieves a B or a C is
P(B U C) = P(B) + P(C)
= 32/120 + 27/120
= 59/120
= 0.49167
b) to pass a final, a students needs to get A, B, or C. Hence we get
P(A U B UC) = P(A) + P(B) + P(C)
= 59/120 + 37/120
= 96/120
= 0.8
c)
clearly, if a person has not passed he has failed. Hence we get
P(not Pass) = 1 - P(Pass) = 1 - 0.8
= 0.2
d)
Since the probability of one student to pass is 0.8, the probability that among three students, atleast one has passed is
P(none pass) + P(one passed) + P(2 passed) + P(three passed)
= 0.2 X 0.2 X 0.2 + 0.8 X 0.2 X 0.2 + 0.8 X 0.8 X 0.2 + 0.8 X 0.8 X 0.8
= 0.002 + 0.032 + 0.128 + 0.512
= 0.674
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an ice chest contains 8 cans of coke, 3 cans of pepsi, and 2 cans of 7up. what is the probability of pulling out an 7up
The probability of pulling out an 7up from the ice chest that contains the different drinks is 2/13.
What is the probability?Probability determines the odds that an event would happen. The probability the event occurs is 1 and the probability that the event does not occur is 0.
The probability of pulling out an 7up = number of 7ups / total number of drinks
2/(8 + 3 + 2)
2/13
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Does this graph represent a function? Why or why not?
OA. Yes, because it passes the vertical line test.
OB. Yes, because it is a curved line.
OC. No, because it is not a straight line.
OD. No, because it fails the vertical line test.
This graph represents a function Because it passes the vertical line test.
Let us first understand the Vertical Line Test.
In this test, we draw a few random vertical lines on a graph and check whether any one or more than one lines intersect the graph, no matter once or more.
If there exists a line that intersects the graph, we say the graph passes the vertical line test.
What is the vertical line test?
The vertical line test is a visual way to determine if a curve is a graph of a function or not. A function can only have one output, y, for each unique input, x.
Hence this graph passes the vertical line test because there are many vertical lines that intersect it.
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The AID Parcel Service wants to build a new distribution center in Charlotte. The center needs to be in the vicinity of Inerstate-77 and Intersatate-85 interchanges, and the Charlotte International Airport. The coordinates of these three sites and the number of weekly packages that flow to each are as follows:
I-77 I-85 Airport
X=16 X=35 X=40
Y=28 Y=10 Y=18
W=26,000 W=12,000 W=10,000
Determine the best site location using the center-of-gravity technique
Subject - Logistics management
Using the center-of-gravity technique, the best site location for the new distribution center in Charlotte is determined to be at coordinates (X, Y) = (27.92, 19.08).
The center-of-gravity technique is used to find the optimal location for a facility based on the distribution of demand. In this case, we will calculate the weighted average of the coordinates (X, Y) of the three sites, with the weights being the number of weekly packages flowing to each site.
To calculate the X-coordinate of the center of gravity, we use the formula:
Xc = (X1 * W1 + X2 * W2 + X3 * W3) / (W1 + W2 + W3)
Similarly, for the Y-coordinate:
Yc = (Y1 * W1 + Y2 * W2 + Y3 * W3) / (W1 + W2 + W3)
Substituting the given values:
Xc = (16 * 26000 + 35 * 12000 + 40 * 10000) / (26000 + 12000 + 10000) ≈ 27.92
Yc = (28 * 26000 + 10 * 12000 + 18 * 10000) / (26000 + 12000 + 10000) ≈ 19.08
Therefore, the best site location for the new distribution center in Charlotte is approximately at coordinates (X, Y) = (27.92, 19.08) based on the center-of-gravity technique.
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Of the 75 employees in the office building in dc, 40 had taken the subway to work sometime during the past year, 22 had taken the bus sometime during the past year, and 55 had taken either the subway or the bus or both to work last year. If one person is selected at random, show you work and find the following:
a) The probability that the person had taken both the subway and the bus.
b) The probability that the person had taken the bus but not the subway.
c) The probability that the person had taken neither the bus nor the subway
d) The probability that the person had not taken both the bus and the subway
Answer:
a)11/15
b)22/75
c)0/75
d)66/75
Step-by-step explanation:
a) Altogether, 55 people took the bus or the subway out of the 75 employees. As a fraction, this is 55/75 which can be simplified into 11/15
b) 22 out of the 75 people took the bus but not the subway. As a fraction, this is 22/75
c) Everyone took either the subway or the bus or both in the past year, meaning 0 out of 75 people took neither the subway, bus, or both. As a fraction, this is 0/75
d) The people who took the bus and the subway but not both would be 40+22 out of 75. As a fraction, this is 66/75
I hope this helps!
Answer:
a) P(Both) = 7/75
b) P(B&~S) = 1/5
c) P(~B&~S) = 4/15
d) P(~Both) = 68/75
Step-by-step explanation:
First, the 40 subway riders includes SubwayOnly people and also Subway&Bus...BOTH people.
Likewise, 22 bus people are BusOnly people as well as Bus&Subway--BOTH people.
So there is some overlap and we should sort that out before writing these probabilities. Let's use a Venn diagram.
40+22 is 62, but we know theres only 55 public transportation people. 62-55 is 7. Thats the overlap. There are 7 people who ride BOTH bus and subway. We put them in the middle and subtract to find the BusOnly and SubwayOnly people.
40 -7 is 33 SubwayOnly people.
22 - 7 is 15 BusOnly people.
55 people ride some public transpo, so 75 - 55 is 20 who people ride nothing (so cars or walkers).
Now we can write probabilities.
a) BOTH is 7/75
b) BusOnly is 15 people so probability is 15/75, which can be reduced so 15/75 = 1/5
c) NoBus and NoSub people are the 20 car or walkers. 20/75 = 4/15
NotBOTH people are the 20 (car/walkers) also the BusOnly and SubwayOnly. Thats 20+33+15, 68 people. Another way to think of it is ALL - 7 =
75 - 7 =
68 people, so the probability is 68/75.
also see image.
Write 2/8 in simplified form
Answer:
1/4
Step-by-step explanation:
because you basically divided by two on
Answer:
1/4 is the answer mark me brainliest
Find x, I’ll give brainliest I promise.
Answer:
x=16.5(or 17)
Step-by-step explanation:
2(x)+2(x-4)=58
2x+2x-8=58
4x-8=58
4x=66
x=16.5(if rounded to the nearest whole number will be 17)
ur welcome :)
brainliest please?
2, 8, 14, 20, 26... Look at the pattern above. What will the next number in the pattern be?
Answer:
32
Step-by-step explanation:
you just keep adding 6, simple :)
Answer:
32
Step-by-step explanation:
pattern: +6
∴ next number in pattern = 26 + 6
= 32
Find the measure. (Lesson 5-1)
TQ
If TQ = 2x - 6 and RQ = x + 3 then the measure of TQ = 12.
What is Perpendicular Bisector Theorem?The perpendicular bisector theorem states that if a point is on a segment's perpendicular bisector, it is equidistant from the segment's endpoints.
According to the perpendicular bisector theorem, any point on the perpendicular bisector is equidistant from both ends of the line segment on which it is drawn. If a pillar stands at an angle in the center of a bridge, all of its points will be equidistant from the bridge's end points.
Where, TQ = 2x - 6 and RQ = x + 3
By the Perpendicular Bisector Theorem, RQ = TQ.
2x - 6 = x + 3
x = 9
Substitute the value of x in TQ, we get
TQ = 2(9) - 6
= 18 - 6
= 12
Therefore, the value of TQ = 12.
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Two functions represent the composite function h(x) = (x – 1)³ + 10 so that h(x) = (g compose f)(x). Given f(x) = x + a and g(x) = x³ + b, what values of a and b would make the composition true? a = b =
Answer:
a = -1 and
b = 10
Step-by-step explanation:
Given:
h(x) = (x – 1)³ + 10
h(x) = (g compose f)(x).
f(x) = x + a and
g(x) = x³ + b
To find:
The values of a and b = ?
Solution:
First of all, let us have a look at the composite functions.
(g compose f)(x) means we replace the value of \(x\) with \(f(x)\) in the function \(g(x)\).
We know that:
\(g(x) =x^3+b\) and
\(f(x) = x + a\)
Let us find (g compose f)(x) by replacing \(x\) with \(x+a\)
\((g\ compose\ f)(x) = (x+a)^3+b\)
Also, h(x) = (g compose f)(x) = (x – 1)³ + 10
Therefore,
\((x - 1)^3 + 10 = (x+a)^3+b\)
Comparing the corresponding elements of the above expressions:
we get a = -1 and
b = 10
Answer:
a: -1
b: 10
edge 2020