You and your neighbor attempt to use your cordless phones at the same time. Your phones independently select one of ten channels at random to connect to the base unit. What is the probability that both phones pick the same channel
Answers
Answer:
1/100.
Step-by-step explanation:
So, we can make the following deductions from the information given in the question or problem above.
[1]. "You and your neighbor attempt to use your cordless phones at the same time."
DEDUCTION: Two people are involved, that is you and your neighbor are both involved.
[2]. "Your phones independently select one of ten channels at random to connect to the base unit. "
DEDUCTION: Both cordless phones can choose one channels each which is random. The number of channels available is ten.
Therefore, the probability that both your phone and your neighbor phone pick the same channel can be calculated or determined as follows:
The probability that both your phone and your neighbor phone pick the same channel = probability that both your phone will pick one channel out of the ten channels × the probability that your neighbor phone pick one channel out of the ten channels.
The probability that both your phone and your neighbor phone pick the same channel = 1/10 × 1/10 = 1/100.
Therefore, The probability that both your phone and your neighbor phone pick the same channel = 1/100.
Related Questions
3/16 divided by 2 1/4
Answers
Answer:
0.08333333333
Step-by-step explanation:
Stephanie has a spinner with sections labelled 1, 2 and 3.
She spun it 100 times and recorded how many times it landed on each section in
the table below.
Work out the relative frequency of landing on an odd number, giving your answer
as
a) a fraction in its simplest form.
b) a decimal.
Section
1
Frequency 17
2
20
3
63
Answers
Answer:
\(\frac{4}{5}\)
0.8
Step-by-step explanation:
Happy to help:)
Which angles below are equal to ∠CDB?
Answers
Answer:
(x) ∠CAB
Step-by-step explanation:
In ΔCOD and ΔBOA
\(\frac{OA}{OB} = \frac{OD}{OC} \\\\\implies \frac{OC}{OB} = \frac{OD}{OA}\)
Also,
∠COD = ∠BOA (vertically opposite angles)
⇒ ΔCOD and ΔBOA are similar
⇒ ∠CDO = ∠BAO
⇒ ∠CDB = ∠BAC
⇒ ∠CDB = ∠CAB
A donut store has 11 different types of donuts. You can only buy a bag of 3 of them, where each donut has to be of a different type from the rest. How many different bags of 3 can you make
Answers
Answer:
\(165\).
Step-by-step explanation:
Since repetition isn't allowed, there would be \(11\) choices for the first donut, \((11 - 1) = 10\) choices for the second donut, and \((11 - 2) = 9\) choices for the third donut. If the order in which donuts are placed in the bag matters, there would be \(11 \times 10 \times 9\) unique ways to choose a bag of these donuts.
In practice, donuts in the bag are mixed, and the ordering of donuts doesn't matter. The same way of counting would then count every possible mix of three donuts type \(3 \times 2 \times 1 = 6\) times.
For example, if a bag includes donut of type \(x\), \(y\), and \(z\), the count \(11 \times 10 \times 9\) would include the following \(3 \times 2 \times 1\) arrangements:
\(xyz\).\(xzy\).\(yxz\).\(yzx\).\(zxy\).\(zyx\).Thus, when the order of donuts in the bag doesn't matter, it would be necessary to divide the count \(11 \times 10 \times 9\) by \(3 \times 2 \times 1 = 6\) to find the actual number of donut combinations:
\(\begin{aligned} \frac{11 \times 10 \times 9}{3 \times 2 \times 1} = 165\end{aligned}\).
Using combinatorics notations, the answer to this question is the same as the number of ways to choose an unordered set of \(3\) objects from a set of \(11\) distinct objects:
\(\begin{aligned}\begin{pmatrix}11 \\ 3\end{pmatrix} &= \frac{11 !}{(11 - 3)! \times 3 !} \\ &= \frac{11 !}{8 ! \times 3 !} \\ &= \frac{11 \times 10 \times 9}{3 \times 2 \times 1} = 165\end{aligned}\).
7x+8y=18 Find the equation of the line which passes through the point (1,−13) and is parallel to the given line. Express your answer in slope-intercept form. Simplify your answer.
Answers
Answer:
y = -7/8x - 97/8
or 8y + 7x = -97
Step-by-step explanation:
7x + 8y = 18
=> 8y = -7x + 18
y = -7/8 + 18/8
If two lines are parallel, their slopes are equal. So slope is -7/8
given m = -7/8, y = -13, x = 1
y = mx + b
-13 = -7/8(1) + b
-13 = -7/8 + b
b = -13 + 7/8 = -104/8 + 7/8 = -97/8
so y = -7/8x - 97/8
=> 8y = -7x - 97
8y + 7x = -97
12. An office is divided into 8 cubicles. how many of the cubicles are carpeted if only 1/4 of the cubicles are carpeted?
Answers
Answer: The answer is 2 cubicles
Step-by-step explanation: To find how many cubicles are carpeted you must find what 1/4 of 8 is. In order to do that you must multiply 1/4 by 8.
To do this you must first turn 8 into 8/1 (they are both equal to the same value but it is easier to multiply in fraction form) and multiply it into 1/4
8 and 1 = 8 and 4 and 1 = 4, so you are left with 8/4 which is equal to 2
4. The moon’s diameter is approximately one-fourth the diameter of the earth. Compares the volumes of the moon and the earth.
Answers
Okay, here we have this:
Considering the provided information we obtain the following:
Let us take the diameter of the earth as d, so the diameter of the moon is d/4
Thus, the earth radius is d/2, and the moon radius is d/4/2=d/8.
Now, let's find the volume of the the earth and the moon separately to finally compare them:
\(\begin{gathered} \text{Volume of earth=}\frac{4}{3}\pi r^3 \\ =\frac{4}{3}\pi(\frac{d}{2})^3 \\ =\frac{1}{8}\cdot\frac{4}{3}\pi d^3 \\ =\frac{1}{6}\pi d^2 \end{gathered}\)\(\begin{gathered} \text{Volume of moon=}\frac{4}{3}\pi r^3 \\ =\frac{4}{3}\pi(\frac{d}{8})^3 \\ =\frac{1}{512}\cdot\frac{4}{3}\pi d^3 \\ =\frac{1}{384}\pi d^3 \end{gathered}\)Finally let's compare its volumes:
\(\begin{gathered} \frac{Volume\text{ of moon}}{Volume\text{ of earth}}=\frac{\frac{1}{384}\pi d^3}{\frac{1}{6}\pi d^3} \\ =\frac{1}{64} \end{gathered}\)Finally we obtain that the volume of the moon is 1/64 of the volume of the earth.
• 10%
5) An experiment consists of spinning the spinner shown below 200 times and recording the
results in a frequency table. Based on theoretical probability, how many times would you
expect the color blue or green to be spun?
BLUE
GREEN
YELLOW
REd
Answers
Based on their given probabilities, e would expect the color blue or green to be spun approximately 75 times in this experiment.
How many times can the blue or green color be obtained?To find the expected number of times the color blue or green will be spun, we first need to add their probabilities:
0.25 + 0.125 = 0.375
This means that, on average, we would expect to see blue or green spun 0.375 times for every spin. To find the expected number of times this will happen over 200 spins, we can multiply the probability by the number of spins:
0.375 x 200 = 75
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A rotating light is located 15 feet from a wall. The light completes one rotation every 4 seconds. Find the rate at which the light projected onto the wall is moving along the wall when the light's angle is 15 degrees from perpendicular to the wall.
Answers
To find the rate at which the light projected onto the wall is moving along the wall, we can use trigonometry and calculus. Let's denote the angle between the rotating light and the wall as θ.
Given:
Distance from the light to the wall, r = 15 feet
Rate of rotation, dθ/dt = 1 rotation every 4 seconds
We need to find the rate at which the light's projection moves along the wall, which is represented by dx/dt.
Using trigonometry, we know that the tangent of the angle θ is equal to the ratio of the distance along the wall (dx) to the distance from the light to the wall (r).
tan(θ) = dx / r
Differentiating both sides of the equation with respect to time t, we get:
sec^2(θ) * dθ/dt = dx/dt
Since we are given that the angle θ is 15 degrees, we can substitute the values and solve for dx/dt.
sec^2(15°) * (1 rotation / 4 seconds) = dx/dt
Simplify and calculate the value to find the rate at which the light's projection moves along the wall in feet per second.
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Identify whether each function is linear or exponential.
Function A:
Function C
Function D:
You have $200 in
a savings
account that
earns 1% annual
interest
b. Which function has the greatest growth factor? Justify your response.
Answers
Answer:
A)
Function A: Exponential
Function B: Linear
Function C: Exponential
Function D: Exponential
B) Function A
Step-by-step explanation:
Function A: This is exponential because- (1, 3)(2,9)(3,27)
It is not going up by the same number each time. However, it is multiplying by 3 each time which means it is exponential.
Function B: This is linear because- (1, 64)(1, 80)(1, 96)
It is going up by 16 each time, (a constant number) which means it is linear.
Function C: This is exponential because- there is a curve, linear is always a straight line. But, this has a curve which means it is exponential.
Function D: This is exponential because- It is increasing by a percentage and not a constant number. It is increasing by 1% which means it is exponential.
The function that has the greatest growth factor is Function A because, Function A multiplies by 3 each time. Function B is linear, exponential functions always pass linear functions despite how "steep" they are. Eventually, the exponential function will surpass it. Function C is also exponential but is not as "steep" as Function A. Function A multiplies by 3 each time but Function C increases less. Function D is also exponential, and for the same reasons as Function C, Function A has the greatest growth factor.
What is the x-intercept of the linear function y = 1/3x +1
Answers
Answer:
the x intercept is -3
or (-3,0)
Step-by-step explanation:
the x intercept is the point where the line crosses the x axis. The y value is zero, while x is a number.
Therefore, we can make y equal 0 in the function y=1/3x+1, since the point will pass through the line.
0=1/3x+1
subtract 1 from both sides
-1=1/3x
multiply by 3
-3=x
Therefore the x intercept is -3.
As a point is (-3,0)
hope this helps!
Jeanine deposits $525 in a bank account. The simple interest rate is 2 3/5% per year. Find the total amount in the account , including interest , in 6 months. Round your answer to the nearest cent
Answers
Given that the principal (P) is $525, rate of interest (R) is 2(3/5)%, and the time (T) is 6 months (i.e. 0.5 year).
Then the total interest (SI) on the principal is calculated as,
\(\begin{gathered} SI=\frac{P\times R\times T}{100} \\ SI=\frac{525\times(2\frac{3}{5})\times0.5}{100} \\ SI=\frac{525\times(\frac{13}{5})\times0.5}{100} \\ SI=\frac{525\times13\times0.1}{100} \\ SI=6.825 \end{gathered}\)Now, solve for the amount (A) as,
\(\begin{gathered} A=P+SI \\ A=525+6.825 \\ A=531.825 \\ A\approx531.82 \end{gathered}\)Thus, Jeanine will have $531.82 in the account at the end of the 6 months.in
Can someone help with this question?
Answers
Hubble's constant H is about 70 km/sec per megaparsec. (The prefix "mega" means million.) Convert this value for Hubble's constant to km/s/million LY. Hint: -A parsec is 3.26 light-years, and therefore a megaparsec is 3.26 million LY. If you take the given value of the Hubble constant (namely, 70 km/s per megaparsec) and replace the megaparsec with 3.26 million LY, then you will have converted to the desired units.
Answers
Hubble's constant in units of km/s/million LY is approximately 21.47.
what is approximately ?
Approximately means close to or nearly, but not exactly. It is used to indicate that a value or number is an estimation or approximation, rather than an exact value. It is often used when a precise value is not necessary or when the exact value is unknown or difficult to determine.
In the given question,
To convert Hubble's constant from km/s/Mpc to km/s/million LY, we need to multiply it by a conversion factor that accounts for the difference in distance units. We can use the fact that 1 Mpc is equal to 3.26 million LY:
1 Mpc = 3.26 million LY
Therefore, to convert Hubble's constant from km/s/Mpc to km/s/million LY, we can use the following conversion factor:
1 Mpc / 3.26 million LY
Multiplying Hubble's constant by this conversion factor gives:
H = 70 km/s/Mpc x (1 Mpc / 3.26 million LY) = 21.47 km/s/million LY
Therefore, Hubble's constant in units of km/s/million LY is approximately 21.47.
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Here is the histogram of a data distribution.What is the shape of this distribution?A.Unimodal skewed rightB.UniformC.Unimodal skewed leftD.BimodalE.Unimodal symmetric
Answers
Answer:
D. Bimodal
Explanation:
The given histogram has two creast, each crest represent a mode. So, we can say that this is a bimodal graph. Therefore, the answer is
D. Bimodal.
5. What is the correlation coefficient for the given data?
Answers
Let us plot the data on the graph to obtain its correlation coefficient.
5) 'r' is known to be the symbol for the correlation coefficient.
Hence, the correlation coefficient from the graph is
\(r=0.9741\)6) There is a strong correlation for the data set because the r-value is larger than 0.7 which is close to +1.
The backyard of a new home is shaped like a trapezoid with a height of 44 nt and bases of 86ft and 106ft What is the cost of putting sod on the yard, if the
landscaper charges $0.25 por square foot for sod?
Answers
Answer:
Step-by-step explanation:
Area of a trapezoid is the average length of the bases times the height
C = A(0.25)
A = ½(86 + 106)(44) = 4224 ft²
C = 4224(0.25) = $1056.00
I WILL GIVE 30 POINTS TO THOSE WHO FILL IN THE BLANKS CORRECTLY NOOOO SCAMS
Answers
Answer:
864 in^2
Step-by-step explanation:
Area of triangle
15 x 18 x 1/2 = 135
Area of Square
18 x 18 = 324
There are 4 triangles so...
135 x 4 = 540
Therefore the area is
540 + 324 = 864
A total of 27 students are in your class. There are nine more males than females.
How many females are in your class?
Answers
An odometer shows that a car has traveled 41,00$ miles by January 1, 2020. The car travels 19,000 miles each year. Write an equation that represents the number y of miles on the car’s odometer x years after 2020.
Answers
The required equation for number of miles and years for the car is given as; y = 19000x + 41000
How to represent a linear equation?To represent a straight line on a graph consider two points namely x and y intercepts of the line. To find x-intercept put y = 0 and for y-intercept put x = 0. Then draw a line passing through these two points.
The parameters are;
Suppose the year 2020 represents x = 0.
The distance travelled per year can be taken as the slope of the linear equation. Thus, slope = 19000.
And, the distance travelled by January 1, 2020 is 41000.
This tells us that for x = 0, y = 41000.
The linear equation in slope intercept form is given as;
y = mx + c
where;
m is slope
c is y-intercept
Substitute the corresponding values in the above equation to obtain,
y = 19000x + c
At x = 0, y = 41000
41000 = (19000 × 0) + c
c = 41000
Now, the equation can be written as,
y = 19000x + 41000
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Callie has a new kitten. The kitten weighs 3 pounds less than half the weight of Callie’s cat. Together, the cat and the kitten weigh 18 pounds. Which system of equations could be used to find the weight of each animal?
A. y=\(\frac{1}{2}\)x+3
y=-x+18
B. y=\(\frac{1}{2}\)x+3
y=x+18
C. y=\(\frac{1}{2}\)x-3
y+x=18
Answers
Answer:
c
Step-by-step explanation:
if Callie's cat is x and the question says that the kitten is 3 pound less than half(1/2) of x it will then be half of 1/2 of x then - 3(to get the kittens weight)
the if both cats weight 18 it'll be x+y
A message is coded into the binary symbols 0 and 1 and the message is sent over a communication channel.
The probability a 0 is sent is 0.4 and the probability a 1 is sent is 0.6. The channel, however, has a random error that
changes a 1 to a 0 with probability 0.1 and changes a 0 to a 1 with probability 0.2. Show your work below.
a. What is the probability a 1 is received?
b. If a 1 is received, what is the probability a 0 was sent?
Answers
Answer:
A: the probability that a 1 is received is 0.56.
B: the probability that a 0 was sent given that a 1 is received is (2/25) * (1 - P(0 sent)).
Step-by-step explanation:
To solve this problem, we can use conditional probabilities and the concept of Bayes' theorem.
a. To find the probability that a 1 is received, we need to consider the two possibilities: either a 1 was sent and remained unchanged, or a 0 was sent and got flipped to a 1 by the random error.
Let's denote:
P(1 sent) = 0.6 (probability a 1 is sent)
P(0→1) = 0.2 (probability a 0 is flipped to 1)
P(1 received) = ?
P(1 received) = P(1 sent and unchanged) + P(0 sent and flipped to 1)
= P(1 sent) * (1 - P(0→1)) + P(0 sent) * P(0→1)
= 0.6 * (1 - 0.2) + 0.4 * 0.2
= 0.6 * 0.8 + 0.4 * 0.2
= 0.48 + 0.08
= 0.56
Therefore, the probability that a 1 is received is 0.56.
b. If a 1 is received, we want to find the probability that a 0 was sent. We can use Bayes' theorem to calculate this.
Let's denote:
P(0 sent) = ?
P(1 received) = 0.56
We know that P(0 sent) + P(1 sent) = 1 (since either a 0 or a 1 is sent).
Using Bayes' theorem:
P(0 sent | 1 received) = (P(1 received | 0 sent) * P(0 sent)) / P(1 received)
P(1 received | 0 sent) = P(0 sent and flipped to 1) = 0.4 * 0.2 = 0.08
P(0 sent | 1 received) = (0.08 * P(0 sent)) / 0.56
Since P(0 sent) + P(1 sent) = 1, we can substitute 1 - P(0 sent) for P(1 sent):
P(0 sent | 1 received) = (0.08 * (1 - P(0 sent))) / 0.56
Simplifying:
P(0 sent | 1 received) = 0.08 * (1 - P(0 sent)) / 0.56
= 0.08 * (1 - P(0 sent)) * (1 / 0.56)
= 0.08 * (1 - P(0 sent)) * (25/14)
= (2/25) * (1 - P(0 sent))
Therefore, the probability that a 0 was sent given that a 1 is received is (2/25) * (1 - P(0 sent)).
A message is coded into the binary symbols 0 and 1 and the message is sent over a communication channel. The probability a 0 is sent is 0.4 and the probability a 1 is sent is 0.6. The channel, however, has a random error that changes a 1 to a 0 with probability 0.2 and changes a 0 to a 1 with probability 0.1. (a) What is the probability a 0 is received? (b) If a 1 is received, what is the probability a 0 was sent?
4. Chelsea determined that the value of x in the triangle at the right was 5.
a. Find the value of each angle by substituting 5 for x.
b. Was Chelsea's solution, x = 5, correct? How do you know?
15x
x
11x
(8x+5)
Z
Answers
Step-by-step explanation:
a) 11*5=55
15*5=75
8*5+5=45
b) No, because (55+75+45=175°) and the perimeter of a triangle is 180°
Simplify using the order of operations. 2+6*8=
Answers
Answer:
The answer is 50.
Step-by-step explanation:
Use MDAS
Multiplication, Division, Addition and Subtraction
2 + 6 * 8 =
Multiply first then add
2 + 6*8 = ?
= 2 + 48
= 50
5.
Which value of x would satisfy this inequality?
V3
4
2
A А.
С
D
000
4
10
Answers
Answer:
C) 4/5
Step-by-step explanation:
pi/4 = 0.7853981634
\(\frac{\sqrt{3} }{2}\) = 0.8660254038
3/4 = 0.75. It's less than pi/4, so not correct
9/10 = 0.9. It's more than 0.866, so not correct
4/5 = 0.8. It's right for both condition
8/9 = 0.888. It's more than 0.866, so not correct.
n Studies / 22FYF013/ Chapter 2: Statistics STACK statistics pr
The numbers of days work missed by 20 workers in one year (ordered by size) we
[0, 0, 0, 0, 0, 1, 1, 2, 3, 4, 4, 4, 4, 4, 4, 5, 6, 6, 8, 55]
Calculate the mean and median. Enter your answers to 1 d.p.
Mean =
Median =
Please answer all parts of the question
Answers
The mean and median of the given data set are 5.55 and 4.
What are the mean and median?A data set's mean (average) is calculated by adding all of the numbers in the set, then dividing by the total number of values in the set. When a data set is ranked from least to greatest, the median is the midpoint. Identifying the median The data points should be arranged from smallest to largest. The median is the middle data point in the list if the number of data points is odd. The median is the average of the two middle data points in the list if the number of data points is even.So, the data is:
[0, 0, 0, 0, 0, 1, 1, 2, 3, 4, 4, 4, 4, 4, 4, 5, 6, 6, 8, 55](A) Mean of data:
Sum of all terms/number of terms111/205.55(B) Median of data:
The data set has even terms.Average of two middle terms:4 + 4 / 28/24Therefore, the mean and median of the given data set are 5.55 and 4.
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7 There are five women and six men in a group. From this group a committee of 4 is to be chosen. In how many different ways can a committee be formed that contain at least three women?
Answers
Answer:
in three (3) ways a committee can formed
Essential Question How can you write an algebraic expression?
Answers
Answer:
Step-by-step explanation:
In algebraic expressions that use variables (written as letters), you can write them directly after a normal number, with no symbol between them.
...
Use a ⋅ or × sign if you see words like double, per, or product.
Twice 16 → 2 ⋅ 16.
Five per day → 5 ⋅ d or 5d. ...
The product of 8 and 20 → 8 ⋅ 20.
Evaluate the variable expression x + y for the given values of x and y. x = 38,221; y = 51,671
Answers
Answer:
89,892
Step-by-step explanation:
\(x+y\)
\((38,221)+(51,671)\)
\(89,892\)
A man wants to cut down a tree in his yard. To ensure that the tree doesn’t hit anything, he needs to know the height of the tree. He measures his distance from the tree at 13 meters and the angle of elevation to the tree at 53°. What is the height of the tree to the nearest tenth of a meter
Answers
The height of the tree to the nearest tenth of a meter is 73.7m
What is angle of elevation?The angle formed by the line of sight and the horizontal plane for an object above the horizontal.
Given:
base = 13 m
angle of elevation = 53
Using trigonometry
tan 53 = P/B
5.671 = P/ 13
P= 5.671 * 13
P= 73.723
Hence, the height of the tree is 73.7 m.
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