Answer: 1/2
Step-by-step explanation:
Scale factor = (image)/(preimage) = 6/12 = 1/2
For each of the following distance matrices of graphs, identify the diameter, radius and center. Assume the graphs vertices are the numbers 1 through
For each of the following distance matrices of graph, the
The diameter = 3The radius of the graph is given as 2What is the diameter of the graph?This is used to refer to the fact that there would be a maximum distance that exists between the pair of vertices.
What is the radius of the graphThis used to refer to the minimum eccentricities of the vertices
What is the center of the graph?This is used to show all of the vertices that have minimum eccentricities.
How to solve the matrixWe have
e 1 = 3
e 2 = 3
e3 = 2
e4 = 3
e 5 = 3
e 6 = 3
e 7 = 3
e8 = 2
e 9 = 3
e 10 = 2
Then the the diameter = maximum eccentricity = 3
The radius = minimum eccentricity = 2
center = [3, 8,10]
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model aeroplane is made to a scale of 1 by two of the size of the real plane the area of the wings of the real plane are 40 m square find the area of the wings of the model in centimetre square
The area of the wings of the model is 100000 square centimeters
How to determine the model area of the wings?The given parameters are:
Scale factor, k = 1/2
Actual area of wings, A = 40 square meters
The model area is calculated as
Model area = Actual area * k^2
This gives
Model area = 40 * (1/2)^2
Evaluate
Model area = 10 square meters
Convert square meters to square centimeters
Model area = 10 * 10000 square centimeters
Evaluate
Model area = 100000 square centimeters
Hence, the area of the wings of the model is 100000 square centimeters
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Given the series 2 two-thirds startfraction 4 over 9 endfraction startfraction 8 over 27 endfraction startfraction 16 over 81 endfraction startfraction 32 over 243 endfraction ellipsis, which partial sums are correct? check all that apply. s1 = 2 s2 = 4 s subscript 3 = startfraction 28 over 9 endfraction s subscript 4 = startfraction 10 over 9 endfraction s subscript 6 = startfraction 292 over 81 endfraction
The partial sums are correct are That is: (2) and (28/9).
What is a partial sum?A partial sum (simply put) refers to the sum of the various parts that make up a sequence. One of a series of sums of elements of a given sequence, the first sum being the first element, the second sum being the first element added to the second element, the third sum being equal to the sum of the first three elements, and so on.A partial sum of an infinite series is the sum of a finite number of consecutive terms beginning with the first term. When working with infinite series, it is often helpful to examine the behavior of the partial sums.A partial sum would be:
2 + (2/3).
In this case, thus,
Series 1 = 2 - This is correct.
Series 2 = 2 + (2/3) = 8/3 - incorrect
Series 3 = (8/3) + (4/9) = (28/9) Correct
Series 4 = (28/9) + (8/27) = (92/27)
Series 5 = (92/27) + (16/81) = 292/81
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Find unknown angle
kº
68°
kº
Answer:
k = 56
Step-by-step explanation:
2k + 68 = 180
2k = 112
112 ÷ 2 = 56
k = 56
The mean of three numbers is 10 more than the least of the numbers and 15 less than the greatest. The median of the three numbers is 5. What is their sum
Answer:
Sum is
Step-by-step explanation:
In 2020 Ashmija invested $10,000 into an account which is growing at 4.5% annually.
Write an equation to model the amount of money in her account D(t), with respect to time, t. Explain what the values represent. [4 Marks]
Use your equation to find how much she will make in 2050 assuming she hasn't made any withdrawals or extra deposits. [3 marks]
The exponential function that models this situation is:
[tex]D(t) = 10000(1.045)^t[/tex]
Using the function, in 2050, she will have $37,453.
What is an exponential function?An increasing exponential function is modeled by:
[tex]A(t) = A(0)(1 + r)^t[/tex]
In which:
A(0) is the initial value.r is the growth rate, as a decimal.For this problem, the parameters are:
A(0) = 10000, r = 0.045.
Hence the equation is:
[tex]D(t) = 10000(1.045)^t[/tex]
2050 is 30 years after 2020, hence the amount is:
[tex]D(30) = 10000(1.045)^{30} = 37453[/tex]
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When bowling, the scoring rule for a spare is 10 points and then the points scored in the next delivery. Group of answer choices True False
The given statement is True for the scoring rule in bowling.
Scoring Rule in Bowling
The number of frames in a game of bowling is ten. According to the scoring rule in bowling, the bowler will have two opportunities to use their bowling ball to remove as many pins as they can throughout each frame.
Every bowler will complete their frame in a predefined order before the next frame starts in games with more than one bowler, which is typical.
Rule for Spare
A bowler is given a strike if they can remove all 10 pins with their first ball. A spare is achieved when the bowler uses both of the two balls in a frame to remove all 10 pins.
Depending on whether the next two balls (for a strike) or the next ball (for a goal) are scored, bonus points are given for both of these (for a spare), as per the scoring rule.
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The angle measurements in the diagram are represented by the following expressions.
Answer:
since those 2 lines are parrelel that means the angles are the same so
8x+6=4x+38
minus 6
8x=4x+32
minus 4x
4x=32
divide by 4
x=8
Hope This Helps!!!
The value of the x is 11 and the measure of the angle B is 82 degrees.
What are vertically opposite angles?It is defined as the angles when two lines intersect each other and at the intersecting point, some pair of angles are formed which we call vertically opposite angles, as the name describes that they have vertically opposite angles.
We have:
The angle measurements in the diagram are represented by the following expressions:
Angle A = 8x - 6
Angle B = 4x + 38
By using the vertically opposite angle property in angle B
As we know the alternate exterior angle are equal
8x - 6 = 4x + 38
4x = 44
x =11
Measure of angle B = 4(11) + 38 = 82 degrees
Thus, the value of the x is 11 and the measure of the angle B is 82 degrees.
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Someone help me with a step by step explanation to simplifying
100x(5 - 3p)
ty
Answer:
500x - 300xp.
Step-by-step explanation:
100x(5 - 3p)
First distribute the 100x over the parentheses:
= 100x*5 - 100x * 3p
Now simplify:
= 500x - 300xp.
The ages of all employees at a small convenience store are 36, 32, 38, and 28. What is standard deviation of ages for this population
The standard deviation is approximately 3.84
Step 1: Find the mean
Find the sum of the values, and divide by number of terms.
Mean (average) = (36+32+38+28)/4 = 134/4 = 33.5
We must use Standard Deviation formula which is attached as an image below.
X is the mean here, so lets plug in 33.5
Step 2. Distance from the mean squared |x-mean∣²
For each data point, we will plug in the numbers.
|36-33.5|²=2.5²=6.25
|32-33.5|²=1.5²=2.25
|38-33.5|²=4.5²=20.25
|28-33.5|²=5.5²=30.25
Step 3: Find the sum (∑)
We find the sum here by adding all the distances from the mean squared
∑|x-mean|²=59
Step 4: Divide the sum by the amount of points, 4
59/4=14.75
Step 5: Take the square root of step 4
[tex]\sqrt{14.75}[/tex] is about 3.84
The standard deviation is approximately 3.84
find the value of x from the figure
Answer:
x = 30
Step-by-step explanation:
110 and 3x - 20 are supplementary angles, sum to 180° , then
110 + 3x - 20 = 180
90 + 3x = 180 ( subtract 90 from both sides )
3x = 90 ( divide both sides by 3 )
x = 30
Answer:
x = 30
Step-by-step explanation:
Please refer to the attached photo. (Apologies for the terrible drawing.)
For this question, you must be clear of the angle properties.
z + 110 = 180 (Sum of Angles on a straight line)
z = 180 - 110 = 70
z = 3x - 20 (Corresponding Angles)
3x - 20 = z
3x - 20 = 70
3x = 70 + 20
3x = 90
x = 90 / 3 = 30
To remain a member of the student council, a student must attend at least Three-fourths of the activities. Joey attends 15 of the activities and remains on the student council. Which inequality represents the total amount of student council activities, a?
Answer:
20
Step-by-step explanation:
so we need to see that
3/4 x ? = 15
so we say
3 x ? = 15x4
? =60/3
?= 20
Find the length of JN
The length of JN from the figure is 108
Measure of segment of a lineA line is the shortest distance between two points. Given the following parameters
Required
We need the length of JN
JN = JK + KN
JN = 59 + 49
JN = 108
Hence the length of JN from the figure is 108
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Plis help! Will give brainliest! 5th grade math!
Answer:
(32÷(10-8)÷2)-3
Step-by-step explanation:
(32÷(10-8)÷2)-3
(32÷2÷2)-3
(16÷2)-3
8-3 = 5
✅
All the events in the sample space that are not part of the specified event are called _____. Group of answer choices joint events the complement of the event simple events independent events
All the events in the sample space that are not part of the specified event are called Complement of Event.
Complement of event:
The complement of an event is the subset of outcomes in the sample space that are not in the event. A complement is itself an event. The complement of an event A is denoted as A c A^c Ac or A′. An event and its complement are mutually exclusive and exhaustive.
Two events are said to be complementary when one event occurs if and only if the other does not. The probabilities of two complimentary events add up to 1. For example, rolling a 5 or greater and rolling a 4 or less on a die are complementary events, because a roll is 5 or greater if and only if it is not 4 or less.
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Sarah has just opened her own nail salon. Based on experience, she knows that her daily profit, P, can be modelled by = −122 + 168 − 510, where x is the number of clients per day. How many clients should she book each day to maximize her profit?
Answer:
Step-by-step explanation:
p=-12x^2 + 168 - 510
isolate the varible by diveding each side by factors that dont conatin the varible
x= square root of -p+342/3/2
x= - square root of -p+ 342/3/2
I hope this has helped if you need any clarfcation just ask
is P - 1 upon p = 4 find P + 1 upon p whole square
Given that (p - 1/p) = 4, the value of p² + 1/p² is 18. Detail below
Data obtained from the questio(p - 1/p) = 4p² + 1/p² = ?How to determine the value of p² + 1/p²(p - 1/p) = 4
Square both sides
(p - 1/p)² = (4)²
(p - 1/p)² = 16 ....(1)
Recall
(a - b)² = a² + b² - 2ab
Thus,
(p - 1/p)² = p² + 1/p² - (2 × p × 1/p)
(p - 1/p)² = p² + 1/p² - 2
From equation (1) above,
(p - 1/p)² = 16
Therefore,
p² + 1/p² - 2 = 16
Rearrange
p² + 1/p² = 16 + 2
p² + 1/p² = 18
Thus, the value of p² + 1/p² is 18
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Sound the loudness of a sound l in decibels is defined by l= 10 log.r, where r is the relative intensity of the sound. a chofr director wants to determine how many members could sing while maintaining a safe level of sound, about 80 decibels. if one person has a relative intensity of 10 when singing, then how many people could sing with the same relative intensity to achieve a loudness of 80 decibels?
Around 298 people can sing together with the same relative intensity to achieve a loudness of 80 decibels.
Given Information
Loudness of sound is given as, l = 10 log₁₀r
Here, r is the relative intensity.
Relative intensity of a single person when singing = 10
Loudness to be achieved, L = 10 decibels
Calculating the Number of People
Let the number of people with relative intensity 10 singing together be n decibels, then to produce a loudness of 80 decibels, we have,
80 = 10 log₁₀(r × n)
80 = 10 log₁₀(10 × n) [∵ r = 10]
log₁₀(10 × n) = 8
10n ≈ 2980
n = 298
Therefore, 298 people, each with a relative intensity of 10 decibels can sing together to achieve a loudness of 80 decibels.
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Aster first walks 70m in the direction of 37degree north of east then walks 82m 20 degree south of east ,and finally walks 28m inthe direction of 30 degree west of north ,find displacement and angle from initial point ?
Answer:
Step-by-step explanation:
The displacement is 90.7 meter from initial point.
According to the statement
Aster first walks 70m in the direction of 37 degree north of east
Aster walks 82m 20 degree south of east
Aster finally walks 28m in the direction of 30 degree west of north
We use
β= 37 degree +(30 degree −20 degree) = 47 degree
We can use cosine law to solve for R.
R = ((A)^2 + (B)^2 + 2ABcosβ)^1/2
R = ((70)^2 + (28)^2 + 2*70*28cos47)^1/2
R = (4900 + 784 + 3920*0.682)^1/2
R = (4900 + 784 + 2673.5)^1/2
R = (8357.5)^1/2
R = 90.7 m
So, The displacement is 90.7 meter from initial point.
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Four different sets of objects contain 4,5,6, and 8 objects respectively. how many unique combinations can be formed by picking one object from each set?
A. 23
B. 141
C.960
D. 529
The number of unique combinations that can be formed by picking one object from each set is =960. That is option C.
Calculation of unique combinations of a number setNumber combination is a mathematical technique that shows the number of possible arrangements in a collection of items.
The first set of objects = 4. There are a total of 4 possibilities.
The second set of objects = 5. There are a total of 5 possibilities
Therefore from first and second set, the total number of possibilities = 4×5 = 20
For the whole set, the total possibilities;
= 4×5×6×8
= 960
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The lengths of two sides of a triangle are shown below:
Side 1: 3x² - 2x - 1
Side 2: 9x + 2x² - 3
The perimeter of the triangle is 5x³+4x2 - x - 3.
Part A: What is the total length of the two sides, 1 and 2, of the triangle? (4 points)
Part B: What is the length of the third side of the triangle? (4 points)
Part C: Do the answers for Part A and Part B show that the polynomials are closed under
addition and subtraction? Justify your answer. (2 points)
(10 points)
Part A
[tex]3x^2 -2x-1+9x+2x^2 -3=\boxed{5x^2 + 7x-4}[/tex]
Part B
[tex](5x^3 +4x^2 - x-3)-(5x^2 + 7x-4)=\boxed{5x^3 - x^2 - 8x+1}[/tex]
Part C
No, because although they provide examples for specific polynomials being closed under addition and subtraction, there is a loss of generality.
Find the perimeter of a parallelogram with corner points at (2,1), (4,5), (7,5), and (5,1)
Perimeter =
THANK YOU SO MUCHHH
Answer:
14 units
Step-by-step explanation:
Oops, I was solving for the area in the picture. You can still use the picture to find the perimeter. When I change the shape into a rectangle, you can see that the top and bottom lengths are 3 and the side lengths are 4. 3+3+4+4=14
you generate electricity with your own personal wind turbine? That depends on whether you have enough wind on your site. To produce enough energy, your site should have an annual average wind speed of at least 8 miles per
ding to the Wind Energy Association. One candidate site was monitored for a year, with wind speeds recorded every 6 hours. A total of 1114 readings of wind speed averaged 8.019 mph with a standard deviation of 3.813 mph. Youl
I asked to make a statistical report to help the landowner decide whether to place a wind turbine at this site. Complete parts a and b below.
The 95% confidence interval of the statistics is (7.795, 8.243).
How to illustrate the information?Based on the information given, the 95% confidence interval will be:
= 8.019 + (1.962 × 3.183/✓1114)
= 8.243 and
= 8.019 - (1.962 × 3.183/✓1114)
= 7.795
In conclusion, the 95% confidence interval of the statistics is (7.795, 8.243).
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Which of the sets of ordered pairs represents a function?
A = {(−5, 5), (−2, 2), (2, −2), (5, −5)}
B = {(4, 2), (3, −2), (9, 4), (11, −3)}
Only A
Only B
Both A and B
Neither A nor B
Answer:
Both A and B
Step-by-step explanation:
A set of ordered pairs is not a function if there is a repeating output (Y value.)
Y values of A= 5, 2, -2, -5.
Y values of B= 2, -2, 4, -3.
There are no repeating outputs.
Find the center and radius of the circle with the equation: (x-5)^2 + (y+1)^2 = 4 a. center: (-5, 1) radius: 4 c. center: (-5, 1) radius: 2 b. center: (5, -1) radius: 4 d. center: (5, -1) radius: 2
Answer:
d
Step-by-step explanation:
the equation of a circle in standard form is
(x - h)² + (y - k)² = r²
where (h, k ) are the coordinates of the centre and r is the radius
(x - 5 )² + (y + 1)² = 4 ← is in standard form
with centre (5, - 1 ) and r = [tex]\sqrt{4}[/tex] = 2
A coin is flipped, and a number cube is rolled. what is the probability of getting tails on the coin and an even number on the number cube?
The probability of getting tails on the coin and an even number on the number cube is 1/4
What are probabilities?Probabilities are used to determine the chances, likelihood, possibilities of an event or collection of events
How to determine the probability?The sample space of a coin is:
S = {H, T}
The sample space of a die is:
S = {1, 2, 3, 4, 5, 6}
The above means that:
A coin has 2 faces, one of which is the tail.
So, we have:
P(Tail) = 1/2
A number cube has 6 numbers, 3 or which are even.
So, we have
P(Even) = 3/6
The required probability is
P = P(Tail) * P(Even)
This gives
P = 1/2 * 3/6
Evaluate
P = 1/4
Evaluate the quotient
P = 0.25
Hence, the probability of getting tails on the coin and an even number on the number cube is 1/4 or 0.25
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Select the correct answer. which expression is equivalent to , if x > 0? a. b. c. d.
The equivalent expression of the expression is 128x^5y^6/2x^7y^5
How to determine the equivalent expression?The expression is given as:
128x^5y^6/2x^7y^5
Divide 128 by 2
64x^5y^6/x^7y^5
Apply the law of indices
64y^(6-5)/x^(7-5)
Evaluate the differences
64y/x^2
Hence, the equivalent expression of the expression is 128x^5y^6/2x^7y^5
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Complete question
Select the correct answer. which expression is equivalent to 128x^5y^6/2x^7y^5 , if x > 0 and y > 0
Unoccupied seats on flights cause airlines to lose revenue. Suppose a large airline wants to estimate its mean number of unoccupied seats per flight over the past year. To accomplish this, the records of 225 flights are randomly selected and the number of unoccupied seats is noted for each of the sampled flights. The sample mean is 11.6 seats and the sample standard deviation is 4.1 seats. Assume the underlying population of unoccupied seats is normally distributed. Using a t- statistic, construct a 95% confidence interval for the population mean number of unoccupied seats per flight.
The given sample's 95% confidence interval is 11.6 ± 0.5357. I.e., from the lower bound 11.06 to the upper bound 12.14. Its margin error is 0.5357.
How to find the confidence interval?To find the confidence interval C.I,
Determine the mean(μ) of the sampleDetermine the standard deviation(σ)Determine the z-score for the given confidence level using the z-score tableUsing all these, the confidence interval is calculated by the formula, C. I = μ ± z(σ/√n) where n is the sample size and z(σ/√n) gives the margin error. So, we can also write C. I = mean ± margin error.Calculation:It is given that,
Sample size n = 225
Sample mean μ = 11.6
Standard deviation σ = 4.1
Since 95% confidence interval, z-score is 1.96
So, the required confidence interval is calculated by,
C. I = μ ± z(σ/√n) or mean ± margin error
On substituting,
C. I = 11.6 ± 1.96(4.1/√225)
= 11.6 ± 1.96 × 0.2733
= 11.6 ± 0.5357
So, the lower bound = 11.6 - 0.5357 = 11.065 and
the upper bound = 11.6 + 0.5357 = 12.135.
Thus, the confidence interval is from 11.06 to 12.14, and its margin error is 0.0537 for the population mean number of unoccupied seats per flight.
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pls help
me find the volume
Answer:
FIRST
To find the volume of rectangular prism is
Volume = Length x Width x Height
Volume = 20cm x 10cm x 13cm
= 40 x 13
= 520cm cubic or cube
520 is the volume of the rectangular prism
the you divide volume of rectangular prism and volume of solid ball.
Correct me if i am wrong guys.
Answer:
It will take approximately take 17 balls to overflow the container
Step-by-step explanation:
Volume of the rectangle = 20x13x10 = 2600[tex]cm^{3}[/tex]
Volume of the water = 20x10x11 = 2200[tex]cm^{2}[/tex]
Amount of empty space = 2600-2200 = 400[tex]cm^{3[/tex]
Solid ball volume = 23[tex]cm^{3}[/tex] each
To find how many balls can overflow the container = 400/23 = 17.39
URGENT!, will mark brainiest!
Use the box plots comparing the number of male pets and number of female pets attending doggy daycare each day for a month to answer the questions. Two box plots shown.
The top one is labeled Males. Minimum at 1, Q1 at 3, median at 10.5, Q3 at 14, maximum at 21, and a point at 30.
The bottom box plot is labeled Females. Minimum at 0, Q1 at 15, median at 18, Q3 at 21, no maximum shown
Part A: Estimate the I Q R for the males' data. (2 points)
Part B: Estimate the difference between the median values of each data set. (2 points)
Part C: Describe the distribution of the data and if the mean or median would be a better measure of center for each. (4 points)
For the males' data, we can logically deduce the following data elements:
Upper quartile (Q₃) = 14Lower quartile (Q₁) = 2Mathematically, the male IQR can be calculated by using this formula:
IQR = Q₃ - Q₁
IQR = 14 - 2
Male IQR = 12.
Next, we would find the difference between the median values:
Note: The median of male's data is equal to 10 while median of female's data is equal to 18.
Difference, d = 18 - 10
Difference, d = 8.
The distribution of data.The male's data has an outlier probably due to sampling technique used while the female's data doesn't have an outlier. Thus, the median would be a better measure of center for the male's data and the mean being a better measure of center for the female's data.
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Answer: s
Step-by-step explanation: