The mode is 18.5.
What is mode?
In statistics, there are most repeated value among the given set of data. Those are called mode. Among the given set of data, mode is the value which has the maximum frequency. Sometimes, it may be possible to have more than one value which has the equal maximum frequency.
Formula for mode for grouped data is given by:
Mode = l + [(f₁-f₀)/(2f₁-f₀-f₂)]×h.-------------------(1)
Where, l = lower class limit of modal class, h = class size, f₁ = frequency of modal class, f₀ = frequency of class preceding to modal class, f₂ = frequency of class succeeding to modal class.
In the given problem l= 15.5
f₀= 8
f₁= 10
f₂= 8
h= 6
Putting all the values in equation (1) we obtain mode
mode= 15.5 +{(10-8)/(2×10-8-8)} ×6
= 15.5+(2/4)×6
= 15.5+ 3
= 18.5
Hence, the mode is 18.5.
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help plslslslsss giving out 11 points pls no links id appreciate it
The expression that is the difference of two squares is [tex]9a^2 - 4b^6[/tex]
How to find the expression that is the difference of two squares?The difference of two squares is an algebraic expression of the form a² - b², which can be factored as (a + b)(a - b).
Using this rule, we can determine which of the given expressions is the difference of two squares.
[tex]9a^2 - 4b^6[/tex] is the difference of two squares because [tex]9a^2[/tex] is a perfect square [tex](3a)^2[/tex]and [tex]4b^6[/tex] is a perfect square[tex](2b^3)^2[/tex]. Therefore, we can write:
[tex]9a^2 - 4b^6 = (3a + 2b^3)(3a - 2b^3)[/tex]
So, the expressions that are the difference of two squares is [tex]9a^2 - 4b^6[/tex]
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8 students are enrolled in a competition. they all solve the same 8 qs. after correction, it can be seen that each problem has been correctly solved by exactly 5 students. show that there are 2 students who, together, have solved all the problems?
Let's label the 8 questions as Q1, Q2, Q3, Q4, Q5, Q6, Q7, and Q8.
Let's label the 8 students as A, B, C, D, E, F, G, and H.
Since each problem has been correctly solved by exactly 5 students, we can say that the following is true:
Q1: A, B, C, D, E
Q2
Question 9(Multiple Choice Worth 2 points)
(Creating Graphical Representations LC)
A teacher was interested in the subject that students preferred in a particular school. He gathered data from a random sample of 100 students in the school and wanted to create an appropriate graphical representation for the data.
Which graphical representation would be best for his data?
Stem-and-leaf plot
Histogram
Circle graph
Box plot
Question 10(Multiple Choice Worth 2 points)
(Circle Graphs MC)
A New York City hotel surveyed its visitors to determine which type of transportation they used to get around the city. The hotel created a table of the data it gathered.
Type of Transportation Number of Visitors
Walk 120
Bicycle 24
Car Service 45
Bus 30
Subway 81
Which of the following circle graphs correctly represents the data in the table?
circle graph titled New York City visitor's transportation, with five sections labeled walk 80 percent, bus 16 percent, car service 30 percent, bicycle 20 percent, and subway 54 percent
circle graph titled New York City visitor's transportation, with five sections labeled walk 40 percent, bicycle 8 percent, car service 15 percent, bus 10 percent, and subway 27 percent
circle graph titled New York City visitor's transportation, with five sections labeled subway 40 percent, bus 8 percent, car service 15 percent, bicycle 10 percent, and walk 27 percent
circle graph titled New York City visitor's transportation, with five sections labeled subway 80 percent, bicycle 20 percent, car service 30 percent, bus 16 percent, and walk 54 percent
Question 11(Multiple Choice Worth 2 points)
(Circle Graphs LC)
Chipwich Summer Camp surveyed 100 campers to determine which lake activity was their favorite. The results are given in the table.
Lake Activity Number of Campers
Kayaking 15
Wakeboarding 11
Windsurfing 7
Waterskiing 13
Paddleboarding 54
If a circle graph was constructed from the results, which lake activity has a central angle of 54°?
Kayaking
Wakeboarding
Waterskiing
Paddleboarding
Question 12(Multiple Choice Worth 2 points)
(Making Predictions MC)
A recent conference had 750 people in attendance. In one exhibit room of 70 people, there were 18 teachers and 52 principals. What prediction can you make about the number of principals in attendance at the conference?
There were about 193 principals in attendance.
There were about 260 principals in attendance.
There were about 557 principals in attendance.
There were about 680 principals in attendance.
Question 13(Multiple Choice Worth 2 points)
(Making Predictions MC)
A college cafeteria is looking for a new dessert to offer its 4,000 students. The table shows the preference of 225 students.
Ice Cream Candy Cake Pie Cookies
81 9 72 36 27
Which statement is the best prediction about the number of cookies the college will need?
The college will have about 480 students who prefer cookies.
The college will have about 640 students who prefer cookies.
The college will have about 1,280 students who prefer cookies.
The college will have about 1,440 students who prefer cookies.
Question 15
The line plots represent data collected on the travel times to school from two groups of 15 students.
A horizontal line starting at 0, with tick marks every two units up to 28. The line is labeled Minutes Traveled. There is one dot above 4, 6, 14, and 28. There are two dots above 10, 12, 18, and 22. There are three dots above 16. The graph is titled Bus 47 Travel Times.
A horizontal line starting at 0, with tick marks every two units up to 28. The line is labeled Minutes Traveled. There is one dot above 8, 9, 18, 20, and 22. There are two dots above 6, 10, 12, 14, and 16. The graph is titled Bus 18 Travel Times.
Compare the data and use the correct measure of center to determine which bus typically has the faster travel time. Round your answer to the nearest whole number, if necessary, and explain your answer.
Bus 18, with a median of 13
Bus 47, with a median of 16
Bus 18, with a mean of 13
Bus 47, with a mean of 16
1) A histogram would be the best graphical representation for the teacher's data on the subject preferences of students. 2) The correct circle graph is option 2. 3) Option 4: Paddleboarding.
What is a histogram?The frequency or relative frequency of the data points falling within each interval is depicted by the height of the bars in a histogram, which is a graphical representation of the distribution of continuous data. Histograms are frequently used in data analysis to show how a single variable is distributed and to spot any patterns or trends. Additionally, they can be used to compare the distributions of two or more variables or to spot anomalies or outliers in the data.
1) A histogram would be the best graphical representation for the teacher's data on the subject preferences of students.
2) Given the type of transportation we have he total number of visitors as:
(120+24+45+30+81=300)
Now, for walk we have:
120/300 = 40/100 = 40%
For Bicycle we have:
24/300 = 8%
Thus, the correct circle graph is option 2: circle graph titled New York City visitor's transportation, with five sections labeled walk 40 percent, bicycle 8 percent, car service 15 percent, bus 10 percent, and subway 27 percent
3) For the central angle to be 54 the number of campers needs to correspond to this number. The activity that corresponds to 54 degrees is Paddleboarding.
4) For the number of principals in conference we set up a proportionality with total people as follows:
We know that, 52 principals out of 70 people thus:
52/70 = x/750
Now,
x = (52/70) * 750
x = 557.14
Hence, we can predict that there were about 557 principals in attendance at the conference.
5) Given that, out of 225 students 27 prefer cookies thus,
27/225 = 0.12
That is 12% students like cookies.
Now, for the total number of students we have:
0.12 * 4000 = 480
Thus, option A: The college will have about 480 students who prefer cookies.
6) For the given description of the line plot the median is:
For Bus 47 = 16
For Bus 18 = 13
The faster bus is Bus 47, with a median of 16.
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Find the missing value to the nearest hundredth. cos____ = 8/17
1. 0.99 degrees
2. 61.93 degrees
3. 28.07 degrees
4. 25.20 degrees
I need help with the reasons for this two column proof please
Hence, OC bisects AB, as congruent parts of congruent triangles are equal.
What is congruency in figures?When two or more geometric figures are similar in size, form, and orientation, this is referred to as congruency in geometry. Two figures can be overlaid on one another by translation, rotation, and/or reflection when they are congruent because they are almost similar to one another and do not alter in size, form, or orientation.
For the given problem, the complete steps of proof with reasoning are:
(a) OC is perpendicular to AB in circle O (given). i.e ∠OCA and ∠OCB are right angles.
Reason: This is given in the problem statement. It establishes that OC forms a right angle with AB at point C in circle O. i
(b) Draw OA and OB (construction).
Reason: This is a construction step that introduces radii OA and OB from the center O of the circle to points A and B on the circle. This sets up the framework for the subsequent steps and establishes the positions of A and B in relation to the circle and the perpendicular OC.
(c) OA = OB (radii of the same circle are equal).
Reason: Radii of the same circle are always equal in length. This is a basic property of circles, where all radii have the same length, which can be stated as OA = OB based on the definition of a circle.
(d) OC = OC (Reflexive Property of Equality)
Reason: It is a property of line segments that they are equal to themselves. This is known as the Reflexive Property of Equality, which states that any quantity is equal to itself.
(f) AC = BC (common side of congruent triangles).
Reason: AC and BC are line segments that are both radii of the same circle, and OA = OB (Step c). Therefore, by the definition of congruent segments, AC = BC.
(e) Triangle ACO is congruent to triangle BCO (HL congruence criterion for right triangles).
Reason: Angle ACO and angle BCO are both right angles based on the given information that OC is perpendicular to AB (Step a). Also, AC = BC (Step d) and OA = OB (Step c). Therefore, by the Hypotenuse-Leg congruence criterion for right triangles, triangle ACO is congruent to triangle BCO.
(g) OC bisects AB (congruent parts of congruent triangles are equal).
Reason: Since triangle ACO is congruent to triangle BCO (Step e), the corresponding parts of congruent triangles are equal. In this case, OC is a common side (hypotenuse) of both triangles, and AB is a side of both triangles. Therefore, by the definition of a segment bisector, OC bisects AB.
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20. MP Use Math Tools Use the table at the right.
a. What is the approximate volume of the small truck?
b. The Davis family is moving, and they estimate that
they will need a truck with about 1,250 cubic feet.
Which truck would be best for them to rent?
c. About how many cubic feet greater is the volume
of the Mega Moving Truck than the 2-bedroom
moving truck?
2016-3-1002360
Inside Dimensions of Moving Trucks
Width
Length
(ft)
(ft)
Truck
Van
Small Truck
a.
2-Bedroom
Moving Truck
3-Bedroom
Moving Truck
10
Mega
Moving Truck
11-7/3
14/2
20
6-1/2
22/
Height
(ft)
7/7/2
7/7/2
Mlet
7/1/16
8
12
8
The approximate volume of the small truck is 577.5 cubic feet.
A truck that would be best for them to rent is the 3-Bedroom Moving Truck.
The volume of the Mega Moving Truck is about 641.25 cubic feet greater than the 2-bedroom moving truck.
How to calculate the volume of a rectangular prism?In Mathematics and Geometry, the volume of a rectangular prism can be calculated by using the following formula:
Volume of a rectangular prism = L × W × H
Where:
L represents the length of a rectangular prism.W represents the width of a rectangular prism.H represents the height of a rectangular prism.For the approximate volume of the small truck, we have;
Volume of small truck = 11 1/3 × 7 5/12 × 7
Volume of small truck = 577.5 cubic feet.
The approximate volume of each moving truck can be calculated as follows;
2-Bedroom Moving Truck = 14.5 × 7.5 × 7 = 761.25 cubic feet.
3-Bedroom Moving Truck = 21 × 7.5 × 8 = 1,260 cubic feet.
Mega Moving Truck = 22 × 7.5 × 8.5 = 1,402.5 cubic feet.
Difference = 1,402.5 cubic feet - 761.25 cubic feet
Difference = 641.25 cubic feet.
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using a standard deck of playing cards, how many ways are to form a 5-card hand with 2 pairs (i.e. pair of one value, a pair of a different value, and a fifth card of some other value)? what if we require the pairs to be the same color (i.e spade with clubs and diamond with hearts)?
From a "standard-deck" of "playing-cards", the number of ways which are required to form a "5-card" hand with "2-pairs" is 123,552 ways.
A "Standard-Deck" of playing cards generally consists of 52 cards, divided into four suits: hearts, diamonds, clubs, and spades. Each suit contains 13 ranks: Ace, 2 through 10, and three face cards.
To form a 5-card hand with 2 pairs from a standard deck of playing cards, we break it down into two steps:
Step(1) : Select the values for the two pairs.
There are 13-ranks in a standard deck of playing cards, ranging from 2 to 10, and then Jack, Queen, King, and Ace, for a total of 13 possible values.
We need to select 2 of these values to form the two pairs. The number of ways to do this is "C(13, 2)" which is : 78,
So, there are 78 ways to select the values for the two pairs.
Step(2) : Select the specific-cards for each pair and the fifth card.
For each pair, we need to select 2 cards of that value from the 4 cards of each rank in the deck.
The number of ways to do this is "C(4, 2)" which is : 6,
So, there are 6 ways to select the specific cards for each pair.
Finally, for the fifth-card, we can choose any of the remaining "44-cards" in the deck (after selecting the 8 cards for the two pairs).
So, total number of ways to form a "5-card" hand with "2-pairs" from a standard deck of playing cards is,
⇒ 78 × 6 × 6 × 44 = 123,552 ways,
Therefore, the required number of ways are 123,552 ways.
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The given question is incomplete, the complete question is
Using a standard deck of playing cards, how many ways are to form a 5-card hand with 2 pairs?
a culture contains 10,000 bacteria initially. after an hour the bacteria count is 25,000. (a) find the doubling period. (b) find the number of bacteria after 3 hours.
Quadrilateral JKLM has vertices J(3,5), K(7,8), L(13,5), and M(13,0). Which statements are true? Select all that apply.
~a.) Line Segment KL ║ Line Segment JM
~b.) Line Segment KL ≅ Line Segment JM
~c.) Line Segment JK ≅ Line Segment LM
~d.) Line Segment JK ║ Line Segment LM
~e.) Quadrilateral JKLM is a trapezoid.
~f.) Quadrilateral JKLM is an isosceles trapezoid.
The statements that are true are:
→ Line Segment KL ≅ Line Segment JM
→ Quadrilateral JKLM is a trapezoid.
What is a trapezoid?A trapezoid is a quadrilateral with at least one pair of parallel sides. The parallel sides are called the bases of the trapezoid, and the non-parallel sides are called the legs.
According to the given informationIn the quadrilateral JKLM
Using the distance formula, we can find the lengths of the line segments:
JK = √[(7-3)² + (8-5)²] = √58
KL = √[(13-7)² + (5-8)²] = √58
LM = √[(13-13)² + (0-5)²] = 5
JM = √[(13-3)² + (0-5)²] = √109
From this, we can analyze each statement:
a.) Line Segment KL ║ Line Segment JM
We can see from the sketch that the two line segments are not parallel. Therefore, statement a is false.
b.) Line Segment KL ≅ Line Segment JM
We found that the length of KL is equal to the length of JM. Therefore, statement b is true.
c.) Line Segment JK ≅ Line Segment LM
We can see from the sketch that the two line segments are not congruent. Therefore, statement c is false.
d.) Line Segment JK ║ Line Segment LM
We can see from the sketch that the two line segments are perpendicular. Therefore, statement d is false.
e.) Quadrilateral JKLM is a trapezoid.
A trapezoid is defined as a quadrilateral with at least one pair of parallel sides. We can see from the sketch that line segments KL and JM are not parallel, but line segments JK and LM are parallel. Therefore, statement e is true.
f.) Quadrilateral JKLM is an isosceles trapezoid.
An isosceles trapezoid is defined as a trapezoid with congruent base angles and congruent non-parallel sides. We can see from the sketch that neither the base angles nor the non-parallel sides are congruent. Therefore, statement f is false.
Therefore, the statements that are true are b and e.
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Answer:
A) KL⎯⎯⎯⎯⎯∥JM⎯⎯⎯⎯⎯
C) JK⎯⎯⎯⎯⎯≅LM⎯⎯⎯⎯⎯⎯
E) Quadrilateral JKLM is a trapezoid.
F) Quadrilateral JKLM is an isosceles trapezoid.
Step-by-step explanation:
These where the correct answer I got when taking the assignment with that question
If you took the amount of oil consumed in 2 months in 2013 worldwide, you could make a cube of oil that measures 10^3 meters on each side. How many cubic meters of oil is this? Do you think this would be enough to fill a pond, a lake, or an ocean?
Answer:
10^9 cubic meterslakeStep-by-step explanation:
You want to know the number of cubic meters in a cube that is 10^3 meters on each side, and whether that volume amounts to a pond, lake, or ocean.
VolumeThe volume of a cube is given by ...
V = s³
where s is the edge length.
The volume of interest is ...
V = (10³ m)³ = 10⁹ m³
The volume of oil is 10⁹ cubic meters.
LakeThe sizes of ponds and lakes vary, but we might consider a pond to be a body of water larger than about 150 square meters and less than 6 meters in depth. On the other hand, a lake will generally be larger than about 4000 square meters. An average size lake may be about 10 meters in depth.
If we put the given amount of volume in a space with a depth of 40 meters, it would cover an area of about 25 million square meters, roughly 6000 acres. That is the area of a circle about 7 km in diameter. This might be considered a medium-sized lake.
The oil would fill a medium-sized lake.
__
Additional comment
A "lake" is generally a body of water upwards of an acre in area. While an average lake in some areas is about 10 m deep, worldwide, the average is just over 40 m in depth. Some lakes are well over 20,000 acres in area.
A "pond" may be larger than a "lake", but will generally be smaller than 500 acres.
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in a role playing game two special dice are rolled. one die has 4 faces numbered 1 through 4 and the other has 6 faces numbered 1 thorugh 6. what is the probabilty that the total shown on the two dice after they are rolled is greater than or equal to 8?
The probability that the total shown on the two dice after they are rolled is greater than or equal to 8 is 1/9.
the average height of students at uh from an srs of 19 students gave a standard deviation of 3.2 feet. construct a 95% confidence interval for the standard deviation of the height of students at uh. assume normality for the data. a) (1.418, 10.732) b) (1.918, 5.732) c) (2.418, 4.732) d) (6.418, 11.732) e) (5.418, 9.732) f) none of the above
The 95% confidence interval for the standard deviation of the height of students at UH is (1.918, 5.732), which corresponds to option b.
To construct a 95% confidence interval for the standard deviation of the height of students at UH, we will use the Chi-square distribution. Given the sample standard deviation (s) of 3.2 feet, a sample size (n) of 19 students, and assuming normality for the data, we can find the confidence interval as follows:
1. Determine the degrees of freedom: df = n - 1 = 19 - 1 = 18
2. Identify the Chi-square values for the confidence level (95%): χ²_lower = 7.632, χ²_upper = 32.852 (using a Chi-square table or calculator)
3. Calculate the lower and upper bounds of the confidence interval:
Lower bound = sqrt((n - 1) * s² / χ²_upper) = sqrt(18 * (3.2)² / 32.852) ≈ 1.918
Upper bound = sqrt((n - 1) * s² / χ²_lower) = sqrt(18 * (3.2)² / 7.632) ≈ 5.732
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The 95% confidence interval for the standard deviation of the height of students at UH is approximately (1.918, 5.732), Option B.
Construct a 95% confidence interval for the standard deviation of the height of students at UH, we'll use the given data and the Chi-Square distribution.
Here's a step-by-step explanation:
SRS (simple random sample) of 19 students, which means the degrees of freedom (df) = n - 1 = 19 - 1 = 18.
The sample standard deviation (s) is given as 3.2 feet.
Assume normality for the data.
A 95% confidence interval, we'll use the Chi-Square distribution table to find the critical values.
The two tail probabilities are 0.025 and 0.975, so we'll look up the Chi-Square values for 18 degrees of freedom and these probabilities:
[tex]- X^2_{0.025} = 30.191 (upper limit)[/tex]
[tex]- X^2_{0.975} = 8.231 (lower limit)[/tex]
Calculate the confidence interval for the population standard deviation (σ):
[tex][tex](\sqrt((n - 1) \times s^2 / X^2_{upper}), \sqrt((n - 1) \times s^2 / X^2_{lower}))[/tex][/tex]
Plug in the values:
[tex]- n = 19[/tex]
[tex]- s = 3.2[/tex]
[tex]- df = 18[/tex]
[tex][tex]- X^{2} _{upper} = 30.191[/tex][/tex]
[tex][tex]- X^2_{lower} = 8.231[/tex][/tex]
Calculate the confidence interval:
[tex](√((18 \times 3.2^2) / 30.191), \sqrt((18 \times 3.2^2) / 8.231)) \approx (1.918, 5.732)[/tex]
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27,006 / 42 solving steps
Answer:
189
Step-by-step explanation:
27,006 / 42
= [tex]\frac{27}{6/42}[/tex]
= [tex]\frac{27}{\frac{1}{7} }[/tex]
= 27 x 7
= 189
So, the answer is 189
Need help with this!
Answer
Number 14: 7 faces, 15 edges, and 10 vertices.
Number 15: 10 faces, 24 edges, and 16 vertices.
Number 16: 7 faces, 12 edges, and 7 vertices.
:D
Step-by-step explanation:
Which of these expressions are equivalent to p/3
Answer:
B) 3p/9
D)1/3p
Step-by-step explanation:
PLEASE HELP!! 20 POINTS
Select the correct answer from each drop-down menu. Consider this equation. 1/x + 2/x+10 =1/3 Complete the statements to make them true. The least common denominator is . The equation will have valid solutions.
Answer: The least common denominator is 3x(x+10)
The equation will have 2 valid solutions
Step-by-step explanation: sorry if wrong
I need help answering this question and understanding it
The amount of money less per hour which Melanie earn than Olivia is equal to $268.
What is the slope-intercept form?In Mathematics and Geometry, the slope-intercept form of the equation of a straight line is given by this mathematical expression;
y = mx + c
Where:
m represents the slope or rate of change.x and y are the points.c represents the y-intercept or initial value.Based on the information provided about Melanie's earnings, we have the following:
y = 22.2x
When x = 40 hours, the y-value is given by;
y = 22.2(40)
y = $888.
Difference in earnings can be calculated as follows;
Difference = $1156 - $888
Difference = $268.
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Select the GCF of these numbers. 48 and 60 22 ·3 2· 112 32 23 · 5 13· 193 ·232
The GCF of 48 and 60 is 12
To find the greatest common factor (GCF) of 48 and 60, we can start by finding the prime factorization of each number
48 = 2^4 × 3
60 = 2^2 × 3 × 5
Next, we can identify the common factors of both numbers by looking at their prime factorization
The factors of 48 are: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48
The factors of 60 are: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60
The common factors of 48 and 60 are: 1, 2, 3, 4, 6, and 12.
The greatest common factor is the largest number that both 48 and 60 can be divided evenly by. In this case, that number is 12. Therefore, the GCF is 12.
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The given question is incomplete, the complete question is:
Find the GCF of 48 and 60.
the population of weights for men attending a local health club is normally distributed with a mean of 166-lbs and a standard deviation of 26-lbs. an elevator in the health club is limited to 33 occupants, but it will be overloaded if the total weight is in excess of 5940-lbs. assume that there are 33 men in the elevator. what is the average weight beyond which the elevator would be considered overloaded? average weight
This means that if the average weight of the men in the elevator is more than 180 lbs, the elevator would be overloaded.
To determine the average weight beyond which the elevator would be considered overloaded, we can follow these steps:
Find the total weight limit for 33 occupants: 5940 lbs.
Divide the total weight limit by the number of occupants to find the average weight per person: 5940 / 33 = 180 lbs.
Now, we need to find the difference between the average weight per person (180 lbs) and the mean weight of the population (166 lbs): 180 - 166 = 14 lbs.
Since we have the difference and the standard deviation (26 lbs), we can now calculate the Z-score:
Z = (difference) / (standard deviation) = 14 / 26 ≈ 0.54.
The average weight beyond which the elevator would be considered overloaded is 180 lbs.
The corresponding Z-score for this weight is approximately 0.54.
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A circle with center O(2, 3) contains the point A(5, 11).
The equation of the circle is x² + y² - 4x - 6y - 60 = 0
Equation of a circle :The equation of a circle is generally given by the formula:
=> (x - a)²+ (y - b)² = r²
Where (a, b) is the center of the circle, and r is its radius. The equation describes all the points (x, y) in the xy-plane that are a fixed distance r from the center point (a, b).
Here we have
A circle with centre O(2, 3) contains the point A(5, 11).
Since point A(5, 11) is located on the circle with center O(2, 3), use the distance formula to determine whether A is actually on the circle.
The distance between two points (x₁, y₁) and (x₂, y₂) is given by:
=> d = √(x₂ - x₁)² + (y₂ - y₁)²)
Using this formula, the distance between O(2, 3) and A(5, 11) is:
d = √(5 - 2)² + (11 - 3)²)
= √(3² + 8²)
= √(9 + 64)
=√(73)
This distance is the radius of the circle with center O.
Therefore, the equation of the circle is:
(x - 2)² + (y - 3)² = (√(73))²
x² - 4x + 4 + y² - 6y + 9 = 73
x² + y² - 4x - 6y - 60 = 0
Therefore,
The equation of the circle is x² + y² - 4x - 6y - 60 = 0
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The cost of 1 cup of tea and 6 cakes is £13. The cost of 1 cup of tea and 4 cakes is £9 a) How much do 2 cakes cost? b) How much does 1 cake cost?
The answers are:
a) 2 cakes cost £5
b) 1 cake costs £2.5.
What is an algebraic expression?
An algebraic expression is a mathematical phrase that contains variables, constants, and mathematical operations. It may also include exponents and/or roots. Algebraic expressions are used to represent quantities and relationships between quantities in mathematical situations, often in the context of problem-solving.
To find the cost of 1 cupcake, we need to subtract the cost of the tea from the total cost of 3 cupcakes:
3 cupcakes + 1 tea = £9
3 cupcakes = £9 - 1 tea = £9 - £1.5 (assuming the cost of 1 tea is the same in both cases) = £7.5
1 cupcake = £7.5 ÷ 3 = £2.5
So 2 cupcakes would cost:
2 cupcakes = 2 × £2.5 = £5
Therefore, the answers are:
a) 2 cakes cost £5
b) 1 cake costs £2.5.
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The pattern continues. Fill in the blanks.
2 x 4 + 1 = 3 x 3
3 x 5 + 1 = 4 x 4
4 x 6 + 1 = __ + __
__ x 7 + 1 = __ x __
__ x __ + __ = __ + __
Describe patterns that you see.
What will the equation look like when the first term is 25?
Based on the given pattern:
2 x 4 + 1 = 3 x 3
3 x 5 + 1 = 4 x 4
4 x 6 + 1 = __ + __
__ x 7 + 1 = __ x __
__ x __ + __ = __ + __
The general pattern is that the first term is multiplied by one more than itself, and then 1 is added to the result, which is equal to the second term squared.
When the first term is 25, the equation would look like:
25 x 26 + 1 = __ + __
The first blank would be filled with 26, and the second blank would be filled with 676 (which is 26 squared). So the complete equation would be:
25 x 26 + 1 = 26 + 676
Scientists measure a bacteria population and find that it is 10,000. Five days later, they
find that the population has doubled. Which function f could describe the bacteria
population d days after the scientists first measured it, assuming it grows exponentially?
A. f(d) 10,000. 2ª
B. f(d) = 10,000. (√2)ª
C. ƒ(d) = 10,000 • (-)ª
D. f(d) = 10,000.25d
=
S
Answer:
Hm
Step-by-step explanation:
The bacteria population is observed to double after five days, which means that its growth rate is 100% over a period of five days. This corresponds to a daily growth rate of r = 100%/5 = 20%.
If the initial population is 10,000, then the bacteria population after d days can be modeled by the exponential function:
f(d) = 10,000 * (1 + r/100)^d
Substituting r = 20% and simplifying, we get:
f(d) = 10,000 * (1.2)^d
Therefore, the correct option is:
D. f(d) = 10,000 * (1.2)^d
Given that £1 = $1.62
a) How much is £650 in $?
b) How much is $405 in £?
Answer:
a 1053
b 250
multiply 650 by 1.62 for part a.
for part b divide by 1.62 since pound is less than dollar
hope this helps :)
state the name for this figure
Answer:
square, quadrilateral, rhombus, parallelogram, rectangle
Answer:
Quadrilateral, rectangle, parallelogram, rhombus, square
Step-by-step explanation:
It is a quadrilateral bc it has four sides.
It is a rectangle bc it has four right angles.
It is a parallelogram bc it has two pairs of parallel sides.
It is a rhombus bc all four sides are congruent.
It is a square bc it is both a rectangle and a rhombus.
Find the avatar rate of change f(x)=3√x-1 +2; 9 ≤ x ≤ 65
Answer: To find the average rate of change of the function f(x) over the interval [9, 65], we can use the formula:
average rate of change = (f(b) - f(a)) / (b - a)
where a = 9, b = 65, f(a) = f(9) = 3√8 + 2, and f(b) = f(65) = 3√64 + 2.
Plugging in these values, we get:
average rate of change = (f(65) - f(9)) / (65 - 9)
average rate of change = (3√64 + 2 - 3√8 - 2) / 56
average rate of change = (3(4) + 2 - 3(2) - 2) / 56
average rate of change = (12 - 4) / 56
average rate of change = 8 / 56
average rate of change = 1 / 7
Therefore, the average rate of change of the function f(x) over the interval [9, 65] is 1/7.
Step-by-step explanation:
Answer:
Step-by-step explanation:
Answer: To find the average rate of change of the function f(x) over the interval [9, 65], we can use the formula:
average rate of change = (f(b) - f(a)) / (b - a)
where a = 9, b = 65, f(a) = f(9) = 3√8 + 2, and f(b) = f(65) = 3√64 + 2.
Plugging in these values, we get:
average rate of change = (f(65) - f(9)) / (65 - 9)
average rate of change = (3√64 + 2 - 3√8 - 2) / 56
average rate of change = (3(4) + 2 - 3(2) - 2) / 56
average rate of change = (12 - 4) / 56
average rate of change = 8 / 56
average rate of change = 1 / 7
Therefore, the average rate of change of the function f(x) over the interval [9, 65] is 1/7.
A random sample of size is selected from a population with. A. What is the expected value of (to 2 decimals)? B. What is the standard error of (to 2 decimals)? C. Show the sampling distribution of (to 2 decimals). D. What does the sampling distribution of show? Blank
A) The expected value of the sampling distribution is 0.40.
B) The standard error is 0.05.
C) The sampling distribution will be centered around the population proportion of 0.40, with a spread given by the standard error of 0.05.
D) By examining the sampling distribution, we can see how likely it is to obtain a certain sample proportion by chance alone, and therefore make conclusions about the population based on the sample.
A) The expected value (also called the mean) of a sampling distribution is equal to the population parameter being estimated. In this case, the population parameter is the proportion, p, which is 0.40.
B) The standard error is the standard deviation of the sampling distribution. For a proportion, the formula for the standard error is √((p(1-p))/n), where p is the population proportion and n is the sample size. Plugging in the values given, we get √((0.40(1-0.40))/100) = 0.049.
C) The sampling distribution of a proportion is approximately normal if both np and n(1-p) are greater than or equal to 10. In this case, np = 1000.40 = 40 and n(1-p) = 100*0.60 = 60, so the conditions for normality are met.
D) The sampling distribution of a proportion shows the distribution of all possible sample proportions of a given size that could be drawn from a population with a known proportion.
The sampling distribution allows us to make inferences about the population proportion, such as constructing confidence intervals or conducting hypothesis tests.
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Complete Question:
A random sample of size 100 is selected from a population with p =0 .40.
A. What is the expected value (to 2 decimals)?
B. What is the standard error (to 2 decimals)?
C. Show the sampling distribution (to 2 decimals).
D. What does the sampling distribution of show?
Increase £15837. 77 by 18. 5%
Give your answer rounded to 2 DP.
If the amount of £15837.77 is to be increased by 18.5%, then the resulting amount after the increase is £18764.75.
A percentage is a number or ratio expressed as a fraction of 100. It represents a portion of something relative to the whole, and is commonly used to express changes or comparisons between two values
To increase a number by a percentage, you can use the following formula
New value = Original value + (Percentage increase / 100) × Original value
Using this formula, we can find the new value of £15837.77 after an 18.5% increase
New value = 15837.77 + (18.5 / 100) × 15837.77
= 15837.77 + 2926.98
= 18764.75
Therefore, an 18.5% increase on £15837.77 is £18764.75, rounded to 2 decimal places.
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what is f square plus g square i need the answer for my test!!
The value of f square plus g square is 61.
How to find square of any number?
To find the square of a number, you can multiply that number by itself.
Write the number you want to square. Let's use the number "x" as an example.
Raise the number to the power of 2 by using the exponentiation operator (^) or by multiplying the number by itself. Either way, the result is the same. The expression to calculate the square of a number can be written as x² = x × x = x²
For example, to find the square of 5, you can multiply 5 by 5, which gives you 25.
So,the square of 5 is 25.
In mathematical notation, the square of a number "x" can be represented as "x²". So, the square of 5 can also be written as 5², which equals 25.
If f = 5 and g = 6, then f square (f²) is 5² = 25 and g square (g²) is 6² = 36. Therefore, f² + g² = 25 + 36 = 61. So, f square plus g square when f is 5 and g is 6 is 61.
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Correct question is "What is f square plus g square? Where f is equal to 5 and g is equal to 6."
we call a number a mountain number if its middle digit is larger than any other digit. for example, 284 is a mountain number. how many 3-digit mountain numbers are there?
If we consider a mountain number with its middle digit is larger than any other digit, then there are possible three-digit mountain numbers are equals the 240.
A number is called a 'mountain' if its decimal digits insitiate with 1, i.e. 'base camp', increase continuously to one largest digit, then decrease continuously back to one i.e. back to base camp. We have a number is called a mountain number. Now, there are 100 to 999 total 3-digit numbers. Now, with 2 in the middle, we have = 2 numbers[1 x 2] - 120 = 121
With 3 in the we have = 6 numbers[2 x 3] - 130, 131, 132, 230, 231, 232.......and so on.With 4 in the middle,we have = 12 numbers[3 x4]With 5 in the middle, we have = 20 numbers[4 x 5]With 6 in the middle, we have = 30 numbers[5 x 6]With 7 in the middle, we have = 42 numbers[6 x 7]With 8 in the middle, we have = 56 numbers[7 x 8]With 9 in the middle, we have = 72 numbers[8 x 9]So, we have a total of Total Number = 2 + 6 + 12 + 20 + 30 + 42 + 56 + 72 = 240 "mountain numbers". Hence, the required number , value is 240.
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