The correct statements are Two data sets could have different means but the same standard deviation, and could have the same mean but different standard deviations. If two data sets have different means they must have different standard deviations. Correct options are A, C , D.
The mean and standard deviation are both measures of the central tendency of a data set, but they capture different aspects of the distribution. The mean represents the average value of the data, while the standard deviation measures how spread out the data is around the mean.
It is possible for two data sets to have different means but the same standard deviation if one data set is more spread out than the other, but the values are symmetrically distributed around the mean. For example, the data sets {1, 2, 3, 7, 8, 9} and {0, 4, 5, 5, 5, 9} have different means (5 and 4.67, respectively) but the same standard deviation (3.16).
Similarly, two data sets could have the same mean but different standard deviations if one data set is more spread out than the other. For example, the data sets {1, 2, 3, 4, 5} and {1, 3, 3, 3, 5} have the same mean (3) but different standard deviations (1.41 and 1.26, respectively).
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Complete question is:
Which of the following statements is true?
multiple select question.
A. two data sets could have different means but the same standard deviation.
B. if two data sets have the same mean they must have the same standard deviation.
C. two data sets could have the same mean but different standard deviations.
D. if two data sets have different means they must have different standard deviations.
This equation shows how the accuracy of Johnny's watch is related to how long it's been since he last set it. s = d + 16 The variable d represents the number of days passed since Johnny last set his watch, and the variable s represents how many seconds behind the watch is. How far behind is Johnny's watch if he last set it 2 days ago?
If Johnny sets his watch 2 days ado then after two days watch will behind 18 seconds.
What is addition ?
Addition is a basic mathematical operation that combines two or more numbers to give a total or sum. It is one of the four elementary arithmetic operations, along with subtraction, multiplication, and division. The operation involves adding or combining the values of two or more numbers, which are called addends, to produce a new value, which is the sum or the total.
If Johnny last set his watch 2 days ago,
we can substitute d = 2 into the equation:
s = d + 16
To find out how many seconds behind his watch is.
s = d + 16
s = 2 + 16
s = 18
So, Johnny's watch is 18 seconds behind if he last set it 2 days ago.
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Seti held a party. He says, ‘There were 11 people at my party, and everyone had 3 friends there.’ Is this possible? Explain your answer
Answer:
y
Step-by-step explanation: People there: S (Seti), A, B, C, D, E, F, G, H, I, J
friend group:
S is friends with A, B
A is friends with B, C
B is friends with C, D
C is friends with D, E
E is friends with F, G
F is friends with G, H
G is friends with H, I
H is friends with I, J
I is friends with J, S
J is friends with S, A
Answer:
Yes, it is possible
Step-by-step explanation:
Think the people as points in space and the friendship between two people as a line connecting two points.
Then the question is equivalent to asking whether it is possible for all 11 points being connected by lines such that every point is connected to exactly three other points.
Clearly this is possible, since we always have, for each point, ten other points to connect it to, so we can select any three of the ten.
Part B: Logan made a profit of $235 as a mobile groomer. He charged $75 per appointment and received $40 in tips, but also had to pay a rental fee for the truck of $10 per appointment. Write an equation to represent this situation and solve the equation to determine how many appointments Logan had. (5 points)
Answer:
# of appointments is 3
Step-by-step explanation:
He makes $75 per appointment, which means this immediate value is directly dependent on the number of appointments (x). So it can be given by 75x.
Tips are simply added, tips are not directly dependent on the number of visits as customers will tip differently so we can add $40 to the equation.
Now we must negate the expenses, each appointment there is a fee of $10. So it can be given as 10x.
We know that this all must equal $235.
So the equation is as follows:
235 = (75x)+40-(10x)
Simplifying we get
235 = 65x + 40
195 = 65x
195/65 = x
x = 3
Therefore, Logan had 3 appointments.
in how many ways can we arrange a standard deck of 52 cards so that all cards in a given suit appear contiguously (e.g., first all the spades appear, then all the diamonds, then all the hearts, and then all the clubs)?
There are 71,536,320 ways to arrange a standard deck of 52 cards so that all cards in a given suit appear contiguously.
There are 4 suits in a standard deck of 52 cards, and we need to arrange all the cards in a given suit contiguously. Once we choose a suit to be arranged in this way, we can treat it as a block of 13 cards that need to be arranged. Therefore, we have reduced the problem to arranging 4 blocks of 13 cards each, where each block represents a suit.
Within each suit, there are 13! ways to arrange the cards. However, once we arrange the cards in one suit, we fix the relative positions of the cards in the other suits. Therefore, we only need to consider the number of ways to arrange the suits themselves.
There are 4! = 24 ways to arrange the 4 suits. For each of these arrangements, there is only one way to arrange the cards within each suit contiguously. Therefore, the total number of ways to arrange the deck of cards so that all cards in a given suit appear contiguously is:
13! x 24 = 71,536,320
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A. A fish is 12 m below the surface of the ocean. What is its elevation?
B. A seabird is 28 m above the surface of the ocean. What is its elevation?
C. If the bird is directly above the fish, how far apart are they?
We can say that by equation 12 metres below the ocean's surface, a fish may be found. 28 metres above the ocean's surface, a sea bird may be seen and distance between them is 40 meters.
What is equation?A mathematical equation is a formula that joins two statements and uses the equal symbol (=) to indicate equality. A mathematical statement that establishes the equality of two mathematical expressions is known as an equation in algebra. For instance, in the equation 3x + 5 = 14, the equal sign places the variables 3x + 5 and 14 apart. The relationship between the two sentences on either side of a letter is described by a mathematical formula. Often, there is only one variable, which also serves as the symbol. for instance, 2x – 4 = 2.
We require knowledge about an object's elevation to tackle such issues.
12 metres below the ocean's surface, a fish may be found.
28 metres above the ocean's surface, a sea bird may be seen.
A fish is 12 metres below the ocean's surface.
The fish's elevation is negative since it is below sea level. Consequently, the fish's elevation is -12 metres.
B.) A marine bird flies 28 metres above the water's surface.
given that the seabird is above the water. The sea bird is 28 metres above sea level.
If the bird soars straight over the fish, (C),
If the fish and the bird are immediately above one another,
Distance between fish and bird = |(elevation of the fish)| + |(elevation of the sea bird)|
= |-12| + |28|
= 12 + 28
= 40 meters
distance between them is 40 meters.
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which of the following statements is true? a.) to imply causation, the correlation must be -1. b.) a high correlation can indicate a relationship but cannot prove causation. c.) a high correlation indicates that explanatory variable is a direct cause of the response variable. d.) having a low correlation is sufficient enough to imply causation.
The statement that is true is:
b.) A high correlation can indicate a relationship but cannot prove causation.
Correlation measures the strength and direction of the relationship between two variables, but it does not necessarily imply causation. A high correlation means that there is a strong linear relationship between the two variables, but it does not indicate whether one variable causes the other. There can be other factors that influence the relationship. Therefore, it is important to use other methods, such as experiments or observational studies, to determine causation. Correlation is useful for identifying associations between variables, but it cannot be used as evidence of a causal relationship.
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Use synthetic division to find the quotient and remainder when x³ + 9x² + 12x - 5 is divided by x+7 by completing the parts below.
(a) Complete this synthetic division table.
-7)
19 12 -5
000
OOOO
(b) Write your answer in the following form: Quotient +
3
x³ + 9x² +
+ 9x + 12x-5
x+7
=
x+7
Remainder
x+7
X
The division can be written as: x³ + 9x² + 12x - 5 = (x + 7)(x² + 7x + 10) - 75
What is synthetic division ?
Synthetic division is a simplified method of polynomial division that can be used to divide a polynomial by a linear binomial. It's used to find the quotient and remainder of a polynomial division without having to perform long division.
In synthetic division, the coefficients of the polynomial are arranged in a table along with the coefficients of the divisor, and then divided and multiplied using the same rules as in long division. The remainder of the division is the last entry in the table, and the quotient is the polynomial whose coefficients are the entries in the table, excluding the remainder.
To perform synthetic division, we divide x³ + 9x² + 12x - 5 by x + 7 by dividing each coefficient by x + 7 and then writing the result in a table with the dividend on top and the divisor on the bottom. Here's what the table would look like:
+ 7 | 1 9 12 -5
-------------------
x^3 | x^3 9 12 -5
x^2 | x^2 +7x 3 -35
x | x +7 10 -70
-------------------
10 43 -75
The quotient of the division is x² + 7x + 10, and the remainder is -75.
Therefore, the division can be written as: x³ + 9x² + 12x - 5 = (x + 7)(x² + 7x + 10) - 75
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For a given recipe, 16 cups of flour are mixed with 8 cups of sugar. How many cups of flour should be used if 12 cups of sugar are used?
The number of cups of flour should be used if 12 cups of sugar are used is 6.
Determine the purpose of the relationship. Start by identifying what you want the ratio to show. Each ratio uses different data, so you need to make sure you're using the correct information to get the details you need.
set the formula. A ratio compares two numbers, usually by division. When comparing one data point (A) to another data point (B), the formula is A/B. That is, divide information A by information B. For example, if A is 5 and B is 10, the ratio is 5/10.
Solve the equation. Divide data A by data B to get the ratio. In the example above, 5/10 = 0.5.
16 cups of flour are mixed with 8 cups of sugar and for 12 cup ratio should be same
so 16/8 = 12 /x
x = 6
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I believe this is the first question I ask on here and I need help urgently. Does anyone have an answer? This is a question for "Geometry Checkpoint 3 - Part 2" .
Check the picture below.
so the figure is really just a semi-circle, a rectangle and three triangles, let's simply get their area and sum them all up.
[tex]\stackrel{ \textit{\LARGE Areas} }{\stackrel{ semicircle }{\cfrac{1}{2}\pi (2)^2}~~ + ~~\stackrel{ rectangle }{(4)(5)}~~ + ~~\stackrel{ triangle }{\cfrac{1}{2}(\underset{b}{3})(\underset{h}{2})}~~ + ~~\stackrel{ triangle }{\cfrac{1}{2}(\underset{b}{4})(\underset{h}{1})}~~ + ~~\stackrel{ triangle }{\cfrac{1}{2}(\underset{b}{4})(\underset{h}{2})}} \\\\\\ 2\pi ~~ + ~~20~~ + ~~3~~ + ~~2~~ + ~~4 ~~ \approx ~~ \text{\LARGE 35.28}[/tex]
Hunter designs two flags for his adventure club.
What is the length of the base,x, of the larger flag?
Enter your answer as a decimal.
See the attachment for the problem to be answered.
The length of the base, x, of the larger flag is 6.25 ft.
What are similar triangles?Triangles with the same shape but different sizes are said to be similar triangles. Squares with any side length and all equilateral triangles are examples of related objects. In other words, if two triangles are similar, their corresponding sides are proportionately equal and their corresponding angles are congruent.
The two flags are similar using the AA criteria.
Thus, the ratio of the segments of the two triangle are equal.
4/5 = 5/x
4x = 25
x = 25/4
x = 6.25 ft
Hence, the length of the base, x, of the larger flag is 6.25 ft.
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a coordinator will select 4 songs from a list of 10 songs to compose an event's musical entertainment lineup. how many different lineups are possible?
There are [tex]10^{4}[/tex] = 10,000 different possible musical entertainment lineups that can be created from a list of 10 songs.
This is computed by using the formula for combinations without repetition, which is [tex]n^{r}[/tex], where n is the number of items in the list and r is the number of items to be selected. In this case, n = 10 and r = 4, which results in [tex]10^{4}[/tex] = 10,000.
It is important to note that this calculation does not take into account any repetitions of songs, so if the same song appears more than once in the list, then the actual number of possibilities could be less. For instance, if there is a list of 10 songs, but 5 of them are the same, then the number of possible lineups would be[tex]10^{4/5}[/tex]! = 800, taking into account the repetitions.
To illustrate this further, if we were to list all the possible lineups, then we would end up with 10,000 unique combinations of 4 songs. For instance, a possible lineup could be Song 1, Song 5, Song 8, Song 10. Another possible lineup could be Song 4, Song 7, Song 9, Song 10. This process could be repeated with any combination
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Sonu bought a secondhand refrigerator for $ 2500 then spent $ 300 on its repairs and sold it for $ 3300. Find his Loss (or) gain.
Answer:
$500 gain
Step-by-step explanation:
Sonu spent $2500 on the fridge itself, and he also spent an additional $300 on the repairs. He spent a total of $2800. He sold the fridge for $3300.
To find the loss or gain, we can subtract 2800 from 3300 to see how much total profit he made.
3300-2800=500
Sonu made a $500 gain.
Answer:
$500 gain
Step-by-step explanation:
mark me please
Danielle earns a 7.75% commission on everything she sells at the electronics store where she works. She also earns a base salary of $725 per week. What were her sales last week if her total earnings for the week were $1,058.25?
Danielle's sales last week were $
Danielle's sales last week were $. At her job at an electronics store, Danielle receives a $4,295.16 commission on every sale.
What is an electronics store?
Courses in calculus (single and multivariable), complex analysis, differential equations (both ordinary and partial), linear algebra, and probability are typically required for jobs in electronics engineering. Additionally, topics like Z-transforms and Fourier analysis are frequently covered in electrical engineering curricula.More mathematics is required for electronics and telecommunications technicians, such as complex numbers, trigonometry, basic geometry, fundamental statistics, and differential and integral calculus.Every subject wants their students to be able to examine mathematics using technology, such as spreadsheets.Let's start by first finding out how much commission Danielle earned last week. We know that her total earnings were $1,058.25 and her base salary was $725 per week. Therefore, her commission must have been:
$1,058.25 - $725 = $333.25
We also know that Danielle earns a 7.75% commission on everything she sells. Let's use "x" to represent her total sales last week. Then we can set up an equation to solve for x:
0.0775x = $333.25
Solving for x, we get:
x = $333.25 / 0.0775
x = $4,295.16
Therefore, Danielle's sales last week were $4,295.16.
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given: jg/hg=kg/ig, 1=2
prove: ef || hi
The triangles ΔIGH and ΔGFE are similar triangles. So, GJ / GE = HG / FG, then the side FE is parallel to the side HI.
What is the triangle?The polygonal shape of a triangle has a number of sides and three independent variables. Angles in the triangle add up to 180°.
The ratio of the corresponding sides will be constant then the triangles will be similar triangles and the third sides of the triangles will be parallel.
GJ / GH = GK / GI, then the side KJ is parallel to the side HI.
In triangles ΔIGH and ΔGFE, then we have
∠IGH = ∠FGE (Vertival angle)
∠1 = ∠2 (Given)
Then the triangles ΔIGH and ΔGFE are similar triangles. Then we have
GJ / GE = HG / FG, then the side FE is parallel to the side HI.
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An athletic track is given in the figure.
The two straight parts are 80 m long.
The total length of the track is 400 m.
Find the radius of the curved part of the track
on both sides.
Subtract the length of the two straight parts
from the entire length of the track.
The radius of the curved part of the track will be 37.3m.
Solution:
Given that
The length of straight parts = 80m each
The total length of the track = is 400m
So, the total length of curved parts = 400 - (80*2) = 240m
Therefore, the radius of the curved parts =
[tex]2\pi r = 240\\r = 240/2\pi \\[/tex]
Hence, r = 37.3m.
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Brandon has a cup of quarters and dimes with a total value of $ 9. 6. The number of quarters is 348 less than 8 times the number of dimes. How many quarters and how many dimes does Brandon have?
To represent Brandon's total collection of quarters and dimes, let's use variables.
Let:
q be the number of quarters
d be the number of dimes
The following equations can be used to represent the given information:
The quarters and dimes are worth a total of $9.6:
0.25q + 0.10d = 9.6
The quantity of quarters is 348 less than 8 times that of dimes.
q = 8d - 348
To get a solution for one of the variables, we can use substitution. We may solve for d by substituting the expression for q from equation 2 into equation 1:
0.25q + 0.10d = 9.6
0.25(8d - 348) + 0.10d = 9.6 (substitute q = 8d - 348)
2d - 87 + 0.10d = 9.6
2.10d = 96.6
d = 46
Now that we know d = 46, we can use equation 2 to solve for q:
q = 8d - 348
q = 8(46) - 348
q = 16
Therefore, There are 46 dimes and 16 quarters in Brandon.
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Han spent 60 minutes practicing the piano over the weekend. Priya practiced the violin for 75% as much time as Han practiced the piano. How long did she practice?
By using the unitary method to find out that Priya practiced the violin for 45 minutes, which is 75% of the time Han spent practicing the piano.
Unitary method is a method that involves finding the value of one unit and then using that value to find the value of multiple units. This method is particularly useful in solving problems that involve proportions, ratios, and rates.
Now let's apply the unitary method to the given problem. We know that Han practiced the piano for 60 minutes over the weekend. We also know that Priya practiced the violin for 75% as much time as Han practiced the piano. To find out how long Priya practiced, we need to first find out how long 75% of Han's practice time is.
To do this, we can use the following equation:
75% of Han's practice time = 75/100 x 60 minutes
= 45 minutes
So Priya practiced the violin for 45 minutes over the weekend.
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Vector A⃗ =ai^−bk^A→=ai^−bk^ and vector B⃗ =−cj^+dk^B→=−cj^+dk^.In terms of the positive scalar quantities aa, bb, cc, and dd, what is A⃗ ⋅B⃗ A→⋅B→?
The dot product of two vectors [tex]\vec{A}[/tex] and [tex]\vec{B}[/tex] in terms of the positive scalar quantities a, b, c, and d is:
[tex]\vec{A}.\vec{B}=-ab[/tex]
How to get the scalar product of two vectors?The scalar product of two vectors [tex]\vec{A}[/tex] and [tex]\vec{B}[/tex] is given by the formula:
[tex]\vec{A}.\vec{B}=(a_1*b_1) + (a_2*b_2) + (a_3*b_3)[/tex]
Where a₁, a₂, and a₃ are the components of vector [tex]\vec{A}[/tex] and b₁, b₂, and b₃ are the components of vector [tex]\vec{B}[/tex].
In this case, vector A = (ai - bk) and vector B = (- cj + dk), so the components of vector A are a₁ = a, a₂ = 0, and a₃ = -b, and the components of vector B are b₁ = 0, b₂ = -c, and b₃ = d.
Plugging these values into the formula for the dot product, we get:
[tex]\vec{A}.\vec{B}=(a*0) + (0*-c) + (-d*b)\\\\\vec{A}.\vec{B}= 0 + 0 + (-bd) \\\\\vec{A}.\vec{B}=-bd[/tex]
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Question 12(Multiple Choice Worth 2 points)
(Systems of Linear Equations MC)
Which point is a solution of the system of linear equations?
x - 3y = 4
y = -3x + 2
The solution of the given system of linear equations is (1, -1)
What are linear equations?A linear equation is an algebraic equation of the form y=mx+b. involving only a constant and a first-order (linear) term, where m is the slope and b is the y-intercept.
Given is a system of linear equations, x - 3y = 4 and y = -3x + 2, we need to find the point which is the solution of the system,
The linear equations are :-
x-3y = 4...(i)
y = -3x+2....(ii)
Put eq(ii) in eq(i)
x-3(-3x+2) = 4
x+9x-6 = 4
10x = 10
x = 1
Put x = 1 in eq(ii)
y = -3+2
y = -1
Therefore, the solution point is (1, -1)
We can find the solution point by graphing method also, we will plot the graph of the lines and the line where intersects is the solution point is (1, -1) [attached]
Hence, the solution of the given system of linear equations is (1, -1)
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The complete question is (Multiple Choice Worth 2 points)
(Systems of Linear Equations MC)
Which point is a solution of the system of linear equations?
x - 3y = 4
y = -3x + 2
A) (9,0)
B) (-5, 8)
C) (1, 1)
D (1, -1)
person a starts walking north at 4 ft/s from a point p. five minutes later, person b starts walking south at 5 ft/s from a point 500 feet due east of p. at what rate are the people moving apart 15 minutes after person b starts walking?
The rate at which the people are moving apart 15 minutes after person B starts walking is √2660 feet per second. To the nearest tenth of a foot per second, this is 51.3 feet per second.
Let's call the rate at which the people are moving apart "d".
15 minutes after person B starts walking, person A has been walking for 15 + 5 = 20 minutes, for a total distance of 20 * 4 = 80 feet north from point P.
At the same time, person B has been walking for 15 minutes, for a total distance of 15 * 5 = 75 feet south from point 500 feet due east of P.
The distance between the two people is the square root of the sum of the squares of their north-south and east-west separations, or:
d = √(80^2 + (500)^2) = √(80^2 + 250000) = √250100 = 500
Since the rate at which they are moving apart is the derivative of their separation with respect to time, we can find it by taking the derivative of the above equation with respect to time:
d/dt = √(2 * 80 * 4dt / dt + 2 * 500 * 5dt / dt) = √(160 + 2500) = √2660
To the nearest tenth of a foot per second, this is 51.3 feet per second.
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Mary is ( x -1 ) years old now. How old
i) was he 4 years ago?
ii) will he be 8 years from now?
iii) is he now, if his age in 8 years time will be three times his age 4 years ago
Mary age is ( x -1 ) years old now. 4 years ago= ( x -1 )-4 =0, x=4+1=5,
now he is x -1 =5-1=4, 4 years ago=5-4=1 year, iii) (3*8/3+8)=16 year old
Will he be 8 years from now .now she is 4 year old now.
if he is x year old . he will be 8 years from now=(3x+8)=0
x=- 8/3. now his age is (3x+8) =(3*8/3+8)=16
A time of human existence, defined in years starting at birth, that is typically characterized by a certain stage or degree of mental or physical development and involves the potential for legal responsibility. the discretionary age. the legal drinking age. The legal drinking age was increased by the state from 18 to 21. Age is a notion that describes a person's age at a specific period. It is described as the measurement of the amount of time that has passed between the date of the live birth to a particular point in time, typically the date the data was collected. Age range, according to the Longman Dictionary of Contemporary English, is the term for a group of people who fall between two certain ages.
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Can someone please pelass help with the attached image
Answer:
C) E=118°, T=118°
Step-by-step explanation:
The angles inside a quadrilateral (shape with four sides) always add to 360°. So this means:
W+E+S+T=360°
29°+E+95°+T=360°
E+T=360°-124°=236°
Note that the shape contains two congruent triangles (they share equal sides) ΔEWS and ΔTWS. This means their angles are the same so E=T
If E=T and E+T=236°, then E=T=236°/2=118°
Answer:
C) E-118°, T=118° is the answer
Lamar and Allie are organizing a car wash to raise money to buy new hockey sticks for their school's hockey team. The number of hockey sticks they will be able to purchase for the team depends on the number of cars they wash.
s = the number of hockey sticks Lamar and Allie will be able to purchase
c = the number of cars Lamar and Allie wash
Which of the variables is independent and which is dependent?
The independent variable of the question is c:the number of cars Lamar and Allie wash while the dependent variable is s: the number of hockey sticks Lamar and Allie will be able to purchase
How to find the independent and dependent variables?The independent variable is defined as the variable that you change and control in your experiment. The dependent variable is defined as the variable that you don't have control over and is affected by the way that the independent variable reacts.
The parameters given are;
s = the number of hockey sticks Lamar and Allie will be able to purchase
c = the number of cars Lamar and Allie wash
Now, since the number of cars they wash determines how much money they will get to buy a new car, then we can say that c is the independent variable while s is the dependent variable as it depends on c to be actualized.
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Olivia
has 1/8 pound of butter. She needs to divide the butter equally among 4 batches of muffins she is baking. How much butter is used in each batch of muffins?
If she needs to divide the butter equally then quantity of butter that should be in 4 batches each is 1/32 pond.
According to the question:
Olivia has 1/8 pound of butter. She needs to divide the butter equally among 4 batches of muffins she is baking.
Quantity of butter = 1/8
Number of batches = 4
To find how much butter is used in each batch of muffins, we just have to divide 1/8 pond of butter to 4.
If she needs to divide the butter equally then quantity of butter that should be in 4 batches each = 1/8 ÷ 4 = 1/32 pond
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4 red bricks have a mean weight of 5 kg.
5 blue bricks have a mean weight of 9 kg.
1 green brick has a weight of 6 kg.
Donna says,
"The mean weight of the 10 bricks is less than 7 kg. "
Is Donna correct?
You must show how you get your answer.
Donna is not correct, as the mean is of 7.1 kg, which is greater than 7 kg.
How to obtain the mean of a data-set?The mean of a data-set is obtained as the sum of all observations in the data-set divided by the number of observations.
The sum of the data-set in this problem is given as follows:
4 x 5 + 5 x 9 + 1 x 6 = 71 kg.
The number of observations is given as follows:
10.
Hence the mean is given as follows:
71/10 = 7.1 kg > 7 kg.
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What are the coordinates of the point on the directed line segment from (1, 2)to(6,7) that partitions the segment into a ratio of 2 to 3?
Coordinates of the point on the directed line segment from (1, 2) to (6,7) that partitions the segment into a ratio of 2 to 3 are (3, 4).
Using proportions, it is found that the coordinates of the desired point are (2,2).
The first point is A(1, 2)
The second point is B(6, 7)
The desired point is C(x, y)
The point C partitions the segment AB into a ratio of 3 to 2, hence:
[tex]C - A = \frac{2}{5}(B - A)[/tex]
This proportion is applied using both the x and y coordinates of the points, hence:
[tex]x - 1 = \frac{2}{5}(6 - 1)[/tex]
x - 1 = 2
x = 3
Now, [tex]y - 2 = \frac{2}{5} (7 - 2)[/tex]
y - 2 = 2
y = 4
Therefore the coordinates of the points are (3, 4).
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Pls show your work thank you will mark the Brainliest
[tex]{ \qquad\qquad\huge\underline{{\sf Answer}}} [/tex]
Let's evaluate ~
[tex]\qquad \sf \dashrightarrow \: \dfrac{4.8 \times 10 {}^{8}}{ 1.6 \times 10 {}^{ - 4} } [/tex]
[tex]\qquad \sf \dashrightarrow \: \dfrac{4.8 }{ 1.6 } \times \dfrac{10 {}^{8} }{10 {}^{ - 4} } [/tex]
[tex]\qquad \sf \dashrightarrow \: 3 \times10 {}^{(8 - ( - 4))} [/tex]
[tex]\qquad \sf \dashrightarrow \: 3 \times10 {}^{(8 + 4)} [/tex]
[tex]\qquad \sf \dashrightarrow \: 3 \times10 {}^{12} [/tex]
So, The correct choice is : A.) 3 × 10¹²
Solve for x. Round to the nearest tenth .
Thank you!
The solution of x in the triangle is 11.5
How to determine the solution of xFrom the question, we have the following parameters that can be used in our computation:
The triangle
Using the Pythagoras theorem, we have the following equation
x^2 = 13^2 - 6^2
Evaluate the expression
x^2 = 133
Take the square roots of both sides
x = 11.5
Hence, the solution is 11.5
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Find the sum. Give your answer as a
simplified mixed number
Answer:
22/7 or 3 1/14
Step-by-step explanation:
the most common denominator is 28 for both so the denominator is 28
then added them and simplified them in mixed and normal form because I forgot which was which. Hopefully this is correct, if not I am sorry.
The total mass of a box and some oranges was 25 kg. The total mass of
the same box and some apples was 11 kg. The mass of the oranges was
3 times the mass of the apples.
Find the mass of the oranges.
In a case whereby the total mass of a box and some oranges was 25 kg. The total mass of the same box and some apples was 11 kg. The mass of the oranges was 3 times the mass of the apples, the mass of the oranges is 21kg.
How can the mass of the oranges be determined?The concept that will be used here is simplificatiopn.
We can set up as:
let a represent the box
let b represent the orange
lect c represent the apple
Then a + b = 25
a+ c = 11 ....................................................(2)
b = 3c.......................................(3)
substract equation 2 from 1
b-c = 11 ....................................(4)
substitute eqn 3 into 4
b-c = 14
3c - c =14
2c= 14
c= 7
from eqn 3
b = 3c
b = 3*7 =21
Then mass of orange = 21 kg
from eqn 2
a+ c = 11
a= 11-7= 4
mass of empty box = 4kg
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