Find the coordinates of point S that lies along the directed line segment from R(-14, -1) to T(4, -13) and partitions the segment in the ratio of 1:5.
Answer: The required co-ordinates of the point S are (-11, -6).
Step-by-step explanation: We are given to find the co-ordinates of the point S that lies along the directed line segment from R(-14, -1) to T(4, -13) and partitions the segment in the ratio of 1:5.
We know that
the co-ordinates of a point that divides the line segment joining the points (a, b) and (c, d) in the ratio m : n is given by
[tex]\left(\dfrac{mc+na}{m+n},\dfrac{md+nb}{m+n}\right).[/tex]
According to the given information, we have
(a, b) = (-14, -1), (c, d) = (4, -13) and m : n = 1 : 5.
Therefore, the co-ordinates of the point S are given by
[tex]\left(\dfrac{1\times4+5\times(-14)}{1+5},\dfrac{1\times(-13)+5\times(-1)}{}\right)\\\\\\=\left(\dfrac{4-70}{6},\dfrac{-13-5}{6}\right)\\\\\\=\left(\dfrac{-66}{6},\dfrac{-18}{6}\right)\\\\=(-11,-3)[/tex]
Thus, the required co-ordinates of the point S are (-11, -6).
Your little brother just learned how to flip and catch a coin. He believes that by catching the coin in mid-air, he can influence the probability that it will land heads up. Based on your understanding of theoretical probability, explain to your little brother why his theory of influence is false.
If a coin is fair then it has two faces , one is heads and the another is tails.
The probability getting any favorable outcomes is given by the formula :-
[tex]\dfrac{\text{Number of favorable outcomes}}{\text{Total outcomes}}[/tex]
So the factor effecting probability is just the number of favorable outcomes and total outcomes.
If a coin is tossed then the probability of getting heads will be :-
[tex]P(H)=\dfrac{1}{2}=0.5=50\%[/tex]
To get heads always this should be 1 , which can be happen if number of favorable outcomes is equal to total outcomes.
i.e. Number of heads = Number of total outcomes, this means coin should be biased.
Catching the coin in mid-air can never be a factor for this.
Therefore, the little brother's theory is false.
Answer:
Sample Response: The probability of a coin landing heads up is 1/2, or 50%. That fact will not change if the coin is caught in midair.
Step-by-step explanation:
Based on the graph, what are all of the solutions to f(x) = x3 − 7x − 6? x = −6 x = −2, −1 x = −2, −1, 3 x = −6, −2, −1, 3
You are dealt two cards successively (without replacement) from a shuffled deck of 52 playing cards. find the probability that the first card is a king and the second card is a queen.
there are 4 kings and 4 queens in a deck
chance of getting a king is 1/52
chance of getting a queen without the king being put back would be 1/51
1/52 x 1/51 = 1/2652 probability
The probability of drawing first a king and then a queen from a standard deck without replacement is 0.603%, which is calculated by multiplying the individual probabilities of drawing a king and then a queen (1/13 * 4/51).
The student is asking about how to calculate the probability of drawing two specific cards from a deck of cards in succession without replacement. In a standard deck of 52 cards, the probability of drawing a king first is 4/52 since there are four kings in the deck. After drawing a king, there are 51 cards left, and the probability of drawing a queen next is 4/51 because there are four queens in the deck. These events are dependent because the outcome of the second draw depends on the first.
To find the combined probability of both events happening, we multiply the probabilities of each event:
P(first card is a king) = 4/52
P(second card is a queen after drawing a king) = 4/51
So, the probability is (4/52) * (4/51), which simplifies to 1/13 * 4/51.
Combined probability = (1/13) * (4/51) = 4/663 = 0.006033182503770739, or about 0.603% when expressed as a percentage.
(08.05)The box plot shows the total amount of time, in minutes, the students in a class spend traveling to school each day: A box plot is titled Daily Travel Time and labeled Time (min). The left most point on the number line is 10 and the right most point is 45. The box is labeled 16 on the left edge and 36 on the right edge. A vertical line is drawn inside the rectangle at the point 28. The whiskers are labeled as 11 and 43. What information is provided by the box plot?
The left-most point on the number line is 10.
Minimum value = 10
The right-most point is 45.
Maximum value= 45
First quartile or lower quartile = 16
Third quartile or upper quartile = 36
The median is 28.
Given thatThe box plot shows the total amount of time, in minutes, the students in a class spend traveling to school each day:
A box plot is titled Daily Travel Time and labeled Time (min).
The left-most point on the number line is 10 and the right-most point is 45.
The box is labeled 16 on the left edge and 36 on the right edge.
A vertical line is drawn inside the rectangle at point 28.
The whiskers are labeled as 11 and 43.
We have to determineWhat information is provided by the box plot?
According to the questionIn the box plot, the information is given as follows.
The left-most point on the number line is 10.Minimum value = 10
The right-most point is 45.Maximum value= 45
First quartile or lower quartile = 16Third quartile or upper quartile = 36The median is 28.To know more about Median click the given below.
https://brainly.com/question/9969858
one teaspoon equals 0.5 centimeters. how many liters equals 50 teaspoons? Round the answer to the nearest hundredth.
50 teaspoons would equal 50*0.5 = 25 centimeters
1 cm = 0.001 liter
25*0.001 = 0.025 liters
Which sequence of transformations creates a similar but not congruent triangle?
A. Dilation and reflection
B. Reflection and rotation
C.Reflection and translation
D.Translation and rotation
Answer:
A
Step-by-step explanation:
how many different ways can an after school club of 13 students line up
Answer: 6227020800
Step-by-step explanation:
Jorani flips two standard american quarters. how many ways can she get at least one head?
A collection of 24 coins, consisting of nickels, dimes, and quarters, has a value of $3.40. if there are twice as many quarters as nickels, and one-third as many nickels as dimes, how many coins of each kind are there?
Graph the functions and approximate an x-value in which the quadratic function exceeds the exponential function. y = 4x y = 7x2 + 4x - 2
x = -0.5
x = 0
x = 0.5
x = 2
Answer:
Option 3th is correct
x = 0.5
Step-by-step explanation:
The given functions are:
Function 1: [tex]y = 4^x[/tex]
Function 2: [tex]y=7x^2+4x-2[/tex]
The values of function at x = -0.5, 0, 0.5 and 2 are as follow:
x values Function 1 Function 2
-0.53 0.5 -2.25
0 1 -2
0.53 2.086 2.0863
2 16 34
From the above table. It is clear that the quadratic function [tex]y=7x^2+4x-2[/tex] exceeds the exponential function [tex]y = 4^x[/tex] at x = 0.53
Therefore, the approximate x-value in which the quadratic function exceeds the exponential function at x = 0.5
A cone is a solid that has one circular base and only one face. true or false
The following is a geometric sequence.
1, 2, 6, 24
TRUE
FALSE
5. Given the following triangle side lengths, identify the triangle as acute, right or obtuse. Show your work. a. 3in, 4in, 5 in b. 5in, 6in, 7in c. 8in, 9in, 12in
The triangle with measures 3 in., 4 in. and 5 in. made up right angle triangle.
What is a triangle?A triangle is a three-sided polygon, which has three vertices. The three sides are connected with each other end to end at a point, which forms the angles of the triangle. The sum of all three angles of the triangle is equal to 180 degrees.
a) Given that, 3 in., 4 in. and 5 in.
By using Pythagoras theorem, we get
5²=3²+4²
25=9+16
25=25
So, the triangle is right triangle.
b) The given sides of triangle measures 5 in., 6 in. and 7 in.
To determine whether the triangle is acute, right, or obtuse, add the squares of the two smaller sides, and compare the sum to the square of the largest side.
7²<5²+6²
49<25+36
49<61
So, the triangle is acute angle triangle.
c) The given sides of triangle measures 8 in., 9 in. and 12 in.
12²>8²+9²
144>64+81
144>125
So, the triangle is obtuse angle triangle.
Therefore, the triangle with measures 3 in., 4 in. and 5 in. made up right angle triangle.
Learn more about the triangle here:
brainly.com/question/2773823.
#SPJ7
The length of a rectangle is 3 mm greater than the width. the area is 154 mm squared. find the length and the width.
area = l x w
l = w+3
sqrt(154) = 12.4 round o 12
12-1 = 11
11+3 = 14
11 * 14 = 154
width = 11
length = 14
How to simplify all this numbers to make one equation?
Answer the questions that aren't covered please? Thanks
HELP ME!!!! PLEASE!!!! Ughhh
An expression is shown below:
square root of 32 plus square root of 2
Which statement is true about the expression?
It is rational and equal to 4.
It is rational and equal to 5.
It is irrational and equal to 5 multiplied by square root of 2.
It is irrational and equal to 4 multiplied by square root of 2.
Answer:
It is irrational and equal to [tex]5[/tex] multiplied by square root of [tex]2[/tex]
Step-by-step explanation:
we have
[tex]\sqrt{32}+\sqrt{2}[/tex]
Remember that
[tex]32=2^{5}[/tex]
substitute in the expression
[tex]\sqrt{2^{5}}+\sqrt{2}=4\sqrt{2}+\sqrt{2}=5\sqrt{2}[/tex]
therefore
It is irrational and equal to [tex]5[/tex] multiplied by square root of [tex]2[/tex]
Find the surface area of a hemisphere with a diameter of 26 cm. Round your answer to the nearest tenth.
NEED HELP!!!!
Which of the following types of statement cannot be used to explain the steps of a proof? Check all that apply.
1.Postulate
2.Theorem
3.Conjecture
4.Guess
Choose more then 1
Answer:
Please don't use the answer that was given ,,, the correct answer is GUESS and Conjecture
Step-by-step explanation:
Which of the following is the coefficient in the algebraic expression 8x+z^2
Answer:
The coefficients are 8 and 1.
Step-by-step explanation:
In order to determine the answer, we have to know about algebraic expressions.
An algebraic expression is conformed by terms or only one term.
A term is just a variable with a coefficient. Also similar terms have the same variable but no always the same coefficient. Therefore if the algebraic expression has two terms, so there are two coefficients. The coefficient with value "1" is not necessary write it.
In this case, we have two terms:
"x" variable."z" variable.So, we have two coefficients:
For x, the coefficient 8.For z, the coefficient 1.Finally, the coefficients are 8 and 1.
someone answer and explain how to do this plz
area = the height times the base divided by 2
13*4=52
52/2 = 26
area = 26 sq. units
Determine the equation of the graph and select the correct answer below.
y = (x + 1)2 + 3
y = (x + 1)2 − 3
y = (x − 1)2 − 3
y = (x − 1)2 + 3
?? Please help answer and solve, showing the steps you took
The lifetimes of lightbulbs of a particular type are normally distributed with a mean of 392 hours and a standard deviation of 9 hours. find the first quartile, q1.
The 1st quartile q1 is also called the 25th percentile (the bottom 25% of a data set). In this case, if we choose 100 light bulbs, then the 1st quartile will be the 25 bulbs with shortest useful life.
To solve this problem, we would have to use the z statistic.
Using the standard distribution tables for z, we locate for the value of z at P
= 0.25:
z = - 0.674
Then to calculate for the 1st quartile, we use the
formula:
Q1 = x + z * s
where x is the mean, and s is the standard deviation, therefore:
Q1 = 392 + (- 0.674) (9)
Q1 = 385.934
To find the first quartile of a normal distribution, use the z-score corresponding to an area of 25%. For these lightbulbs with a mean of 392 hours and standard deviation of 9 hours, the first quartile is approximately 386 hours.
Explanation:In statistics, the quartiles of a dataset divide the data into four equal parts. The first quartile, Q1, is the value below which 25% of the data fall. To determine Q1 for the lifetime of a certain type of lightbulb, we use the properties of the normal distribution.
First, realize that 25% of data falls below Q1, and hence using the z-table, we find that z=-0.675 corresponds to an area of 0.25. We then use the formula for a z-score in a normal distribution, z = (X - μ)/σ. Solving for X we find X = z*σ + μ.
Plugging in the known values we get Q1 = -0.675*9 + 392 = 386.025 hours. So, for these lightbulbs, 25% will have failed by around 386 hours.
Learn more about First Quartile here:https://brainly.com/question/24329548
#SPJ11
you borrow $90 from your grandmother. you pay back $15 each week.
a. write an equation in standard for that represents the amount owed y after x weeks.
b. find the y intercept of the graph. what does this represent?
c. find the x intercept of the graph. what does this represent?
Answer: a) y = 90-15x
b) y = 90
c) x = 6
Step-by-step explanation:
Since we have given that
Amount borrowed from his grandmother = $90
Amount he pay back each week = $15
Let the number of weeks be 'x'.
Let total amount owed be 'y'.
So, it becomes
[tex]y=90-15x[/tex]
a) write an equation in standard for that represents the amount owed y after x weeks.
Our equation is [tex]y=90-15x[/tex]
b. find the y intercept of the graph. what does this represent?
For this , we put x = 0.
[tex]y=90-15(0)\\\\y=90[/tex]
So, the y-intercept of the graph is 90.
It represents that the graph intersect y-axis at (0,90)
c. find the x intercept of the graph. what does this represent?
For this, we put y = 0.
[tex]0=90-15x\\\\90=15x\\\\x=\dfrac{90}{15}\\\\x=6[/tex]
So, the x intercept of the graph is 6.
It represents that the graph intersect the x-axis at (6,0)
Solve this quadratic equation by completing the square.
x^2+10x=7
What is the algebraic expression for "the difference between seven times a number and three times that number"?
7 - 3x
7x - 3
7x - 3x
Answer:
(C)7x-3x
Step-by-step explanation:
The given algebraic expression is:
"The difference between seven times a number and three times that number"
Let the number be equal to =x, then according to the statement, we have
seven times a number=7x and three times that number=3x
The difference between seven times a number and three times that number=7x-3x
which is the required algebraic expression.
Hence, option C is correct.
Find an explicit rule for the nth term of a geometric sequence where the second and fifth terms are 5 and 625, respectively.