The simplified form of the expression is, negative five sixths times x plus eight.
What is word problem?
A math word problem is a mathematical question that is stated as one sentence or more and asks students to use their arithmetic skills in a "real-life" situation. Therefore, in order for kids to understand the word problem, they need to be familiar with the terminology that goes along with the mathematical symbols that they are used to.
Given that: quantity negative two thirds times x minus 6 end quantity minus quantity negative 14 plus one sixth times x end quantity
It can be write in mathematical form as,
[tex](-\frac{2}{3}x-6) - (-14+\frac{1}{6}x)[/tex]
Simplifying the parenthesis,
[tex]= -\frac{2}{3}x-6+14-\frac{1}{6}x\\ = 8 - \frac{15}{18}x\\ = 8 - \frac{5}{6}x\\= -\frac{5}{6}x+8[/tex]
Hence, the simplified form of the expression is, negative five sixths times x plus eight
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T/F according to semistrong form efficiency, an analyst who finds some unique information buried in a firm's published financial statements will be at an advantage to the rest of the market
On the basic of properties of Semi Strong form efficiency, we conclude the given statement that According to the Semi- strong form of efficiency, analysts who find unique information hidden in a company's published financial statements have an advantage over the rest of the market is False.
Semi Strong form :
The efficiency theory of the semi-strong format uses all publicly available information when calculating the current price of a stock, allowing investors to use either technical or fundamental analysis to find the best value in the market. We follow the belief that no higher return can be generated.
Those who agree with this version of theory believe that only information not available to the public can help investors drive returns to higher levels of performance than the general market. To test the semi -strong version of EMH, we can see if the stock price fluctuates up or down if private his message has been published before. For example, proposed mergers and ambiguous earnings announcements are known to insiders but not to the public. Therefore, this information will not be correctly reflected in the stock price until it is published. At this point, investors and traders take this new information into account, so the stock may bounce or fall depending on the nature of the news.
From the semi-strong efficiency information above, we can say that the information hidden in the company's published financial statements does not benefit the rest of the market.
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50 people were asked if they like tea, coffee and hot chocolate.
Every person liked at least one of the drinks.
17 of the people like all three drinks.
31 of the people like hot chocolate
34 of the people like tea.
21 of the people like tea and coffee.
7 of the people like tea and hot chocolate but not coffee
2 of the people like coffee and hot chocolate but not tea
Two of the 50 people are chosen at random.
Work out the probability that they both like coffee
The probability that they both like coffee is 0.405
How is the probability calculated?n(H∪T∪C) = 50
n(H∩T∩C) = 17
n(H) = 31
n(T) = 34
n(T∩C) = 21
n( T∩H -C)= 7
n( C∩ H- T) = 2
By applying combination property,
No. of ways of selecting 2 random people = x = [tex]50C_{2}[/tex]
No. of people liking coffee = n( C∩ H- T) +n( C∩ T- H) +n(H∩T∩C) +n(C)
=2 +4 + 17 +9
= 32
No. of ways of selecting 2 random people liking coffee from 32 = y
= 32[tex]C_{2}[/tex]
Probability of selecting 2 random people, both liking coffee = y/x
y / x = [tex]\frac{32C_{2}}{50C_{2}}[/tex]
[tex]=\frac{32*31}{50*49} \\\\=\frac{992}{2450} \\\\= 0.405(\text{ approximately })[/tex]
The probability that they both like coffee is 0.405
What is probability?The possibility of any random event's outcome is referred to as probability. To determine the likelihood that any event will occur is the meaning of this term. A measure of how likely something is to happen is called a probability. It gauges how likely the occurrence is to occur and aids in the clear and intelligible representation of difficult data. Chance plays a huge role in probability. Statistical methods, on the other hand, are more concerned with how we manage different types of data. The terms "dependent" and "independent" are used to describe two events where the likelihood of one event occurring has no bearing on the likelihood of the other.To learn more about probability , refer:
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Medical School Applications A medical college dean read that the average number of applications a potential medical school student sends is 7.8. She thinks that the mean is higher. So she selects a random sample of 35 applicants and asks each how many medical schools they applied to. The mean of the sample is 8.7. The population standard deviation is 2.6. Test her claim at α 0.01
A Sample of medical students Applications in a medical College .
To check the claim of college Dean is correct or not we will use hypothesis testing with Z-test.
H₀ : μ = 7.8
= 7.8 Hₐ : μ > 7.8
There we see fail to reject the null hypothesis.
So, her claim that mean in higher is right.
We have given that,
Medical school applications of students in a medical College is a sample .
Sample size, n = 35
Mean of sample , X-bar = 8.7
population standard deviations, σ = 2.6
significance level, α = 0.01
Consider null and alternative hypothesis to test:
H₀ : μ = 7.8
Hₐ : μ > 7.8
Test Statistic (Z-score) :
Z = ( X-bar - μ ) / σ / √n
Z = ( 8.7 - 7.8 ) / ( 2.6 /sqrt(35 ))
Z = 2.0479 ~ 2.05
Test Criteria :-
We can reject null hypothesis if Z > Zₐ
Zₐ = Z₀.₀₁ = 2.33
that is 2.33 > 2.05 or Zₐ> Z
Thus, fail to reject null hypothesis .
There is insufficient evidence to support the claim that mean is higher.
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Screen, teen, and pychological well-being. In a tudy of three nationally repreentative largecale data et from Ireland, the United State, and the United Kingdom (n ), teenager between the age of 12 to 15 were aked to keep a diary of their creen time and anwer quetion about how they felt or acted. The anwer to thee quetion were then ued to compute a pychological well-being core. Additional data were collected and included in the analyi, uch a each child' ex and age, and on the mother' education, ethnicity, pychological ditre, and employment. The tudy concluded that there i little clear-cut evidence that creen time decreae adolecent well-being. (a) What type of tudy i thi?
(b) Identify the explanatory variable. (c) Identify the repone variable. (d) Comment on whether the reult of the tudy can be generalized to the population, and why. (e) Comment on whether the reult of the tudy can be ued to etablih caual relationhip
A. What type of study is this?
ANSWER: An observational study
B. Identify the explanatory variables.
ANSWER: Screen time
C. Identify the response variable.
ANSWER: Adolescent well-being
D. Comment on whether the results of the study can be generalized to the population, and why.
ANSWER: It cannot as there was no control group and even though it states that these populations are nationally representative of these nations there is not quite enough information to prove that. There also seems to be no randomization.
E. Comment on whether the results of the study can be used to establish causal relationships.
ANSWER: No, there is too many lurking variables in an observational study to establish causation.
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When checking for scene safety for the use of an AED Which of these best describes the dangers that would stop us?.
When checking for scene safety for the use of an AED the dangers that would stop us include
Combustible liquids close to the sufferer, flammable gases, a patient resting in standing waterWhat is an AED?An automated external defibrillator (AED) is a small, portable machine that shocks the heart with electricity through the chest.
After a sudden cardiac arrest (SCA), the shock may be able to stop an irregular heartbeat (arrhythmia) and restore a regular rhythm .
SCA happens when the heart develops a problem and abruptly stops beating. Without immediate treatment, it quickly results in death.
The dangers that would stop us from using a scene for an AED include
volatile gases, combustible liquids near the patient, and a patient lying in water
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What is the length of BC?.
the length of BC is 10cm, in the given triangle.
What is are of the triangle?
The territory included by a triangle's sides is referred to as its area. Depending on the length of the sides and the internal angles, a triangle's area changes from one triangle to another. Square units like m2, cm2, and in2 are used to express the area of a triangle.
Assuming that BR = 3 cm AR = 4 cm AC = 11 cm
Knowing that tangents to an exterior point are always equal,
BR = BP = 3 cm then.
4 cm when AR = AQ
QC= AC- AQ= 11 - 4 = 7 cm
Q = P = 7 cm
As a result, BC = BP+PC = 3 + 7 = 10 cm.
As a result, BC has a 10 cm length.
Hence the length of BC is 10cm.
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Assume that the risk-free rate of interest is 6% and the expected rate of return on the market is 11%. i am buying a firm with an expected perpetual cash flow of $1,000 but am unsure of its risk. if i think the beta of the firm is 1.1, when in fact the beta is really 2.2, how much more will i offer for the firm than it is truly worth?
i will offer $2,813.3 more for the firm than it is truly worth. if the risk-free rate of interest is 6% and the expected rate of return on the market is 11% with an expected perpetual cash flow of $1,000.
it can be calculate as follows:
Risk-free return (Rf) = 6%
Market return (Rm) = 11%
beta 1 = 1.1
Actual Beta (B2) = 2.2
capital cost Kc =Rf + B1 (Rm-Rf)
Capital cost using estimated beta = 6 + 1.1 (11 - 6) = 11.5 %
Capital cost using actual beta = 6 + 2.2 (11- 6) = 17 %
Cash flows are received till perpetuity $1000
Valuation of the firm = cash flow
cost of capital
Valuation at 11.5% cost of capital = 1000 = approximately $8,695.65
0.115
Valuation at 17% cost of capital = 1000 = approximately $5,882.35
0.17
Excess value over true value delivered = $8,695.65 - $5,882.35= $2,813.3
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Solve the equation. Remember to check for extraneous solutions.
x-5/x+5=6/x+5 +5
⇒The first step is to eliminate the fraction by multiplying all the terms with the lowest common denominator.
⇒In this case the lowest common denominator is (x+5), meaning all the terms will be multiplied by (x+5)
⇒[tex]\frac{x-5}{x+5} (x+5)=\frac{6}{x+5} (x+5)+5(x+5)[/tex]
⇒Multiply out the brackets.
[tex]x-5=6+5(x)+5(5)\\x-5=6+5x+25[/tex]
⇒Group the like terms together and simplify.
[tex]x-5x=6+25+5\\-4x=36\\\frac{-4x}{-4} =\frac{36}{-4} \\x=-9[/tex]
⇒∴ x=-9
you have set up a netflow collector using ip address 172.17.8.25 on udp port 2055. which of the following commands will redirect records to the new collector?
ip flow-export destination 172.17.8.25 2055 is the set up a netflow collector using ip address 172.17.8.25 on udp port 2055.
What is netflow collector?
A NetFlow-enabled router or switch can record statistical, infrastructural, routing, and other information about IP traffic flows using the NetFlow protocol, which was created by Cisco Systems. One of the three typical functional elements used for NetFlow analysis.A NetFlow exporter is a router, switch, probe, or host software agent that tracks important statistics and other information about IP packet flows and creates flow records that are delivered to a flow collector in the form of UDP packets.An application called NetFlow Collector is in charge of accepting flow record packets from one or more flow exporters, ingesting the data from the flow records, pre-processing and storing flow records.Hence, the ip flow-export destination 172.17.8.25 2055 is the set up a netflow collector using ip address 172.17.8.25 on udp port 2055.
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What is the solution to this system of linear equations x − 3y − 2 x 3y 16?.
The solution for this system of linear equation is (-16, -5 1/3).
What is Linear equation?
A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. The variables in the preceding equation are y and x, and it is occasionally referred to as a "linear equation of two variables."
It is preferable to employ substitution while trying to solve this system of linear equations.
The first equation yields x = 3y.
In the second equation, change the value of x to be represented by the expression on the right.
-2(3y) + 3y = 16
Calculating the value of y yields;
y = -5 1/3
Solving for x with this value of y results in;
x = -16
The solution for this system of linear equation is (-16, -5 1/3).
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The slope of a line is -. find the slope of a line that is perpendicular to this line. -3 3
The required slope of line perpendicular to the given line is 1/3.
What are perpendicular lines and its slope?perpendicular lines have slants that are negative reciprocals of each other. The given line's incline is 5, and that implies that the slant of the other line should be its negative equal. Angle between perpendicular lines is 90 degree.
According to question:Slope of first line (m) = -3
let the slope of other line is n,
then, we know that
m×n = -1
-3×n = -1
n = 1/3
Thus the slope onother line is 1/3.
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Answer:
1/3
Step-by-step explanation:
In a poll to estimate presidential popularity, each person in a random sample of 1,030 voters was asked to agree with one of the following statements: 1. The president is doing a good job. 2. The president is doing a poor job. 3. I have no opinion. A total of 525 respondents selected the first statement, indicating they thought the president was doing a good job.
a. Construct a 90% confidence interval for the proportion of respondents who feel the president is doing a good job. (Use z Distribution Table.) (Round your answers to 3 decimal places.) Confidence interval for the proportion is up to .
b. Based on your interval in part (a), is it reasonable to conclude that a majority of the population believes the president is doing a good job?
No Yes
The confidence interval for the proportion of respondents who feel the president is doing a good job is 48.40% < p < 53.53%
It is given that,
sample size, n = 1030
The number of people who think that the president is doing a good job, x = 525
The sample Proportion = x/n = 525/ 1030
= 0.509709
now using,
SE = sqrt [p × (1 - p) / (n)]
= sqrt [ (0.5097 × ( 1 - 0.5097)) / 1030]
= 0.015576
Z- critical for a 90% confidence interval for the proportion of respondents = 1.645 (using z Distribution Table)
thus, the lower bound = 0.509709 - 1.645 (0.015576) = 0.484085 that is 48.40%
and upper bound = 0.509709 + 1.645 (0.015576) = 0.535332 that is 53.53%
The confidence interval is 48.40% < p < 53.53%.
b. yes, a majority (53.53%) of the population believes the president is doing a good job.
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What does adding doubles mean?.
Adding doubles mean that the result will be obtained by adding 2 times of the numbers.
According to the question,
We have the following information:
We have to know what does it mean to add doubles.
Now, we know that doubles mean that the same number is added two times or in other words it has been multiplied by 2.
For example, the double of 3 is 6 and the double of 4 is 8 because we have multiplied both the numbers by 2.
Now, adding the doubles of 3 and 4 means that we will add 6 and 8 and the result in this case is 14.
Hence, adding doubles mean that the result will be obtained by adding 2 times of the numbers.
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How do you find the x and y intercepts of an equation to find the x-intercept substitute 0 for X to find the y-intercept substitute 0 for X?.
Substitute 0 for y to find the x-intercept and Substitute 0 for x to find the y-intercept.
This is obvious because if y is set to 0, the only variable left is x (indicating that the x intercept has been found), and vice versa.
We set y = 0 and solve the equation for x to find the x-intercept. This is because the line crosses the x-axis when y=0. When an equation is not in the form y = mx + b, we can solve for the intercepts by plugging in 0 and solving for the remaining variable. Set x = 0 and solve for y to find the y-intercept.
The line crosses the x-axis when y=0. When an equation is not in the form y = mx + b, we can solve for the intercepts by plugging in 0 and solving for the remaining variable. Set x = 0 and solve for y to find the y-intercept.
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What is the scale factor used when going from the larger rectangle to the smaller one?.
Use the scaling factor equation: greater length over smaller length to go from a smaller to a larger figure. Use the formula scale factor = smaller length over larger length if you're scaling down from a larger to a smaller figure.
What is scale factor in math?
The ratio of one object's scale to that of a new object, which has its representation but is larger, is known as a scale factor (bigger or smaller). By multiplying each side by a certain number, say 2, we can increase the size of a rectangle with sides of 2 cm and 4 cm.How can I calculate the scale factor?
The scale factor is calculated using the following fundamental formula Scale factor = Dimension of the new shape Dimension of the old shape. The formula for calculating the scale factor is written as Scale factor = Larger figure dimensions Smaller figure dimensions in the event that the original figure is magnified.Learn more about scale factor
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several properties are used to evaluate this expression. identify the property used in each step. 21 (36 0 19) 21 (36 19): 21 (19 36): (21 19) 36: 40 36 76
Properties used to evaluate the expressions,
21 ( 36 0 19 ) : 21 (36 19) - Identity property21 (36 19) : 21 (19 36) - Commutative property21 (19 36) : (21 19) 36 - Associative property(21 19) 36 : 40 36 76 - Closure PropertyAddition is the basic arithmetic operation in maths. In addition, we add the integers. There are few properties of addition to add the given integers.
Additive identity property of Addition:A + 0 = 0 + A = A
⇒ 21 ( 36 + 0 + 19 ) = 21 ( 36 + 19 )
Commutative property of Addition:A + B = B + A
⇒ 21 ( 36 + 19 ) = 21 + ( 19 + 36 )
Associative property of Addition:A + ( B + C ) = ( A + B ) + C
⇒ 21 + ( 19 + 36 ) = ( 21 + 19 ) + 36
⇒ ( 21 + 19 ) + 36 = 40 + 36
Closure property of Addition:A + B = C
⇒ 40 + 36 = 76
⇒ 21 + ( 36 + 0 + 19 ) = 76
Therefore, 21 ( 36 0 19 ) : 21 (36 19) uses Identity property, 21 (36 19) : 21 (19 36) uses Commutative property, 21 (19 36) : (21 19) 36 uses Associative property and (21 19) 36 : 40 36 76 uses Closure Property.
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Which of the following are the recommended percentage groupings of the ABC classifications of the dollar volume of products?A items get 25%, B items get 15%, and C items get 60%A items get 15%, B items get 45%, and C items get 40%A items get 25%, B items get 35%, and C items get 40%A items get 10%, B items get 40%, and C items get 50%A items get 20%, B items get 30%, and C items get 50%
Recommended percentage grouping of ABC classification is A items get 20%, B items get 30% and C items get 50%.
What is Dollar volume?
DOLLAR VOLUME is the result of multiplying the closing price by the principal market's trading volume on a given trading day.
DOLLAR VOLUME refers to the dollar volume of shares of Common Stock traded on the Principal Market on a Trading Day for any given Trading Day.
When referring to residential real estate, the term "dollar volume" simply refers to the sum of all residences' sales prices during a specific time period (month, quarter, year). It does not divide out by unit count like average sales price, but rather represents the largest dollar-based measure of sales activity.
Hence, Recommended percentage grouping of ABC classification is A items get 20%, B items get 30% and C items get 50%.
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How to do this
Help project do tomorrow
The number of tables and chairs will the school purchase for the cafeteria exists tables and chairs will the school purchase for the cafeteria exists 10 tables and 80 chairs.
What is meant by mathematical operation?A function that converts zero or more input values into a clearly defined output value is referred to in mathematics as an operation. The operation's complexity is measured by the number of operands.
A value is computed utilizing operands and a math operator as part of the mathematical "operation." In order to be applied to the provided operands or integers, the math operator's symbol has predetermined rules.
In each table, there are 8 chairs. 8 × 40 = 320
1 table cost 200$
Each set of table + chairs is 200 + 320 = 520
Total amount of money the school can spend is 5200
Therefore 5200 ÷ 520 = 10
So there are 10 sets of Table + chairs
So there are 10 tables
Total amount of chairs is 8 × 10 = 80
Therefore, the number of tables and chairs will the school purchase for the cafeteria exists tables and chairs will the school purchase for the cafeteria exists 10 tables and 80 chairs.
The complete question is:
To furnish a school cafeteria a school can spend $5200 on tables and chairs. Tables cost $200 each and chairs cost $40. There are 8 times as many chairs as tables. How many tables and chairs will the school purchase for the cafeteria?
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Graph the function below by moving the vertical asymptotes and the x intercept to the correct location, then make sure the end behavior of the function is correct. f(x) = x+2/(x + 4) (x + 1)
For given function f(x) = x+2/(x + 4) (x + 1), the graph of function is as shown below and the end behaviour of function is as x → -∞, f(x)→0, as x → +∞, f(x)→0
In this question, we have been given a function f(x) = x+2/(x + 4) (x + 1)
We need to gaph the given function.
From given function we can observe that the function f(x) is not defined for x = -4 and x = -1
Also, the degree of numerator = 1 and the degree of denominator is 2
We know that if the degree of the denominator > degree of the numerator, then a horizontal asymptote is at y = 0 (x - axis)
The graph of function f(x) is as shown below.
The x-intercept for the graph function f(x) is at (-2, 0)
Also, as x → -∞, f(x)→0
and as x → +∞, f(x)→0
Therefore, for given function f(x) = x+2/(x + 4) (x + 1), the graph of function is as shown below and the end behaviour of function is as x → -∞, f(x)→0, as x → +∞, f(x)→0
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a 16-ft. ladder is leaning against a house. the ladder angle of elevation is 470. how far above the ground is the top of the ladder?
a 16-ft. ladder is leaning against a house. the ladder angle of elevation is 470, the distance between the wall and the foot of the ladder is 10.991ft.
Given ,
Length of the ladder is 16ft
Angle of elevation is 47 degree
To calculate the distance between the wall and the foot of the ladder
Cos thete = BC/AC
Cos 47 deg = BC / 16
16*0.6819 = BC
BC = 10.911 ft
Therefore , the distance between the wall and the foot of the ladder is 10.991ft
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A random sample of 40 ucf students has a mean electricity bill of $110. Assume the population standard deviation is $17. 90. Construct a 90% confidence interval for the mean electricity bill of all ucf students. Round final answer to two decimal places. No $ needed in your answer.
Using the t-distribution, it is found that the 90% confidence interval for the mean electricity bill of all ucf students is (108.79, 121.21).
It is referred to as the simple random sampling technique when each member of a population has an equal likelihood of being chosen. This sampling technique relies solely on chance to determine the selection. A random number generator or any other approach that relies solely on chance can be used to carry out such a sampling strategy.
Using the t-distribution, it is found that the 90% confidence interval for the mean electricity bill of all ucf students is (105.25, 114.75).
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The world record for the most number of speed skips in 60 seconds is 332 skips. If the record holder skipped at a constant ratio of seconds to skips, how many skips did she make in 15 seconds?
suppose x is a binomial random variable with parameters n and p given below. compute the indicated probability in each of these cases. a) If n=4n=4 and p=0.4p=0.4 then P(X=0)=P(X=0)= . b) If n=4n=4 and p=0.1p=0.1 then P(X=4)=P(X=4)= . c) If n=5n=5 and p=0.1p=0.1 then P(X=0)=P(X=0)= . d) If n=3n=3 and p=0.3p=0.3 then P(X=0)=P(X=0)=
The probability of each of these cases when binomial random variable with parameters n and p are given:
a. 0.4116, b. 0.5625, c. 0.329, d. 0.375, e. 0.0046
What is probability?The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, broadly speaking, 0 denotes the event's impossibility and 1 denotes certainty. Simply put, probability is the likelihood that something will occur. When we don't know how an event will turn out, we might discuss the likelihood or likelihood of several outcomes. Statistics is the study of events that follow a probability distribution.
Here,
The formula is,
P(x)=(n/x)(P)ˣ(1-P)ⁿ⁻ˣ
a. n=4, x=1, p=0.3
P(x)=0.4116
b. n=2, x=0, p=0.25
P(x)=0.5625
c. n=5, x=2, p=0.33
P(x)=0.329
d. n=4, x=2, p=0.5
P(x)=0.375
e. n=3, x=3, p=1/6
P(x)=0.0046
When a binomial random variable with parameters n and p is given, the probability of each of the following cases is given is: a. 0.4116, b. 0.5625, c. 0.329, d. 0.375, and e. 0.0046
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Please help me with this work it’s statements and reasons
The proof of ∠WVY = ∠XVZ for the given angles in the figure has been proved.
What is an angle?An angle is a geometry in plane geometry that is created by 2 rays or lines that have an identical terminus.
In another word, the angle is the measurement of the angular distance for example for linear motion we have a meter inch but for angular rotation, we don't have the measurement so the angle is useful to measure the angular rotation.
As per the given,
∠WVX = ∠YVZ
Since,∠WVX = ∠WVY - ∠YVX
∠YVZ = ∠XVZ - ∠YVX
Compare both,
∠WVY - ∠YVX = ∠XVZ - ∠YVX
∠WVY = ∠XVZ (proved)
Hence "The proof of ∠WVY = ∠XVZ for the given angles in the figure has been proved".
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Please answer this question.
Answer:
biggest size = 89 in ; smallest size = 30 in
Step-by-step explanation:
Tmax = 2 x 132 / 3 + 1
2 x 44 + 1
88 + 1
89 in
Tmin = 132/4 - 3
33 - 3
30 in
Would you use SSS or SAS to prove the triangles congruent?.
Answer:
SSS (side-side-side) and SAS (side angle side) both prove that two triangles are congruent, it depends on the data you have whether to use one or the other
Directed line egment ¯¯¯¯¯¯ A B ha endpoint A ( − 8 , 7 ) and B ( 7 , − 3 ) What are the coordinate of P uch that P i the point partitioning ¯¯¯¯¯¯ A B in the ratio 1 : 4 ? Write each coordinate a a implified fraction if neceary
The coordinate of point P is (-5,5).
It is given that AB has endpoint A(-8,7) and B(7,-3) also P is the point partitioning AB in the ratio 1:4.
We have to find the coordinates of P.
So distance in x-coordinate between A and B is,
ABx = 7 - (-8) = 15 units
distance in y-coordinates between A and B is,
ABy = -3 - 7 = -10 units
Now the point P partitioning AB in the ratio 1:4
i.e [tex]\frac{AP}{AB}[/tex] = [tex]\frac{1}{1+4}[/tex]
[tex]\frac{AP}{AB}[/tex] = [tex]\frac{1}{5}[/tex]
we will find x-coordinate of point P
⇒ [tex]\frac{APx}{ABx}[/tex] = [tex]\frac{1}{5}[/tex]
⇒ [tex]\frac{APx}{15}[/tex] = [tex]\frac{1}{5}[/tex]
⇒ APx = 3
Therefore the x-coordinates of P is
Px = Ax + APx
⇒ Px = -8 + 3 = - 5
And y-coordinate of pint P is,
[tex]\frac{APy}{ABy}[/tex] = [tex]\frac{1}{5}[/tex]
[tex]\frac{APy}{-10}[/tex] = [tex]\frac{1}{5}[/tex]
APy = -2
i.e Py = APy + Ay
= -2 + 7
Py = 5
Therefore the coordinate of point y is (-5,5).
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a number,h, rounded to 2sf is 0.072 what is the error interval
Answer:
Step-by-step explanation:
What is 2sf?
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The number of students in 2001 is 150.4 thousand and the number of students in 2018 is 467.5 thousand
The number of students in 2001The function in the question is given as
y = 123.1(1.069)ˣ
Where
x is the number of years from 1998 through 2013
So, the value of x in 2001 is
x = 2001 - 1998
Evaluate
x = 3
Substitute x = 3 in the equation y = 123.1(1.069)ˣ
y = 123.1(1.069)³
Evaluate
y = 150.4
The number of students in 2018In the year 2018, the value of x is calculated as
x = Current year - 1998
So, we have
x = 2018 - 1998
Evaluate
x = 20
Substitute x = 20 in the equation y = 123.1(1.069)ˣ
y = 123.1(1.069)²⁰
Evaluate
y = 467.5
Hence, the number of students in 2018 is 467.5
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the continuous random variable n has a normal distribution with mean 7.5 and standard deviation 2.5. for which of the following is the probability equal to 0 ?
Using the normal distribution we find that P(X=8) equals zero.
What is probability?The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true.An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.The likelihood that an event will occur increases with its probability.A straightforward illustration is tossing a fair (impartial) coin.The chance of both outcomes ("heads" and "tails") is equal because the coin is fair, "heads" is more likely than "tails," there are no other conceivable outcomes, and the likelihood of either outcome.According to our question-
Measures how many standard deviations a measurement is from its mean.
After finding the Z-score, look at the Z-score table to find the p-value (percentile of x) associated with that Z-score.
As with any continuous distribution, the probability of an exact value, P(X = x), is 0.
So t we know that P(X=8) equals zero.
Hence, Using the normal distribution we find that P(X=8) equals zero.
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