What the SAS similarity theorem is?.
The SAS standard for similarity of triangles states that triangles are similar if two sides of one triangle are proportional to two sides of another triangle and their included angles are congruent.
Statement : The statement can be expressed as follows:
If two triangles ABC and DEF are such that
∠A=∠D and AC /DF =AB/DE
then △ABC∼△DEF
Proof :
Given: △ABC and △DEF are such that
AC /DF =AB/DE and ∠A=∠D
To Prove : △ABC∼△DEF
Construction : Draw a line PQ such that DP= AB , DQ= AC
In △ABC and △DPQ
AB = DP ( by construction)
DQ= AC ( by construction)
∠A=∠D (given)
=> △ABC ≅△DPQ (by SSA congruence property)
AB/DE = AC/DF (given )
=> DP/DE = DQ/DF ( using AB = DP ; DQ= AC)
=> PQ||EF (by converse of B.P.T)
Now , ∠P =∠E and ∠Q =∠F ( by corresponding angles)
△DEF ≅ △DPQ (Using AAS congruence )
=> △ABC ∼△DEF ( because two congrunt triangles are always similar )
Hence proved .
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What is 18.92 divided by11 equals 18.92 at the top 11 at the bottom explain your answer PLEASE I HAVE TO SUMMIT THIS IN 19 MIN!
Answer:
Is there a diagram or picture??
Step-by-step explanation:
According to the WHO MONICA Project the mean blood pressure for people in China is 128 mmHg with a standard deviation of 23 mmHg. Assume that blood pressure is normally distributed.
Round the probabilities to four decimal places.
It is possible with rounding for a probability to be 0.0000.
a) State the random variable.
Select an answer rv X = a randomly selected person in China rv X = the mean blood pressure of a sample of people in China rv X = the mean blood pressure of all people in China rv X = blood pressure is normally distributed rv X = the blood pressure of a randomly selected person in China
b) Find the probability that a randomly selected person in China has a blood pressure of 83.8 mmHg or more.
c) Find the probability that a randomly selected person in China has a blood pressure of 113.4 mmHg or less.
d) Find the probability that a randomly selected person in China has a blood pressure between 83.8 and 113.4 mmHg.
e) Find the probability that randomly selected person in China has a blood pressure that is at most 70.5 mmHg.
f) Is a blood pressure of 70.5 mmHg unusually low for a randomly selected person in China?
Why or why not?
Select an answer yes, since the probability of having a value of blood pressure at least that high is less than or equal to 0.05 yes, since the probability of having a value of blood pressure at the most that value is less than or equal to 0.05 no, since the probability of having a value of blood pressure at least that high is less than or equal to 0.05 no, since the probability of having a value of blood pressure at the most that value is less than or equal to 0.05 yes, since the probability of having a value of blood pressure at least that high is greater than 0.05 yes, since the probability of having a value of blood pressure at the most that value is greater than 0.05 no, since the probability of having a value of blood pressure at least that high is greater than 0.05 no, since the probability of having a value of blood pressure at the most that value is greater than 0.05
g) What blood pressure do 78% of all people in China have less than?
Round your answer to two decimal places in the first box.
Put the correct units in the second box.
The answer to the question probability of randomly selected person has a blood pressure of 182.6 mmHg is 0.0088.
What is standard deviation?
A measure of a group of values' variance or dispersion in statistics is called the standard deviation. When the standard deviation is low, the values are more likely to fall within a narrow range, also known as the expected value, whereas when the standard deviation is high, the values tend to be closer to the mean.
The lowercase Greek letter sigma, which stands for the population standard deviation, or the Latin letter s, which stands for the sample standard deviation, are most frequently used in mathematical equations and texts to represent standard deviation. Standard deviation is also sometimes referred to as SD.
The mean blood pressure for people in china is 128 mmHg.
The standard deviation of 23 mmHg.
For blood pressure of 182.6 mmHg
=p(x> 182.6)
=p(z> 182.6-128/23)
=p(z> 2.37)
=0.0088
Hence the probability of a randomly selected person has a blood pressure of 182.6 mmHg is 0.0088.
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Peter estimates that it takes him 1/4 hours to prepare dough, 1/10 hours to grate cheese, 1/3 of an hour to prepare toppings, and 2/5 an hour to bake the pizza.
What fraction of time did it take peter in total to prepare the pizza?
What was the actual time it took in minutes and hours?
Answer:
13/12 hours or 1 hour and 5 minutes--------------------------------
Add up all fractions to get total time to prepare the pizza1/4 + 1/10 + 1/3 + 2/5 = Common denominator is LCM(3,4,5,10) = 6015/60 + 6/60 + 20/60 + 24/60 = 65/60 hours = (13/12 hours simplified fraction)65 minutes =1 hour and 5 minutesAnswer:
13/12 hours
1 hour 5 minutes
Step-by-step explanation:
Given timings:
1/4 hours to prepare dough.1/10 hours to grate cheese.1/3 of an hour to prepare toppings.2/5 if an hour to bake the pizza.To find the total time it took Peter to prepare the pizza, sum the fractions.
[tex]\implies \dfrac{1}{4}+\dfrac{1}{10}+\dfrac{1}{3}+\dfrac{2}{5}[/tex]
[tex]\implies \dfrac{1 \cdot 15}{4\cdot 15}+\dfrac{1\cdot 6}{10\cdot 6}+\dfrac{1 \cdot 20}{3\cdot 20}+\dfrac{2 \cdot 12}{5\cdot 12}[/tex]
[tex]\implies \dfrac{15}{60}+\dfrac{6}{60}+\dfrac{20}{60}+\dfrac{24}{60}[/tex]
[tex]\implies \dfrac{15+6+20+24}{60}[/tex]
[tex]\implies \dfrac{65}{60}[/tex]
[tex]\implies \dfrac{13 \cdot 5}{12 \cdot 5}[/tex]
[tex]\implies \dfrac{13}{12}[/tex]
Therefore, it took Peter 13/12 hours to prepare the pizza.
Convert hours into minutes by multiplying the hours by 60:
[tex]\implies \dfrac{13}{12} \cdot 60=\dfrac{780}{12}=65\; \sf minutes[/tex]
As 60 minutes = 1 hour, then:
⇒ 65 minutes = 1 hour and 5 minutes.
Therefore, the actual time it took for Peter to prepare the pizza is 1 hour and 5 minutes.
what is 3 3/4 - 2 1/5 as a mixed number
Answer:
1 11/20
Step-by-step explanation:
3 3/4 - 2 1/5 = 3 15/20 - 2 4/20 = 1 11/20
The distribution of ages of licensed drivers shopping at the Kalish County Mall is normally distributed with mean 41 and standard deviation 7. A person will be selected at random. Round your answers to the nearest hundredth. What is the probability that the person is age 48 or older?
The probability that the person is age 48 or older is; 0.16
How to calculate probability from z-score?
The formula for z-score of a normal distribution is;
z = (x' - μ)/σ
where;
x' is sample mean
μ is population mean
σ is standard deviation
We are given;
σ; standard deviation = 7
μ; population mean = 41
The probability that the person is age 48 or older is expressed as;
P(X ≥ 48); z = (48 - 41)/7
z = 1
From online p-value from z-score calculator, we have;
p-value = 0.158655
Approximating to the nearest hundredth = 0.16
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In a urvey of 3072 adult aged 57 through 85, it wa found that 86. 9% of them ued at leat one precription medication contrut a 90% confidence interval eatimate if the percentage of adult aged 57 through 85 year who ue at leat one precription medication
A 90% confidence interval will be 82.5% < p < 84.9%
What is the confidence interval in statistics?
A confidence interval is the mean of your estimate plus and minus its variation. Within a certain level of confidence, this is the range of values you expect your estimate to fall between if you redo your test. In statistics, confidence is another word for probability.
We have to find a 90% confidence interval estimate of adults who used at least one prescription medication.
Here, the sample proportion [tex]\hat {p} = 0.837[/tex]
We know that for true population proportion confidence interval is given by
[tex]C.I.= \left( \hat{p}-z_{c}\sqrt{\frac{\hat{p}(1-\hat{p})}{n}} , \hat{p}+z_{c}\sqrt{\frac{\hat{p}(1-\hat{p})}{n}}\right)[/tex]
For 90% confidence interval [tex]z_c[/tex] = 1.645 from normal table
[tex]C.I.= \left( 0.837-1.645\sqrt{\frac{0.837(1-0.837)}{3072}} , 0.837+1.645\sqrt{\frac{0.837(1-0.837)}{3072}}\right)[/tex]
[tex]C.I.= \left( 0.837-1.645\sqrt{\frac{0.837(0.163)}{3072}} , 0.837+1.645\sqrt{\frac{0.837(0.163)}{3072}}\right)[/tex]
[tex]C.I.= \left(0.837-1.645\times 0.007 , 0.837+1.645\times 0.007 \right)[/tex]
[tex]C.I.= \left(0.837-0.012 , 0.837+0.012\right)[/tex]
[tex]C.I.= \left(0.825 , 0.849\right)[/tex]
Converting our confidence interval into percentages by multiplying it by 100 we get (82.5%, and 84.9%).
Thus, a 90% confidence interval will be 82.5% < p < 84.9%.
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Use a stem-and-leaf plot to display the data. The data represent the ages of the top 30 highest paid CEOs. 64 74 55 55 62 63 50 67 51 60 59 50 52 50 59 62 64 57 61 60 49 63 62 60 55 56 48 58 64 57
Below is the stem-and-leaf plot to represent the ages of the top 30 highest-paid CEOs.
What is the stem-and-leaf plot?
A stem-and-leaf display, also known as a stem-and-leaf plot, is a device used to visualize the shape of a distribution by presenting quantitative data in a graphical format, similar to a histogram. They developed from the work of Arthur Bowley in the early 1900s and are useful tools in exploratory data analysis.
Stem Leaf
4 8 9
5 0 0 0 1 2 5 5 5 6 7 7 8 9 9
6 0 0 0 1 2 2 2 3 3 4 4 4 7
7 4
Hence, this is the stem-and-leaf plot to represent the ages of the top 30 highest-paid CEOs.
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A confidence interval is made from a __________ to estimate the truth for a ______________.
To determine the accuracy of a "population parameter," a "sample statistic" is used to create a confidence interval.
Define the word confidence interval?Although they are connected, confidence level and confidence interval are not the same thing.
A wide range of values that are bound by the statistic's mean and that are likely to include an unidentified population parameter. The proportion of probability, or surety, that perhaps the confidence interval might include the real population parameter when a random sample is drawn numerous times is referred to as the confidence level. We are 99% confident (confidence level) that the majority of all these observations (confidence intervals) include the genuine population parameter, to use colloquial language. The researchers come at an upper and lower limit that 95% of the time contain the true mean by creating a 95% confidence interval that use the sample's median and standard deviation and adopting a normal distribution represented by the bell curve.Thus, to evaluate the accuracy of a "population parameter," a "sample statistic" is used to create a confidence interval.
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What would probably happen if you try to make bread without using year?
Answer:
Your dough may not rise as tall as you're used to, and you may also notice differences in flavor and texture.
Step-by-step explanation:
If your question was without using yeast.
Answer:
The bread won't rise if you don't add yeast to the dough, which helps makes it thick. Starting with a tiny amount, the bread expands as it is kneaded and allowed to rise. Therefore, the only difference you would see if you used less than the advised quantity, let's say half as much, is that the bread rises considerably more slowly and not as much.
please help geometry
Answer:
6
Step-by-step explanation:
45-45-90 tri so x=6
3sqrt2^2=18
18+18=36
sqrt36=6
what is the probability that there is exactly one car and exactly one bus during a cycle? answer .030 what is the probability that there is at most one car and at most one bus during a cycle? answer .120 what is the probability that there is exactly one car during a cycle? exactly one bus? answer .300 s
The probability of exactly one car and exactly one bus during a cycle is 0.030.
What is probability?
Probability is that the branch of arithmetic regarding numerical descriptions of however possible an incident is to occur, or however possible it's that a proposition is true. The chance of an incident could be a range between 0 and 1.
Main body:
A) The joint pmf of X and Y is computed as,
p(x,y)=P(X=x and Y=y)
Such that, p(x,y)≥0 and ∑ p(x,y)=1.
The probabilities that there is exactly one car and exactly one bus during a cycle is denoted by
P (X =1,Y =1) = p(1,1).
From the given joint probability table, p(1,1)=0.030.
Therefore, the probability that there is exactly one car and exactly one bus during a cycle is 0.030.
Hence probability of exactly one car and exactly one bus during a cycle is 0.030.
B) Required to find the probability that there is at most one car and at most one bus during a cycle,
P(X ≤ 1 and Y ≤1 ), and is computed as follows:
P(X ≤ 1 and Y ≤1)=p(0,0)+p(0,1)+p(1,0)+p(1,1)
From the given joint probability table,
P(X ≤ 1 and Y≤1)=0.025+0.015+0.050+0.030=0.120
Therefore, the probability that there is at most one car and at most one bus during a cycle is 0.120.
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Write a method that takes a regularpolygon as a parameter, and changes the number of sides so it becomes an equilateral triangle (i. E. Set the number of sides to 3).
Answer: public static void randomize(RegularPolygon r){
int side = (int)((20-10) * Math.random()) + 10;
int length = (int)((12-5) * Math.random()) + 5;
// assuming the regularpolygon class has setSide and setLength methods.
r.set.Side(side);
r.setLength(length);
The randomize method is used to access and change the state of the RegularPolygon class attributes sides and length. The method accepts the class as an argument and assigns a random number of sides and length to the polygon object.
Step-by-step explanation:
the following are four observations collected from each of three treatments. test the hypothesis that the treatment means are equal. use the 0.05 significance level.
From the following four observations among the given hypothesis with significance level is 0.05 the null hypothesis is not true.
Null hypothesis is all means are equal and in alternative at least there is a difference in one mean.
As given in the question,
Significant level is equal to 0.05
a. Null hypothesis : Null hypothesis is the one where there is no significant difference between the means of all the treatment groups.
Where as alternative hypothesis is the one which represents that there is significant difference between the means of all the treatment groups.
Therefore, from the following four observations among the given hypothesis with significance level is 0.05 the null hypothesis is not true.
Null hypothesis is all means are equal and in alternative at least there is a difference in one mean.
The complete question is:
The following is sample information. Test the hypothesis that the treatment means are equal. Use the .05 significance level.
Treatment 1: 8, 6, 10, 9
Treatment 2: 3, 2, 4, 3
Treatment 3: 3, 4, 5, 4
a. State the null and alternative hypothesis
b. What is the decision rule?
c. Compute the SST,SSE and SS total
d. Compute an ANOVA table
e. State decision regarding null hypothesis
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In a survey of randomly selected students, 8 out of every 10 students said they use their phones to play games. If there are 820 students at
Jamison Middle School, how many students can be expected to play games on their phones?
Answer:
656
Step-by-step explanation:
820/10 to get 1/10 of 820 (82)
Multiply by 8 to get 656
bryon collects data on the depth of a river at various points and the velocity of the river at these points. his data have a correlation coefficient of -0.9382.
The scatterplot that represents Bryson's data is the scatterplot that is downward sloping.(Check the graph attached)
What is negative correlation?
Correlation is a statistical measure used to measure the relationship that exists between two variables.Negative correlation means that the two variables move in opposite directions. If one variable increases, the other variable decreases. When there is a negative correlation, the graph of the variables is downward sloping.A link between two variables known as "negative correlation" occurs when one variable rises measure as the other falls, and vice versa. In statistics, -1.0 denotes a perfect negative correlation, 0 denotes no connection, and +1.0 denotes a perfect positive correlation. The relationship between two variables is always absolutely opposite when there is a perfect negative correlation.To know more about negative correlation check the below link:
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The function f(x) is a cubie function and a limited table of values is provided below. Write the equation of the cubic polynomial in standard form.
The required cubic polynomial is
f(x) = [tex]-2x^3-2x^2-28x+48[/tex]
What is a polynomial?
An algebraic expression of the form [tex]a_0 + a_1x+ .... + a_nx^n[/tex] ([tex]a_0 \neq 0[/tex]) is called a polynomial of degree n.
The zeroes of the cubic polynomial are -4, 2, 3
Let the cubic polynomial is
f(x) = a(x - (-4))(x - 2)(x - 3)
f(x) = a(x + 4)(x - 2)(x - 3)
If x = -5, f(x) = 112
112 = a(-5 + 4) (-5 - 2)(-5 - 3)
112 = -56a
a = [tex]-\frac{112}{56}[/tex]
a = -2
f(x) = -2(x+ 4)(x - 2)(x - 3)
[tex]f(x) = -2(x+ 4)(x^2 -3x -2x +6)\\f(x) = -2(x + 4)(x^2 - 5x + 6)\\f(x) = -2(x^3 - 5x^2+4x^2+6x - 20x+24)\\f(x) = -2(x^3 - x^2 - 14x +24)\\f(x) = -2x^3 -2x^2 - 28x + 48[/tex]
(x +4)(x - 2)(x - 3)
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Triangle abc is an isosceles triangle in which side ab = ac. What is the perimeter of triangle abc? 5 + units 10 + units units 50 units.
The perimeter of triangle abc = 10+√10 unit where the triangle is an isosceles triangle.
What is meant by perimeter?A perimeter is a closed path that surrounds or covers a two-dimensional shape or length.The perimeter of a circle or an ellipse is its circumference. Calculating the perimeter has a variety of practical applications.
A shape's perimeter is the length of its outline. To get the perimeter of a rectangle or square, sum the lengths of all four sides. In this situation, x is the rectangle's length, and y is its width.
Length of ac = 3-(-2) = 5 unit
ab=ac
ab = 5 unit
By Pythagorean theorem
bc²=3²+1² =10
bc=√10 unit =3.16 unit
Perimeter of triangle abc=ab + ac +bc = 5 + 5 + √10
= 10+√10 unit
Therefore, Perimeter of triangle abc = 10+√10 unit
Hence, The perimeter of triangle abc = 10+√10 unit where the triangle is an isosceles triangle.
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How do you find the rational function of a graph?.
Before graphing a given rational function, it is occasionally necessary to simplify it. If, other than at asymptotes, there are any excluded values then graphing the function requires an additional step.
The function y=f(x), where f(x) is a rational expression, is the formula for a rational function.
Drawing the graphs of the rational functions might be challenging. Finding the asymptotes and intercepts is a good place to start when attempting to sketch a graph of a rational function.
The steps in graphing rational functions are as follows:
Find the rational function's asymptotes, if any exist.
Create dotted lines for the asymptotes.
Find the rational function's x-intercept (s) and y-intercept, if any.
For various x values, determine the values of y.
Plot the spots and then create a straight line to connect them and check to see if the graph crosses the vertical asymptotes.
Make sure the function is not a continuous smooth curve at the excluded value if you want to portray an undefined function. Typically referred to as the "hole in the rational function," this excluded value
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How do you tell if a polynomial graph is positive or negative?.
If the leading coefficient is positive, bigger inputs only make the leading term more and more positive
How do you tell if a graph has a positive or negative coefficient?
If the leading coefficient is positive, bigger inputs only make the leading term more and more positive. The graph will rise to the right. If the leading coefficient is negative, bigger inputs only make the leading term more and more negative. The graph will descend to the right.
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you flip a coin for which the probability of heads is 0.50.5 and the probability of tails is 0.5.0.5. if the coin comes up heads, you win $1. otherwise, you lose $1. determine the expected value of your winnings. (use decimal notation. give your answer as an exact number.) expected value:
The expected value of winnings is 0.
The expected value will be calculated by taking the sum of winning and loosing = E(x) = ΣxP(x), where X is the outcome and P is the probability of that outcome.
The probability of winning = X P(x)
The probability of winning = 1 × 0.5
The probability of winning = 0.5
The probability of loosing = -1 × 0.5 (-1 because it will be the loss)
The probability of loosing = -0.5
Calculating their sum = 0.5 + (-0.5)
Expected value = 0.5 - 0.5
Expected value = 0
Hence, the expected value is 0.
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What is a 4 0 phenotypic ratio?.
The visibility rate for the only dominant phenotype is 100%. There is no phenotypic ratio since there is no second phenotype. The ratio that would be used to represent this outcome is 4:0 phenotypic ratio.
In the given question we have to explain about a 4:0 phenotypic ratio.
The visibility rate for the only dominant phenotype is 100%. There is no phenotypic ratio since there is no second phenotype. The ratio that would be used to represent this outcome is 4:0. However, the genotypic ratio considers probable allele combinations rather than the observable trait (phenotype).
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How many extraneous solutions does the equation have 2m 2m 3 2m 2m 3 1?.
Zero extraneous solutions does the equation have (2m)/(2m+3)-(2m)/(2m-3) = 1.
What is Quadratic Equation?
ax^2 + bx + c = 0 is a quadratic equation, which is a second-order polynomial equation in a single variable a ≠0. It has at least one solution because it is a second-order polynomial equation, which is guaranteed by the algebraic fundamental theorem. The answer might be simple or complicated.
Given that;
[tex]\frac{2m}{2m+3}-\frac{2m}{2m-3} = 1[/tex]
⇒ [tex]\frac{2m(2m-3)-2m(2m+3)}{(2m+3)(2m-1)}=1[/tex]
⇒ [tex]\frac{4m^2-6m-4m^2-6m}{(4m^2-9)}=1[/tex]
⇒ [tex]\frac{-12m}{4m^2-9}=1\\[/tex]
⇒ [tex]-12m = 4m^2-9[/tex]
4m^2 +12m - 9 = 0(1)
The formula for calculating the roots of the quadratic equation ax^2 + bx + c can be utilized because (1) is a quadratic equation.
[tex]\frac{-b\pm \sqrt{b^2-4ac} }{2a}[/tex]
Variable m is in equation (1), where a = 4, b = 12, and c = -9.
The roots are calculated as:
[tex]\frac{-12\pm \sqrt{12^2-4\times 4\times (-9)} }{2\times 4}[/tex]
[tex]\frac{-12\pm \sqrt{2\times 144} }{8}[/tex]
[tex]\frac{-12\pm 12\sqrt{2} }{8}[/tex]
[tex]\frac{-3}{2} \pm \frac{3}{2}\sqrt{2}[/tex]
[tex]\frac{-3}{2} - \frac{3}{2}\sqrt{2} \ and \ \frac{-3}{2} + \frac{3}{2}\sqrt{2}[/tex]
Subsitituting [tex]\frac{-3}{2} - \frac{3}{2}\sqrt{2}[/tex] in equation (1);
[tex]9+18+18\sqrt{2}-18-18\sqrt{2} -9 = 0[/tex]
0 = 0
The root -3/2 - 3([tex]\sqrt{2}[/tex])/2 is therefore not an auxiliary solution.
Now substituting [tex]\ \frac{-3}{2} + \frac{3}{2}\sqrt{2}[/tex] in equation (1);
[tex]9+18+18\sqrt{2}-18-18\sqrt{2} -9 = 0[/tex]
0 = 0
Therefore, the root -3/2 + 3([tex]\sqrt{2}[/tex])/2 IS NOT AN ADDITIONAL SOLUTION.
The above problem can be solved using either of the two roots.
There is no superfluous solution to the equation (2m)/(2m+3)-(2m)/(2m-3) = 1 as a result.
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Eighty percent of seniors at the local high school graduate each year. If there are 750 seniors this year, how many will graduate?.
By calculating the percentage of seniors that graduate each year, it can be concluded that this year 600 seniors will graduate.
It is given to us that -
Eighty percent of seniors at the local high school graduate each year
There are in total 750 seniors this year
We have to find out the number of seniors who will graduate.
Since it is mentioned that Eighty percent of seniors at the local high school graduate each year and there are in total 750 seniors this year, then the number of seniors who will graduate this year will be equal to -
80% of 750
= (80/100) * 750
= 600
Therefore by calculating the percentage of seniors that graduate each year, it can be concluded that this year 600 seniors will graduate.
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If you roll two dice, the probability of getting a sum of 7 is 6/36, or 1/6. If you roll the two dice 10 times, the probability of getting a sum of 7 in at least 3 of the 10 rolls is closest to which of the following?
a 0.225
b 0.515
c 0.7
d 0.775
The correct option is option (a). Using Binomial Probability distribution,
the probability of getting a sum of 7 in at least 3 of the 10 rolls is 0.225..
We have given that,
probability of getting a sum of 7 on rolling of two dice once (p) = 6/36
so, 1 - p = 1 - 6/36 = 30/36 = 5/6
Using Binomial Probability distribution,
X ~ B ( 10, 1/6)where "X" is random variable
the probability of getting a sum of 7 in at least 3 of the 10 rolls is
P( X ≥3 ) = 1 - P(X< 3)
= 1 - [ P(X= 0) + P(X= 1) + P(X= 2) ]
= 1 - [ 10C0 (1/6)0 (5/6)10 + 10C2 (1/6)1(5/6)9 + 10C3(1/6)3 (5/6)7
= 1- [ 0.1615 + 0.3230112 + 0.290710 ]
= 1 - [ 0.775522]
= 0.22475 ~0.225
Hence, the required probability is 0.225
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the vertices of the trapezoid are the origin along with a (4m, 4n), b (4q, 4n), and c (4p, 0). find the midpoint of the midsegment of the trapezoid.
The midpoint of the midsegment of Trapezoid is E(2m, 2n) and F (2(q+p), 2n).
According to the question,
The vertices of the trapezoid are A(4m , 4n) , B(4q , 4n) , C(4p , 0) and D(0,0).
Let mid-point of midsegment of Trapezoid be E and F
Using section formula
E (x- coordinate)= 1*4m + 0 /2
E (x- coordinate)=2m
E (Y- coordinate)= 4n/2
E (Y- coordinate)=2n
So, the coordinates of E (2m, 2n)
similarly,
F (x- coordinate)= (1*4q + 1*4p)/2
F (x- coordinate)=2(p + q)
F (Y- coordinate)= 4n/2
F(Y- coordinate)=2n
So, the coordinates of F (2(q +p), 2n)
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If an average of 39 customers are served per hour, what is the probability that the next customer will arrive in 3 minutes or less?
The probability that the next customer will arrive in 3 minutes or less is 6.0286.
What is the Poisson distribution?
The Poisson distribution is a discrete probability distribution in probability theory and statistics that expresses the probability of a given number of events occurring in a fixed interval of time or space if these events occur with a known constant mean rate and regardless of the time since the last event.
This is a Poisson distribution formula:
P(X > t) = e^(-λt)
Where,
λ is the arrival rate
t is the arrival time
λ = 39/60
t = 3 minutes
We want to find the probability that the next customer will arrive in 3 minutes or less. This is expressed as;
P (X ≤ 3) = 1 - (P(X > 3))
so,
P (X ≤ 3) = 1 - e^((39/60) × 3)
P (X ≤ 3) = 1 - 7.0286
P (X ≤ 3) = 6.0286
hence, the probability that the next customer will arrive in 3 minutes or less is 6.0286.
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An ANOVA procedure is applied to data obtained from 6 sample where each sample contains 20 observations. The degrees of freedom for the critical value of F are 6 numerator and 20 denominator degree of freedom. 5 numerator and 20 denominator degree of freedom. 5 numerator and 114 denominator degree of freedom. 6 numerator and 20 denominator degree of freedom
The degree of freedom for the numerator is 5 and the degree of freedom for the denominator is 114.
What is Analysis of variance (ANOVA)?Analysis of variance (ANOVA) is a type of statistical test used to determine if there is a statistically significant difference among two or more categorical groups by testing for differences of means using variance. An ANOVA test is used to analyze the differences between group means in a sample.
In this case, the number of groups, k is the number of distinct groups = 6
The total number of samples, N = number of groups x number of samples per each group
Thus, N = 6 x 20 = 120
Degree of freedom (df):
df within = df of numerator = k – 1 = 6 – 1 = 5
df between = df of denominator = N – k = 120 – 6 = 114
Hence, the required degrees of freedom are 5 numerator and 114 denominator.
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How do you tell if the leading coefficient of a graph is positive or negative?.
it is negative or positive depending upon the sign of the coefficients associated with the variable x
How do you define leading coefficient?
In a polynomial function, the leading term is the term containing the highest power of x. The coefficient of the leading term is called the leading coefficient.
it is negative or positive depending upon the sign of the coefficients associated with the variable x
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Given the equation of a circle, identify the center and the radius by completing the square.
x² + y² - 32x+24y +396 = 0
Center:
Radius:
The center and the radius by completing the square of the given equation of circle is x² + y² - 32x+24y +396 = 0 is C( -16, 12) and radius is 2.
The equation of the circle is given as x² + y² - 32x+24y +396 = 0.
Comparing the given equation with general equation of circle, x² + y² + 2gx + 2fy + c = 0.
The center of circle is C = (-g, -f)
The radius of circle is r = √g² + f² - c
Therefore, from the given equation,
2g = -32
g = -16
2f = 24
f = 12
C( -16, 12)
And the radius is
r = √(-16)² + (12)² - 396
= √256 + 144 -396
=√4
= 2
Hence, the center and the radius by completing the square of the given equation of circle is x² + y² - 32x+24y +396 = 0 is C( -16, 12) and radius is 2.
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