Assume this year's flu vaccine has a 80% chance of being effective. If the vaccine is given to 337 randomly selected people, answer the following.
Answers
a) The wording for the random variable is given as follows:
n X = the number of 337 randomly selected people who get the vaccine and do not get the flu;
b) The symbol is: n = 337.
c) The symbol is: p = 0.8.
d) P(X = 265) = 0.0426.
e) P(X < 265) = 0.2451.
f) P(X > 265) = 0.7123.
g) P(X = 268) = 0.0545.
h) P(X < 268) = 0.3859.
i) P(X > 268) = 0.5596.
How to obtain probabilities using the normal distribution?The z-score of a measure X of a variable that has mean symbolized by [tex]\mu[/tex] and standard deviation symbolized by [tex]\sigma[/tex] is obtained by the rule presented as follows:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score represents how many standard deviations the measure X is above or below the mean of the distribution, depending if the obtained z-score is positive or negative.Using the z-score table, the p-value associated with the calculated z-score is found, and it represents the percentile of the measure X in the distribution.The binomial distribution is the probability of x successes on n trials, with p probability of a success on each trial. It can be approximated to the normal distribution with [tex]\mu = np, \sigma = \sqrt{np(1-p)}[/tex].The parameters for the binomial distribution in this problem are given as follows:
n = 337, p = 0.8.
Hence the mean and the standard deviation for the approximation are given as follows:
[tex]\mu = 337 \times 0.8 = 269.6[/tex][tex]\sigma = \sqrt{337 \times 0.8 \times 0.2} = 7.34[/tex]Using continuity correction, the probability that exactly 265 people do not get the flu is the p-value of Z when X = 265.5 subtracted by the p-value of Z when X = 264.5.
X = 265.5:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
Z = (265.5 - 269.6)/7.34
Z = -0.56
Z = -0.56 has a p-value of 0.2877.
X = 264.5:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
Z = (264.5 - 269.6)/7.34
Z = -0.69
Z = -0.69 has a p-value of 0.2451.
Hence:
0.2877 - 0.2451 = 0.0426.
Then:
e) P(X < 265) = 0.2451 -> p-value of Z when X = 264.5.
f) P(X > 265) = 1 - 0.2877 = 0.7123 -> one subtracted by the p-value of Z when X = 265.5.
For exactly 268, we have the same logic as follows:
X = 265.5:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
Z = (268.5 - 269.6)/7.34
Z = -0.15
Z = -0.15 has a p-value of 0.4404.
X = 267.5:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
Z = (267.5 - 269.6)/7.34
Z = -0.29
Z = -0.29 has a p-value of 0.3859.
Hence:
0.4404 - 0.3859 = 0.0545.
Then:
h) P(X < 268) = 0.3859 -> p-value of Z when X = 267.5.
i) P(X > 268) = 1 - 0.4404 = 0.5596.
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Related Questions
a) ( combining like terms)
Simplify (7a + 10b) − (4a − 6b).
b) Simplify the expression. ( combining like terms)
−5x + 8y + 2x − 3y
c) Solve and graph the inequality x - 4 ≤ -1 (the name of the game is ...)
Answers
a) Combining like terms (7a + 10b) − (4a − 6b) = 3a + 16b
b) The Simplify expression −5x + 8y + 2x − 3y the answer is -3x + 5y
c) The inequality x - 4 ≤ -1 Graph is given below.
What do you mean by algebraic expression?
When addition, subtraction, multiplication, division, and other mathematical operations are performed on variables and constants, the result is a mathematical statement known as an algebraic expression.
Any combination of terms that have undergone operations like addition, subtraction, multiplication, division, etc. is known as an algebraic expression (or variable expression).
An algebraic expression is composed of various parts.
a) Given expression:
(7a + 10b) - (4a - 6b)
= 7a + 10b - 4a + 6b
On combining like terms we get,
(7a - 4a) + (10b + 6b)
= 3a + 16b
Therefore, (7a + 10b) − (4a − 6b) = 3a + 16b
b) Given expression :
−5x + 8y + 2x − 3y
On combining like terms we get,
-5x + 2x + 8y - 3y
= (-5x + 2x) + (8y - 3y)
= -3x + 5y
therefore, −5x + 8y + 2x − 3y = -3x + 5y
c) Given expression:
x - 4 ≤ -1
⇒ x ≤ -1 + 4
⇒ x ≤ 3
Graph of the function is given below:
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explain why the solution of 5x minus 3 is greater than 14.5 or 2x plus 5 divided by 3 is less than 4 has a solution of all the real numbers, with one exception
Answers
From the compound inequality explained below in concept, it has been proven that compound inequality has a solution of all real numbers except 3.5.
How to solve Inequality problems?
We are given the inequalities as;
5x – 3 > 14.5 or (2x + 5)/3 < 4
For the first inequality;
Add 3 to both sides to get;
5x > 17.5
Divide both sides by 5 to get;
x > 3.5
For the second inequality, we have;
(2x + 5)/3 < 4
Multiply both sides by 3 to get;
2x + 5 < 12
Subtract 5 from both sides to get;
2x < 7
Divide both sides by 2 to get;
x < 3.5
The first inequality gives the solution as x > 3.5.
The second inequality gives the solution as x < 3.5.
The solution of an “or” compound in equality is everything in both solution sets, so the solution set is all of the numbers less than 3.5 and greater than 3.5. Since neither of the inequalities includes 3.5, the compound inequality has a solution of all real numbers except 3.5.
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This is so confusing could anyone help me with this
Answers
Answer:
I am not exactly sure what they want you to put in the boxes, but hopefully the explanation below will shed some light on what is going on with this problem.
Step-by-step explanation:
The equation would be
y = 3x
It looks like your question wants you to write the equation in the form
r(x) = 3x
y would be the student's score on the test.
x would be the number of questions that the student got right.
The x is the independent variable. It tells us how many questions the student got right.
The y is the dependent variable. It is the student's score. The student's score depends on how many questions the student got right.
R(25) is saying what would be the score if the student got 25 answer correct?
3(25) = 75. The student would get a score of 75
TRUE/FALSE. if the matrix of coefficients of a homogeneous system of n linear equations in n unknowns has an inverse, then the system does not have infinitely many solutions.
Answers
The given statement is true.
How it is true ?
Because if the matrix of coefficients of a homogenous system of n linear equations is non-singular then there will be the inverse for that matrix.
We know ,
If matrix is non-singular then it has unique solution
and if it singular then it has either no-solution or infinite solution.
So, the above statement is always true.
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Suppose an investigator takes a random sample of n = 50 birth weights from several teaching hospitals located in an inner-city neighborhood. In her random sample, the sample mean is y¯ = 3.15 kg and the standard deviation is 250 grams. (a) Calculate a 95% confidence interval for the population mean birth weight in these hospitals. (b) The typical weight of a baby at birth for the US population is 3.25 kg. The investigator suspects that the birth weights of babies in these teaching hospitals is different than 3.25 grams, but she is not sure if it is smaller (from malnutrition) or larger (because of obesity prevalence in mothers giving birth at these hospitals). Carry out the hypothesis test that she would conduct.
Answers
a)95% confidence interval for the population mean birth weight in these hospitals is (3078.9358,3221.0642).
(b)The P-value is 0.0068.
What is hypothesis testing?To test the null hypothesis and the alternative hypothesis, all analysts employ a random population sample. The null hypothesis typically states that two population parameters are identical; for instance, it can claim that the population mean return is equal to zero.
Why is hypothesis testing used?A strategy for determining how reliably one may extrapolate observed results in a study sample to the larger population from is provided by hypothesis testing, a procedure used to assess the strength of the evidence from the sample and give a framework for doing so.
C.I=x-t(alpha/2)xs/sqrt{n}
=3150+_2.01*250/sqrt{50}
=(3078.9358,3221.0642)
b) P value =P(t<-2.83)+P(t>2.83)
use calculator
=0.0034+0.0034
=0.0068
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Hi, I'd be really thankful for a proper answer for this. Thank you!
Answers
1) The probabilities are given as follows:
a) More than 75: 0.0301 = 3.01%.
b) Between 60 and 73: 0.4484 = 44.84%.
c) Less than 50: 0.1057 = 10.57%.
2) The proportion of students who fail the module is of: 0.0062 = 0.62%.
3) The measures are given as follows:
Mode: 60.Median: 60.Variance: 64.How to obtain probabilities using the normal distribution?The z-score of a measure X of a variable that has mean symbolized by [tex]\mu[/tex] and standard deviation symbolized by [tex]\sigma[/tex] is obtained by the rule presented as follows:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score represents how many standard deviations the measure X is above or below the mean of the distribution, depending if the obtained z-score is positive or negative.Using the z-score table, the p-value associated with the calculated z-score is found, and it represents the percentile of the measure X in the distribution.The mean and the standard deviation in this problem are given as follows:
[tex]\mu = 60, \sigma = 8[/tex]
The probability that an score is more then 75 is one subtracted by the p-value of Z when X = 75, hence:
Z = (75 - 60)/8
Z = 1.88
Z = 1.88 has a p-value of 0.9699.
1 - 0.9699 = 0.0301 = 3.01%.
The probability of an score between 60 and 73 is the p-valeu of Z when X = 73 subtracted by the p-value of Z when X = 60, hence:
Z = (73 - 60)/8
Z = 1.63
Z = 1.63 has a p-value of 0.9484.
Z = (60 - 60)/8
Z = 0
Z = 0 has a p-value of 0.5.
Then:
0.9484 - 0.5 = 0.4484 = 44.84%.
The probability of an score less than 50 is the p-value of Z when X = 50, hence:
Z = (50 - 60)/8
Z = -1.25
Z = -1.25 has a p-value of 0.1057.
The proportion who might fail the test is the p-value of Z when X = 40, hence:
Z = (40 - 60)/8
Z = -2.5
Z = -2.5 has a p-value of 0.0062.
Then the statistical measures are obtained as follows:
Mode: 60. -> equals to mean.Median: 60. -> equals to mean.Variance: 64. -> standard deviation squared.More can be learned about the normal distribution at https://brainly.com/question/25800303
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Let alpha and beta be the roots of the quadratic equation x² - 4x - 6 = 0. Find 1/a² + 1/b²
Answers
Answer:
7/9
Step-by-step explanation:
Using vieta's formulas, we know that a + b = 4 and ab = -6.
1/a^2 + 1/b^2 can be written as (a^2 + b^2)/a^2b^2.
(a^2 + b^2)/a^2b^2 can be written as (a+b)^2 - 2ab/(a^2)(b^2)
{4^2 - 2(-6)}/(-6)^2 = 28/36 = 7/9
3 (5+4)² - 4² =
OA. 227
OB. 15
OC. 46
OD. 345
Answers
Answer: 227
Step-by-step explanation: (5 + 4 ) = 9
= 3 x 9^2 - 4^2
9^2 = 81
= 3 x 81 - 4^2
4^2 = 16
= 3 x 81 - 16
3 x 81 = 243
= 243 - 16
243 - 16 = 227
= 227.
g the complete bipartite graphs kn,n and kn,n 1 have the maximum possible number of edges among al
Answers
The complete type of bipartite graphs ,[tex]K_{n.n}[/tex] and [tex]K_{n.n+1}[/tex] will have the maximum possible of all number incliding edges among all the present triangle-free nodes i.e., graphs with all same number of vertices.
Approach: The wide variety of edges can be most whilst each vertex of a given set has an aspect to each different vertex of the opposite set i.e. edges = m * n in which m and n are the wide variety of edges in each the sets. that allows you to maximize the wide variety of edges, m need to be same to or as near n as possible.
The two main sets are X = {A, C}, Y = {B, D}.
The vertices for the given set X join, with the vertices Y and vice-versa.
Similar proposition will always holds for bipartite planar type of graphs: any n-vertex bipartite graph (n ≥ 3) includes at most 2n − four edges, moreover, each n-vertex bipartite planar graph may be prolonged to an n-vertex bipartite planar graph with 2n − four edges.
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Correct Question:
Among what g will have a complete bipartite graphs [tex]K_{n.n}[/tex] and [tex]K_{n.n+1}[/tex] have the maximum possible number of edges among it.
The number has 9 factors. It's between 10 and 99. The sum of the digits is 9. It's even. It's a square number.
Answers
The number with the given features in this problem is given as follows:
36.
How to obtain the number?First we consider that the number is a square number, meaning that it has a perfect square root.
The number is between 10 and 99, hence the possible square numbers between 10 and 99 are given as follows:
16, as 4² = 16.25, as 5² = 25.36, as 6² = 36.49, as 7² = 49.64, as 8² = 64.81, as 9² = 81.The numbers with a sum of the digits of 9 are given as follows:
36, as 3 + 6 = 9.81, as 8 + 1 = 9.The factors of each number are given as follows:
36: {1, 2, 3, 4, 6, 9, 12, 18, 36} -> nine factors, hence it is the number.81: {1, 3, 9, 27, 81} -> Five numbers.More can be learned about square numbers at https://brainly.com/question/27307830
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75 students are currently infected with a respiratory virus that is spreading through a population of college students. the number of infected students is modeled by f(t)
Answers
The number of infected students after 5 days = 694
The number of infected students with respiratory virus is modeled by an exponential function f(t) = 25000 /1+332e^(-0.45t) where time t, is measured in days.
We need to find the number of students infected with the virus after 5 days.
For t = 5,
f(5) = 25000 /1+332e^(-0.45 * 5)
f(5) = 25000 /(1+332*0.1054)
f(5) = 25000 /35.9928
f(5) = 694.58
f(5) ≈ 694
Therefore, the number of students infected with the virus after 5 days = 694
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The complete question is:
75 students are currently infected with respiratory virus- that is spreading through a population of college students_ The number of infected students is modeled by f(t) = 25000 /1+332e^(-0.45t) where time; t, is measured in days. How many students are predicted to be infected with the virus after 5 days? Round your answer to the nearest whole number.
Part 1 of 2
Describe and correct the error a student
made finding the intercepts of the graph
of the line 4x-6y = 12.
1.4(0)-6y = 12
2. 6y=12, so y = 2; the y-intercept is 2.
3.4x-6(0) = 12
4.4x = 12, so x = 3; the x-intercept is 3.
X
UA. In solving for the x-intercept, the student's calculation of x is incorrect. The error occurs in
(Type an integer or a decimal.)
OB In solving for the v-intercent the student substituted 0 for x The student should have suhe
Answers
Answer:
The error is when 6y = 12 it will be -6y = 12 and the intercept would be -2.
Step-by-step explanation:
()
Complete the table using the given rules. Then, compare pattern A to pattern B.
() Pattern A
◄) subtract 20
Pattern B
() subtract 4
100
20
Which statement is true?
Each term in pattern B is 80 less than the corresponding term in pattern A.
Each term in pattern B can be found by dividing the corresponding term in
pattern A by 5.
Answers
Answer:
100; 80, 60, 4020; 16, 12, 8dividing by 5Step-by-step explanation:
You want to fill a table using the given rules, then describe the relationship between the table values.
Pattern AStarting with 100, you want to subtract 20 to get next terms:
100
100 -20 = 80
80 -20 = 60
60 -20 = 40
The next terms are 80, 60, 40.
Pattern BStarting with 20, you want to subtract 4 to get next terms:
20
20 -4 = 16
16 -4 = 12
12 -4 = 8
The next terms are 16, 12, 8.
RelationshipLooking at second terms, we can determine which description is true:
80 -80 = 0 ≠ 16 . . . . . the description "subtract 80" fails
80/5 = 16 . . . . . . . . . . the description "divide by 5" works
Each term in pattern B can be found by dividing the corresponding term in pattern A by 5.
3 trainers for every 12 dogs if there are 72 dogs how many trainers are needed
Answers
Answer:
18
Step-by-step explanation:
72/12=6
6×3=18
.....
solve for x using the quadratic formula x2-12x+52=0
Answers
There are No Real Roots possible for the Quadratic Equation
What is Quadratic Equation?
Quadratics are polynomial equations of the second degree, which means that they contain at least one squared term. Quadratic equations are another name for it. The quadratic equation has the following general form: ax² + bx + c = 0. where x is an unknown variable and the numerical coefficients a, b, and c.
Solution:
x² - 12x + 52 = 0
Formula to Solve the equation is -b +- (D) / 2a
D is the discriminant
D = √b² - 4ac
D = √12*12 - 4*52
D = √144 - 208
D = √-64
Since the value of Discriminant is negative
Therefore there are no real roots possible for the equation
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. 2 + 2 = 5... No, amigo, estás . (wrong) 2. Ellos están porque el avión no sale hoy. (angry) 3. El gimnasio no está a la medianoche. (open) 4. Las turistas están en su habitación. Es un buen hotel. (comfortable) 5. 2 + 2 = 4… Sí, Carlitos está . (sure) 6. Nosotros estamos . ¡Vamos a jugar al fútbol! (bored) 7. La puerta está . (closed) 8. No me gusta comer en la cafetería porque las mesas están . (dirty) 9. La casa de mi abuela está . (clean) 10. Es el día del examen final. Pablo y Rosa están . (nervous)
Answers
Answer:
Step-by-step explanation:
2 and 2 equal 5
The Sum of 2 positive numbers is 32. their difference of the same two numbers is 12. what is the Smaller number?
Answers
Answer:
4 is the smallest number
Step-by-step explanation:
4 times 8 is 32. 4 + 8 is 12. 4 is smaller than 8 so it would be the smaller number
5. show that for motion in a straight line with constant acceleration a, initial velocity v0, and initial displacement s0, the displacement after time t is s
s = 1/2 at2 + vOt + sO
Answers
Since the initial displacement is made by s0 and body moves with initial velocity and acceleration after that, the final displacement after time t is
[tex]s= \frac {1}{2} at ^{2} + v_{0}t+s_{0}[/tex]
What is Displacement?The displacement is only the difference between the locations of the two marks and is unrelated to the route used to get there.
What is formula for acceleration and velocity?The formula is:
[tex]a= \frac {Velocity}{Time}[/tex] (Acceleration)
[tex]v= \frac {Displacement}{Time}[/tex](Velocity)
Initial Displacement = s0
Displacement from position s0 after time t = [tex]\frac {1}{2} at ^{2} + v_{0}t[/tex]
Total Final Displacement (s) = [tex]\frac {1}{2} at ^{2} + v_{0}t+s_{0}[/tex]
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A set of n = 15 pairs of scores (X and Y values) produces a correlation of r = 0.20. If each of the X values is multiplied by 2 and the correlation is computed for the new scores, what value will be obtained for the new correlation?
Answers
The new value of correlation will be 0.20.
What is correlation?
The strength and direction of a relationship between two or more variables are described by the statistical measure of correlation, which is given as a number. However, a correlation between two variables does not necessarily imply that a change in one variable is the reason for a change in the values of the other.
Given that the size of the sample is n = 15.
The correlation is r = 0.20.
The degree of the association between two measurement variables is quantified and determined via correlation analysis. Regression aims to describe the relationship as an equation at the same time. For patients who visit an emergency room (ED), for instance, we could use correlation and regression.
The correlation coefficient is unaffected by the change of origin.
Thus r = 0.20.
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Calculate the given limit using the outstanding limits................
Answers
Answer:
Step-by-step explanation:
Match these values of r with the accompanying scatterplots:
0.406,
−1,
0.748,
−0.748,
and
0.994.
LOADING...
Click the icon to view the scatterplots.
Question content area bottom
Part 1
Match the values of r to the scatterplots.
Scatterplot 1,
r=
▼
Scatterplot 2,
r=
▼
Scatterplot 3,
r=
▼
Scatterplot 4,
r=
▼
Scatterplot 5,
r=
▼
(Photos attached)
Answers
Therefore , Scatter plot1 0.342 ,Scatter plot2 -0.994, Scatter plot 3 0.743 ,Scatter plot4 -0.743 and Scatter plot5 0.994.
Define Scatter plot.An example of a plot or mathematical diagram is a scatter plot, which uses Cartesian coordinates to show the values of typically two variables given a collection of data. One more variable can be presented if the points are programmed.
Here,
The observed data are highly erratic, according to scatter plot 1. The relationship between the two variables is thus weak. There is a 0.342 correlation coefficient.
Observations in the scatter plot 2 are aligned with the straight line. A reduction in y values follows a rise in x values. Therefore, there is a significant negative connection between the two variables. This means that the correlation coefficient is -0.994.
The scatter plot's third scatter plot shows that the observations are slightly yet positively divergent. Consequently, there is a weakly positive connection between the two variables. The correlation coefficient is therefore 0.743.
Scatter plot 4: The observations show a considerably negative deviation from the mean. Consequently, there is a light negative correlation between the two variables. Consequently, the correlational coefficient is -0.743.
Scatter plot 5: The observations are aligned with the straight line in the scatter plot. The matching y values rise as the corresponding x values do. Therefore, there is a significant positive connection between the two variables. So, 0.994 is the correlation coefficient. As follows is the matching table:
Spread layout 1 0.342 Spread plot 2 -0.994 3.743% Scatter plot Dispersion plot4 -0.743 Spread plot5 0.994
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Help with this problem
Answers
The measure of the angle ∠BDC is 68°.
What is the straight line angle?
A straight angle in geometry is one that is 180 degrees in length. It looks like a straight line, which is why it is known as a straight angle. In other words, it is an angle whose sides are in the same straight line but opposite to the vertex.
We have,
∠BDA is a straight angle
so ∠BDA = 180°
We need to find the ∠BDC
∠CDA = -8x + 48°
∠BDC = -7x + 12°
∠BDA = ∠BDC + ∠CDA = 180°
(-8x + 48°) + (-7x + 12°) = 180°
-15x + 60° = 180°
-15x = 120°
x = -8°
∠BDC = -7x + 12°
= -7(-8°) + 12°
= 56° + 12°
= 68°
Hence, the measure of the angle ∠BDC is 68°.
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I don’t know how to do it
Answers
[tex]\begin{array}{llll} \textit{Logarithm of exponentials} \\\\ \log_a\left( x^b \right)\implies b\cdot \log_a(x) \end{array} ~\hspace{7em} \begin{array}{llll} \textit{logarithm of factors} \\\\ \log_a(xy)\implies \log_a(x)+\log_a(y) \end{array} \\\\[-0.35em] \rule{34em}{0.25pt}[/tex]
[tex]\log(x)=2\hspace{5em}\log(y)=3\hspace{4em}\log(2)\approx 0.3\hspace{4em}\log(3)\approx 0.48 \\\\[-0.35em] ~\dotfill\\\\ \log\left(\sqrt[3]{x^4\cdot y^2} \right)\implies \log\left(\left( x^4\cdot y^2 \right)^{\frac{1}{3}} \right)\implies \cfrac{1}{3}\log(x^4 y^2) \\\\\\ \cfrac{1}{3}[\log(x^4)~~ + ~~\log(y^2)]\implies \cfrac{1}{3}[4\log(x)~~ + ~~2\log(y)]\implies \cfrac{1}{3}[4(2)~~ + ~~2(3)] \\\\\\ \cfrac{1}{3}[8~~ + ~~6]\implies {\Large \begin{array}{llll} \cfrac{14}{3} \end{array}}[/tex]
Martina, Ahmad, and Ryan served a total of 87 orders Monday at the school cafeteria. Ahmad served 9 fewer orders than Martina. Ryan served 2 times as many orders as Martina. How many orders did they each serve?
Answers
Martin served 24 orders, Ahmad served 15, and Ryan served 48 orders.
Calculating Unknown Quantity:To find an unknown quantity in a problem we use the algebraic expression. These are combinations of variables and constant terms. Here variables are used to represent the Unknown Numbers.
Here we have
Martina, Ahmad, and Ryan served a total of 87 orders
Since we don't how many orders served each one
Let's assume that each of them with different variables
Martina served 'm' orders
Ahmad served 'a' orders
Ryan served 'r'
Given that
Ahmad served 9 fewer orders than Martina
=> a = m - 9 ---- (1)
Ryan served 2 times as many orders as Martina.
=> r = 2m --- (1)
Given that total served orders = 87
=> m + a + r = 87
=> m + m - 9 + 2m = 87 [ from (1) and (2) ]
=> 4m = 87 + 9
=> 4m = 96
=> m = 24
Number of orders served by Ahmad, a = 24 - 9 = 15
Number of orders served by Ryan, r = 2(24) = 48
Therefore,
Martin served 24 orders, Ahmad served 15, and Ryan served 48 orders.
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If P is the incenter of A JKL, find each measure. K 10 M P 7 17 32" 22' L
Answers
Although part of your question is missing, you might be referring to this full question: If P is the incenter of ΔJKL, find each measure (triangle as attached).
Based on the property of incenter, the measurements of the sides and the angles will be:
JK = 21.2 units
KL = 26.63 units
JL = 28.33 units
m∠K = 36°
By using the property of incenter:
PM = PN = PO = 7 units
∠MJP = ∠OJP = 32°
∠NLP = ∠OLP = 22°
By using the triangle sum theorem,
m∠JKL + m∠KLJ + m∠LJK = 180°
2(m∠NKP) + 2(m∠NLP) + 2(m∠MJP) = 180°
2(m∠NKP) + 2(22°) + 2(32°) = 180°
2(m∠NKP) = 180° - 108°
m∠NKP = 36°
Then, from ΔJMP,
tan(32°) = MP/MJ
tan(32°) = 7/MJ
MJ = 7/tan(32)°
MJ = 11.20
And from ΔPOL,
tan(22°) = OP/OL
tan(22°) = 7/OL
OL = 17.33
And from ΔKNP,
tan(36°) = NP/KN
tan(36°) = 7/KN
KN = 9.63
Hence, JK = MJ + MK = 21.2 units
KL = LN + KN = 26.63 units
JL = JO + OL = 28.33 units
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Which of the following sets of ordered pairs represents a function? A. {(4, 1), (-11, -1), (8, 2), (-1 -2), (9, 4), (-2,-10)} B. {(-2, -1), (-2, 5), (7, 8), (-2, 5), (3,9), (-3, 1)} C. {(8, 2), (6,-2), (7,4), (-11,-4), (8,3), (-9, 5)} D.{(2, 4), (-1,-1), (7, 2), (-1, -2), (6, 3), (2, -9)}
Answers
The answer is A & C
To determine if a set of ordered pairs represents a function, you can check if each input (x value) is associated with only one output (y value).
In set A, input 4 is paired with output 1 and input 8 is paired with output 2. These two inputs are paired with only one output, so the set A can represent a function.
In set B, input -2 is paired with two different outputs.
-1 and 5. This means that -2 has multiple exits, so set B does not represent a function. In set C, input 7 is paired with output 4 and input 8 is paired with output 3. The set C can represent a function because these two inputs are paired with only one output.
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What is the area of this triangle in cm?
50 mm
9 cm
Answers
First convert 50 mm into cm : 5
base :9
height :5
formula of traingle= ½*(b*h)
.'. ½* (9*5)
½*45
.'. area : 22.5 cm²
Which is the vertex angle of a triangle?
Answers
In an isosceles triangle, the angle opposite the base is referred to as the vertex angle.
A triangle refers to a two-dimensional shape which comprises of three sides and three angles. The isosceles triangle is a type of triangle in which two sides are congruent i.e., they are the same length. The third side of an isosceles triangle is of different length and is referred to as the base. The three angles of any triangle add up to a sum of 180°. In isosceles triangles, the two angles located along the base are referred to as the base angles which are always congruent, or equal. The angle opposite the base is referred to as the vertex angle and is different value from the two base angles. The value for the vertex angle can always be calculated by subtracting the base angles from 180° using the general formula: 180° - 2B = A, where B refers to the base angle and A is the vertex angle.
Note: The question is incomplete. The complete question probably is: Which is the vertex angle of an isosceles triangle.
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TRUE/FALSE. if the rank of the augmented matrix of a system of n linear equations in n unknowns is greater than the rank of the matrix of coefficients, then the matrix of coefficients is nonsingular
Answers
It is false that if the rank of the augmented matrix of a system of n linear equations in n unknowns is greater than the rank of the matrix of coefficients, then the matrix of coefficients is nonsingular
The augmented matrix is an extension of a matrix in which we add a column ( non homogeneous part of the system)
Say , Ax = b
Here , b is column part
So , Augmented matrix will be [ A : b ]
The Rank of augmented matrix can be found by performing elementary row operations on a augmented matrix and counting the number of the rows without zero comparing the rank of an augmented matrix
The rank of coefficient matrix can determined if there is a solution to the system of solution
In the question this statement,
If the rank of the augmented matrix of a system of n linear equations in n unknowns is greater than the rank of the matrix of coefficients, then the matrix of coefficients is nonsingular is false
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1.4 inches and the width is 4.1 inches. The company making the cell phone wants to make a new version whose length will be 1.75 inches. Assuming the side lengths in the new phone are proportional to the old phone, what will be the width of the new phone?
Answers
The side lengths of the new phone are proportional to the old phone, then the width of the new phone is 5.125 inches.
What is an arithmetic operation?The four basic mathematical operations are the addition, subtraction, multiplication, and division of two or even more integers. Among them is the examination of integers, particularly the order of actions, which is crucial for all other mathematical topics, including algebra, data organization, and geometry.
As per the given information in the question,
The dimensions of the older phones are,
Length, L(1) = 1.4 inches
Width, W(1) = 4.1 inches
The dimensions of the new phone are,
Length, L(2) = 1.75 inches
Width, W(2) = ?
Then the width of the new phone is,
1.4 × W(2) = 4.1 × 1.75
W(2) = (4.1 × 1.75)/1.4
W(2) = 5.125 inches.
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