Assume that a sample is used to estimate a population mean μ . Find the 99% confidence interval for a sample of size 891 with a mean of 20.8 and a standard deviation of 17.6. Enter your answer as a tri-linear inequality accurate to 3 decimal places.19.281Incorrect < μ < 22.319
Answers
Solution:
The confidence interval is expressed as
where
[tex]\begin{gathered} \bar{x}\text{ or }\mu\Rightarrow sample\text{ mean} \\ z\Rightarrow confidence\text{ level value} \\ s\Rightarrow sample\text{ standard deviation} \\ n\Rightarrow sample\text{ size} \end{gathered}[/tex]Given a 99% confidence interval for a sample size of 891 with a mean of 20.8 and a standard deviation of 17.6, this implies that
[tex]\begin{gathered} \bar{x}=20.8 \\ s=17.6 \\ n=891 \\ z=2.576 \end{gathered}[/tex]By substituting these values into the above equation, we have
[tex]\begin{gathered} CI=20.8\pm(2.576\times\frac{17.6}{\sqrt{891}}) \\ =20.8\pm1.518866748 \\ Thus,\text{ } \\ \Rightarrow lower\text{ bound:} \\ 20.8-1.518866748=19.28113325 \\ \Rightarrow upper\text{ bound:} \\ 20.8+1.518866748=22.31886675 \end{gathered}[/tex]Hence, we have
[tex]19.281<\mu<22.319[/tex]
Related Questions
a pharmaceutical company knows that five percent of all users of a certain drug experience a serious side effect. a researcher examines a sample of 200 users of the drug. a. what is the probability of finding between 8 and 12 cases with side effects? (round final answer to 4 decimal places.) b. what is the probability of finding more than 16 cases with side effects? (round final answer to 4 decimal places.)
Answers
Using the normal distribution, the probabilities are given as follows:
a. Between 8 and 12 cases with side effects: 0.582 = 58.2%.
b. More than 16 cases with side effects: 0.0174 = 1.74%.
Normal Probability DistributionThe z-score of a measure X of a normally distributed variable that has mean represented by [tex]\mu[/tex] and standard deviation represented by [tex]\sigma[/tex] is given by the equation presented below:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure X is above or below the mean of the distribution, depending if the z-score is positive or negative.From the z-score table, the p-value associated with the 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:
p = 0.05, n = 200.
Hence the mean and the standard deviation of the approximation are given as follows:
E(X) = np = 200 x 0.05 = 10.[tex]\sqrt{V(X)} = \sqrt{np(1 - p)} = \sqrt{200(0.05)(0.95)} = 3.08[/tex]For item a, using continuity correction, the probability of between 8 and 12 cases with side effects is the p-value of Z when X = 12.5 subtracted by the p-value of Z when X = 7.5, hence:
X = 12.5:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
Z = (12.5 - 10)/3.08
Z = 0.81
Z = 0.81 has a p-value of 0.7910
X = 7.5:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
Z = (7.5 - 10)/3.08
Z = -0.81
Z = -0.81 has a p-value of 0.2090.
0.7910 - 0.2090 = 0.582 probability.
For item b, the probability of finding more than 16 cases with side effects is one subtracted by the p-value of Z when X = 16.5, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
Z = (16.5 - 10)/3.08
Z = 2.11
Z = 2.11 has a probability of 0.9826.
1 - 0.9826 = 0.0174 = 1.74% probability.
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Write a simplified expression for the area of the rectangle.....
Answers
SINCE A OF A RECTANGLE IS =L×B
[tex] = (12x - 6)(14 \frac{1}{6} ) \\ = (12x - 6)( \frac{25}{6} ) \\ = \frac{25}{6} (12x) + \frac{25}{6} ( - 6) \\ = 50x - 25[/tex]
THE SIMPLIFIED AREA IS =50x-25
Leanne has a bag only containing blue beads and purple beads. (2)/(9) of the beads are blue.
If there are 6 blue beads in the bag, how many beads are purple?
Answers
Proportionately, if there are 6 blue beads in the bag, and blue beards are 6 or 2/9 of the total beads, the number of purple beads in the bag is 21.
What is proportion?Proportion refers to the numerical ratio of a value to another.
Proportion shows the quantity of a value contained in another variable.
Since proportions are fractional values, like ratios, they are represented using decimals, fractions, and percentages.
The ratio of blue beards to purple beads = 2:7 or 2/9
The number of blue beads in the bag = 6
The total number of beads in the bag = 27 (6/2 x 9)
The number of purple beads in the bag = 21 (27 x 7/9)
Thus, based on the given proportional ratio of the blue beads to the purple beads, there are 21 purple beads in the bag.
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Suppose that g(x) = f(x) + 2. Which statement best compares the graph of
g(x) with the graph of f(x)?
A. The graph of g(x) is the graph of f(x) shifted 2 units to the left.
B. The graph of g(x) is the graph of f(x) shifted 2 units up.
C. The graph of g(x) is the graph of f(x) shifted 2 units to the right.
D. The graph of g(x) is the graph of f(x) shifted 2 units down.
Answers
The graph of g(x) with the graph of f(x): Option D, which is a shift of 2 units to the left, is correct.
What is Function?
A function in mathematics from a set X to a set Y allocates exactly one element of Y to each element of X. The sets X and Y are collectively referred to as the function's domain and codomain, respectively.
We are aware that the graph of the modified function is:
for every parent function f(x).
g(x) = f(x + a)
is a left- or right-shift of the parent function f(x), depending on the value of a.
The shift is 'a' units to the left if a>0.
The shift is 'a' units to the right if a0.
Here, G(x) has been changed as follows:
G(x) = F(x + 2)
i.e. a=2>0.
2 units up: G(x) = F(x) + 2.
2 units down: G(x) = F(x) - 2.
2 units to the left: G(x) = F(x + 2).
2 units to the right: G(x) = F(x - 2).
Hence, Option D, which is a shift of 2 units to the left, is correct.
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Help please:)! Really STUCK on this question!
Answers
Answer:
Step-by-step explanation:
it 10
allison drove home at 58 mph, but her brother austin, who left at the same time, could drive at only 46 mph. when allison arrived, austin still had 24 miles to go. how far did allison drive?
Answers
When Allison arrived, Austin still had 24 miles to go. Allison drive 116 miles per hour.
What is distance?
Distance is a measurement of how far apart two things or points are, either numerically or occasionally qualitatively. Distance can refer to a physical length in physics or to an estimate based on other factors in common usage.
As given, Allison drove home at 58 mph, but her brother Austin, who left at the same time, could drive at only 46 mph. Allison arrived, Austin still had 24 miles to go.
Let t be the time they drove.
Then you have this "distance" equation
58t = 46t + 24
saying that both parts of the equation represent the same distance. Then
58t - 46t = 24
12t = 24
t = 2 hours.
Hence the distance is, 2 x 58 = 116 mph.
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Someone please help with this math problem?
Answers
Both equations' solutions are found at the point (-2, 2). When point (-1,4), the 2x-y=-6 yields the correct point. The second equation is as a result. The point (2, 14) is the answer to the first equation because it provides the answer to the first equation but not the second.
What is equation?The word equation and its cognates in other languages may have slightly different meanings; for example, in French an equation is defined as containing one or more variables, while in English any well-formed formula consisting of two expressions related with an equals sign is an equation. An equation is a formula that expresses the equality of two expressions by connecting them with the equals sign =. Finding the values of the variables that result in the equality is the first step in solving an equation with variables. The unknown variables are also known as the variables for which the equation must be solved, and the unknown variable values that satisfy the equality are known as the equation's solutions. Equations come in two varieties: identities and conditional equations.
3x-y=-8
2x-y=-6
given points are (-1,4), (2,14), (-2,2)
On solving the equation,
3x-y=-8
-(2x-y=-6)
x=-2
y=2
The point (-2,2) is the solution to both equations.
The point (-1,4) on putting in the 3x-y=-8 will not give solution but when put in the 2x-y=-6, it gives the result. so it the solution to second equation.
The point (2,14) is the solution to the first equation as it gives the answer to first but not to the second equation.
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x^2+6x+? complete the square
Answers
Answer:
+ 9
Step-by-step explanation:
x²+ 6x
to complete the square
add ( half the coefficient of the x- term )² to x² + 6x
x² + 2(3)x + 3²
= x² + 6x + 9
= (x + 3)² ← a perfect square
what is the anwser
-2|7x-1|= 14
Answers
Answer: -3/4
Step-by-step explanation: Lucky I just learned about this last week! Multiply 7 and -1 by -2 which makes the equation -14x + 2 = 14. Subtract 2 from both sides to make -16x = 12. Then divide each side by -16 and you get -3/4 = x.
Nice helping out!
Answer:
There are no solutions.
Step-by-step explanation:
Hello!
Isolate the absolute value equation first:
-2|7x - 1| = 14|7x - 1| = -7Now stop and think.
An absolute value equation always has a positive outcome, because you are finding the positive value of what's inside. The outcome here is negative, so there is no value of x that makes it so that the absolute value is negative.
So the solution is No Solutions.
This is the only question I’m stuck on can someone explain and help me
Answers
Answer:
x = 58°
∠P = 58°
∠PQR = 64°
Step-by-step explanation:
If you add the two nonadjacent angles together they will equal the exterior angle. Setup up an equation using that info.
[tex]58 +x=2x[/tex]
Solve for x.
[tex]58 +x-x=2x-x\\58=x[/tex]
Since ∠P is the same as x, ∠P = 58°
To find ∠PQR, add ∠P and ∠R together and then subtract from 180°. You subtract from 180° because the sum of the three angles of a triangle equal 180°.
58 + 58 = 116
180 - 116 = 64°
∠PQR = 64°
in addition to the facts in the diagram which other statements are necessary to prove that? ABC is congruent to? EFG by the ASA criterion
Answers
Triangle ABC and the triangle EFG are congruent by the first and third statement.
What is the congruent diagram?
Shapes that are identical to one another are said to be congruent. Both the matching sides and the corresponding angles match. We must examine all of the shapes' angles and sides in order to accomplish this. Two shapes that are similar to one another can be stacked perfectly.
In the given example triangle ABC and triangle EFG having one same side of length 2.
By the ASA (Angle side angle) criteria, we want two angles are same then the triangles are congruent.
When "m ∠ B and m ∠ F" and "m ∠ A and m ∠ E" are same then the triangles are congruent.
Therefore, the first option is correct.
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Divide $180 in the ratio of 2 : 3 : 4
Answers
By dividing $180 in the ratio of 2:3:4, we get 40,60 and 80
Solution
Find the sum of the ratios2 + 3 + 4 = 9
Divide the amount from the sum of the ratios180 ÷ 9 = 20
Hence, we get the quotient of 20.
Multiply the quotient by the ratios20 × 2 = 40
20 × 3 = 60
20 × 4 = 80
Hence, by dividing $180 in the ratio of 2:3:4, we get 40,60 and 80
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Eric ordered a set of red and yellow pins. He received 70 pins in all. 21 of the pins were red. What percentage of the pins were red?
Answers
Answer:
The formula for finding the percentage of something is given as: (No. of items you want to find÷Total no. of items)×100
Percentage of red pins = (21÷70)×100
= 30%
(-7i)(3+3i)(a) Write the trigonometric forms of the complex numbers. (Let0 ≤ theta < 2pi.)(-7i) =(3+31) =(b) Perform the indicated operation using the trigonometric forms. (Let0 ≤ theta< 2pi.)(c) Perform the indicated operation using the standard forms, and check your result with that of part (b).
Answers
A complex number z is given in the form:
z = (x.y) = (realpart) x + imaginary part (iy)
In this case:
z1 = -7i
z2 = 3+3i
To write in trigonometric form:
[tex]\begin{gathered} z\text{ = r\lparen cos}\theta\text{ + isin}\theta) \\ For\text{ z1} \\ r\text{ = }\sqrt{0^2+7^2} \\ \text{ = 7} \\ \theta\text{ =}\tan^{-1}(\frac{7}{0} \\ Since\text{ t}he\text{ }argument\text{ }is\text{ }undefined\text{ }and\text{ y is negative,} \\ \theta=\text{ }\frac{3\pi}{2} \\ In\text{ trig form:} \\ z1\text{ = 7\lparen cos}\frac{3\pi}{2};sin\frac{3\pi}{2}) \\ For\text{ z2} \\ r\text{ = }\sqrt{3^2\text{ +3}^2} \\ \text{ =3}\sqrt{2} \\ \theta\text{ = }\tan^{-1}\frac{3}{3} \\ =\text{ }\frac{\pi}{4} \\ In\text{ trig form:} \\ z2\text{ = 3}\sqrt{2}(cos\frac{\pi}{4};sin\frac{\pi}{4}) \end{gathered}[/tex]Multiplication in trigonometric form:
[tex]z1*z2\text{ = \lparen21}\sqrt{2}\text{ \rparen \lparen cos}\frac{7\pi}{4};\text{ sin}\frac{7\pi}{4})[/tex]Multiplication in standard form:
[tex]\begin{gathered} (-7i)(3\text{ + 3i\rparen} \\ =-21i\text{ - 21i}^2 \\ i^2\text{ = -1} \\ =\text{ -21i + 21} \\ r\text{ = }\sqrt{21^2+21^2} \\ =21\sqrt{2} \end{gathered}[/tex]Martha has 4 different colored pens in her bag. After she uses a pen she just throws it back into bag. If she does this 5 day a week, how many different ways can she use the pens for the week?.
Answers
By likelihood, she can utilize the pens in 1024 distinct ways during the week.
Probability is the study of possible outcomes of events, together with the probabilities and distributions of those occurrences.
Simply put, probability measures how probable something is to occur. We can discuss the probabilities of various outcomes, or how likely they are, whenever we are unsure of how an event will turn out. Statistics is the study of events subject to probability.
To calculate probability, divide the total number of outcomes by the total number of possible possibilities. There are differences between probability and odds.
Odds are computed by dividing the likelihood that an event will occur by the likelihood that it won't.
From the stated circumstance,
Total ways = [tex]4^{5}[/tex]= 1024
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What is the slope of this line?
What is the slope of this line?
Enter your answer as a whole number or a fraction in simplest form in the box.
Answers
Answer: 1
Step-by-step explanation: Rise over run, Rise/run. The rise is how much the line goes up or down vertically. The run is how far the line goes until it intersects through a square. The slope is 1 because if you look at the line specifically at the first dot, you just have to go down one and right one as it intersects the square to find the slope.
Is arc length equal to the measure of the radian?
For instance, if the arc length is 5 units, does it also mean that the measure of the radian is also 5 units, or can it vary??
Answers
The arc length is equal to the measure of the arc in radians only if the radius of the circle is 1 unit, for all the other circles this is false.
Is arc length equal to the measure of the radian?For a circle of radius R, if we have an arc defined by an angle of θ radians, then the length of that arc is:
L = R*θ
Particularly, the length is equal to the measure in radians only if the radius of the circle is R = 1:
L = 1*θ
So the statement is only true for the unit circle but is false for every other circle.
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Which are correct representations of the inequality –3(2x – 5) < 5(2 – x)? Select two options. x < 5 –6x – 5 < 10 – x –6x + 15 < 10 – 5x A number line from negative 3 to 3 in increments of 1. An open circle is at 5 and a bold line starts at 5 and is pointing to the right.
Answers
The correct representation of the inequality is x > 5 or –6x + 15 < 10 – 5x.
How to solve inequality?The inequality can be best represented as follows;
–3(2x – 5) < 5(2 – x)
An inequality is a mathematical expression that has the signs <, >, ≤ and ≥.
Therefore,
–3(2x – 5) < 5(2 – x)
open the brackets
- 6x + 15 < 10 - 5x
Lets solve further by subtracting 15 from both sides of the inequality.
- 6x + 15 < 10 - 5x
- 6x + 15 - 15 < 10 - 15 - 5x
- 6x < - 5 - 5x
add 5x to both sides of the inequality.
- 6x < - 5 - 5x
- 6x + 5x < - 5 - 5x + 5x
-x < - 5
divide both sides by -1
Therefore,
x > 5
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The solution of the given inequality is x > 5 which is the correct representation of x > 5 or –6x + 15 < 10 – 5x.
The inequality is given in the question as
–3(2x – 5) < 5(2 – x)
Open the parenthesis and apply the distributive property of multiplication,
⇒ - 6x + 15 < 10 - 5x
Subtract 15 from both sides of the above inequality,
⇒ - 6x + 15 - 15 < 10 - 15 - 5x
⇒ - 6x < - 5 - 5x
Add 5x to both sides of the inequality,
⇒ - 6x + 5x < - 5 - 5x + 5x
⇒ -x < - 5
Multiply both sides by -1 and flip the sign of inequality
⇒ x > 5
Therefore, the solution of the given inequality is x > 5.
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order the fractions 4/5, 1/2,9/10,3/4 from least to greatest
Answers
Answer:
1/2 -> 3/4 -> 4/5 -> 9/10
Step-by-step explanation:
1/2 = 50%
3/4 = 75%
4/5 = 80%
9/10 = 90%
How to figure out:
1/2 - Divide 100/2 = 50. So 1/2 of 100 is 50 so 50%
3/4 - Divide 100/4 = 25. Now multiply 25 x 3 = 75 so 75%
4/5 - Divide 100/5 = 20. Now multiply 20 x 4 = 80 so 80%
9/10 - Divide 100/10 = 10. Now multiply 10 x 9 = 90 so 90%
Write a number that satisfies the given condition. An integer between - 0.6 and 0.4. The integer between -0.6 and 0.4 is
Answers
Answer:
I think the answer is 0.
Step-by-step explanation:
-0.6,-0.5,-0.4,-0.3,-0.2,-0.1,0,0.1,0.2,0.3,0.4
help me pls and explain to me how to find y intercept
Answers
Answer:
y = -x + 4
Step-by-step explanation:
(-1, 5), (2. 2)
(x₁, y₁) (x₂, y₂)
y₂ - y₁ 2 - 5 -3 -3
m = ----------- = ----------- = --------- = ------- = -1
x₂ - x₁ 2 - (-1) 2 + 1 3
y - y₁ = m(x - x₁)
y - 5 = -1(x - (-1))
y - 5 = -1(x + 1)
y - 5 = -x - 1
+5 +5
----------------------
y = -x + 4
I hope this helps!
Answer:
see explanation
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = 8, - 4) and (x₂, y₂ ) = (- 1, 5) ← 2 ordered pairs from the table
m = [tex]\frac{5-(-4)}{-1-8}[/tex] = [tex]\frac{5+4}{-9}[/tex] = [tex]\frac{9}{-9}[/tex] = - 1 , then
y = - x + c
to find c use any ordered pair from the table
using (2, 2 ) , then
2 = - 2 + c ⇒ c = 2 + 2 = 4
y = - x + 4 ← in slope- intercept form
with y- intercept c = 4
8 times the quantity of X and 8 Translate it into expression
Answers
Given
8 times the quantity of X and 8
Find
Translate into an expression
Explanation
Quantity be X
so , according to the question ,
8 (X + 8)
Final Answer
Hence , the required expression is 8 (X + 8)
If (-6,-38) and (5,28) are twoanchor points on the trend line,then find the equation of the line..y = 6x + [?]
Answers
Step 1
Write the slope, y-intercept form of the equation of a line.
[tex]undefined[/tex]Which equation illustrates the associative property
Answers
Associative property of the sum states that the order the operations are done doesn't matter as long as the sequence of operands also doesn't change. This property is given by:
[tex](x+y)+z=x+(y+z)[/tex]Therefore, the equation that illustrates the associative property is:
[tex]a+(b+c)=(a+b)+c[/tex]how many elements are in the union of three pairwise disjoint sets if the sets contain 10, 15, and 25 elements? how many ways are there to select a student whose major is in one of the departments of the school of science if there are seven departments in this school with 31, 88, 19, 11, 41, 22, and 17 students in each? (assume that no student can have more than one major.) how many ways are there to select a person who lives on a street with five houses if the number of people in these houses are 5, 3, 2, 7, and 6?
Answers
a) 50 elements are in the union of three pairwise disjoint sets if the sets contain 10, 15, and 25 elements.
b) 229 are there to select a student whose major is in one of the departments of the school of science if there are seven departments in this school with 31, 88, 19, 11, 41, 22, and 17 students in each.
c) 23 are there to select a person who lives on a street with five houses if the number of people in these houses are 5, 3, 2, 7, and 6.
The problem we are dealing with is related to union sets.The union of two sets is a set containing all elements that are in set A and set B or including more sets
For the first problem, the sets contain:
n(A)=10, n(B)=15, n(C)=25, n(A∩B)=0 ,n(B∩C)=0 ,n(C∩A)=0,n(A∩B∩C)=0
So, n(A∪B∪C)=n(A)+n(B)+n(C)−n(A∩B)−n(B∩C)−n(C∩A)+n(A∩B∩C)
= 10 +15+25-0-0-0-0-0
= 50
For the second problem, since no student can have more than one major.
So, (A∪B∪C∪D∪E∪F∪G)=n(A)+n(B)+n(C)+n(D)+n(E)+n(F)+n(G)
As we know : n(A)=31, n(B)=88, n(C)=19, n(D)=11, n(E)=41, n(F)=22, n(G)=17
So , (A∪B∪C∪D∪E∪F∪G) = 31+88+19+11+41+22+17= 229
For the third problem, we have
n(A)=5
n(B)=3
n(C)=2
n(D)=7
n(E)=6
So, the number of elements will be (A∪B∪C∪D∪E) = 5+3+2+7+6 =23
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There were 42 boys and 28 girls in a photography club. Then, 6 more girls joined the club. What was the ratio of the numbers of boys to the numbers of girls in the end? Express the ratio in its simplest form.
Answers
Given:
There are given that a total of 42 boys and 28 girls in the photography club.
Explanation:
According to the question:
We need to find the ratio.
So,
We can see a total of 28 girls and 6 more girls.
So,
The total number of girls is:
[tex]28+6=34[/tex]Then,
The numbers of boys to the numbers of girls in the end is:
[tex]\frac{42}{34}=\frac{21}{17}[/tex]Final answer:
Hence, the ratio is shown below:
[tex]21:17[/tex]
The average change in a company's sales income was $9 million over 3 moths. Determine the average change in sales income per month.
Answers
The average change in sales income per month is $ 3 million.
What is average change and how is it assessed?
The average rate at which one quantity changes in relation to another's change is referred to as the average rate of change function. A method that determines the amount of change in one item divided by the corresponding amount of change in another is known as an average rate of change function.
Given, for 3 months, the average change in the company's sales
= $ 9 million
Also, for x months, the average change in the company's sales
= $ (9x/3) million
Therefore, for one month, the average change in the company's sales
= $ (9*1/3) million = $ 3 million
Thus, the average change in sales income per month is $ 3 million.
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Triangle VWX is formed by connecting the midpoints of the side of triangle STU.
The lengths of the sides of triangle VWX are shown. What is the length of SU?
Figures not necessarily drawn to scale.
Answers
The length of the side SU will be equal to 4√2.
What is a Pythagorean theorem?Pythagorean theorem states that in the right angle triangle the hypotenuse square is equal to the sum of the square of the other two sides.
The formula for the Pythagorean theorem will be given as:-
H² = P² + B²
Here,
H = Hypotenuse
P = perpendicular
B= Base
The length of the sides of the triangle is formed by joining the midpoints of the bigger triangle are xw=2, xv=2, and vw = 3.
Here sv = vt = xw = 2 units. Apply the Pythagorean theorem in a triangle xsv.
H² = P² + B²
sx² = xv² + sv²
sx = √ ( 2² + 2² )
sx = √8
sx = √ ( 2 x 2 x 2 )
sx = 2√2
SU = 2 sx
SU = 2 x 2√2
SU = 4√2
Therefore, the length of the side SU will be equal to 4√2.
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21. What are the modes of the following sets of numbers?
a. 3, 13, 6, 8, 10, 5, 6
b. 12, 0, 15, 15, 13, 19, 16, 13, 16, 16
Answers
Answer:
a. 6
b. 16
Step-by-step explanation:
a.
The mode is the number that appears the most
3 appears once
13 appears once
6 appears twice
8 appears once
10 appears once
5 appears once
Since 6 appears the most, it is the mode in this set of numbers
b.
Again, The mode is the number that appears the most
12 appears once
0 appears once
15 appears twice
13 appears twice
19 appears once
16 appears three times
Since 16 appears the most, it is the mode in this set of numbers
The correct answers are: [A]: "6 " ; and: [B]: " 16 ."
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Step-by-step explanation:
The question asks to find the modes of the following sets of numbers:
Set a) "{3, 13, 6, 8, 10, 5, 6}."
Set b) "{12, 0, 15, 15, 13, 19, 16, 13, 16, 16}."
Note that the mode is the number that occurs most frequently within a data set.
To begin: let's find the mode of Set: a:
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First, let's list all the values within Set: a: in order of smallest to largest—to simplify matters:
→ " { 3, 5, 6, 6, 8, 10, 13 }."
In this data set, there is only one value that occurs more than once—
which is 6. As such, the mode of "Data Set: a" is 6 .
Then: To continue: let's find the mode of Set: b:
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Second, Let's list all the values within Set: b: in order of smallest to largest—again; to simplify matters:
→ " { 0, 12, 13, 13, 15, 15, 16, 16, 16, 19 } ."
In this data set, we see the following:
Each of the three values: 0, 12, and 19 appear only once;
13 and 15 individually, appear twice; and:
16 appears "three times".
As such:
The value, 16 appears the most in this data set; and:
→ The mode of "Data Set: b"—is 16.
_____
The correct answers are: [A]: "6 " ; and: [B]: " 16 ."
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Hope this is helpful to you!
If you have any questions—Please "comment" below!
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Solve the system of equations below for x, y, and z. (4x - 2y + 3z = 9 x - 2y = -3 2x + 3y = 1
Answers
The solutions are x = -1, y = 1 and z = 5
What is a Linear equation?In Mathematics, the equation which has highest degree 1 is known as a Linear equation. Linear equations are used to calculate unknown values. Here to represent unknown values we will use variables like x, y, z or a, b, c .. etc.
According to the number of variables in given equations, the given equations will be called a Linear equation in one variable or Linear equation in two variables and so on. To solve linear equations we will use Elimination method
Here, we have three linear equations with 3 and 2 variables
4x - 2y + 3z = 9 ----(1)
x - 2y = -3 -----(2)
2x + 3y = 1 -----(3)
Here, to find x, y and z we will use Elimination method
First of all solve (2) and (3) as given below
2 × (2) ⇒ 2x - 4y = - 6 -----(4)
1 × (3) ⇒ 2x + 3y = 1
Now subtract (3) from (4)
(4) - (3) ⇒ 2x - 4y -2x - 3y = - 6 - 1
⇒ - 7y = -7
⇒ y = 1
Substitute y = 1 in (2)
(2) ⇒ x - 2(1) = -3
x - 2 = -3
x = -1
Now substitute x = -1 and y = 1 in (1)
(1) ⇒ 4(-1) - 2(1) + 3z = 9
- 6 + 3z = 9
3z = 15
z = 5
From above calculations
The values of x = -1, y = 1 and z = 5
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