The variance is:
[tex]\sigma^2=\frac{\Sigma(x-\mu)^2}{N}[/tex]So we have 5 values, which means that N=5 and the mean is:
[tex]\mu=\frac{26+34+17+24+24}{5}=25[/tex]So the variance is 29.6.
Ignore c. I only need help with a and b
Part A.
The composition of f ang g is given by
[tex](f\circ g)(x))=f(g(x))=\frac{(3x+7)-7}{3}[/tex]where we have inserted 3x-7 in the place of x in function f. Then, we have
[tex](f\circ g)(x))=f(g(x))=\frac{3x+7-7}{3}=\frac{3x}{3}=x[/tex]Therefore, the answer is
[tex](f\circ g)(x))=x[/tex]Part B
Similarly to the previous case, we have
[tex](g\circ f)(x))=g(f(x))=3(\frac{x+7}{3})-7[/tex]which gives
[tex](g\circ f)(x))=g(f(x))=x+7-7=x[/tex]then, the answer is
[tex](g\circ f)(x))=x[/tex]Part C.
In the first case, x belongs to the domain of g and g(x) belongs to the domain of f. Then, the domain of the composition (fog)(x) is all real numbers.
Similarly, in the second case, x belongs to the domain of f and f(x) belongs to the domain of g. Then, the domain of the composition (gof)(x) is all real numbers. Then, the domains are the same (all real numbers).
Construct a 95% confidence interval of the population proportion using the given information x=180, n = 300 the lower bound is the upper bound isRound to three decimal places as needed
Given;
[tex]x=180,n=300[/tex]Then, we can find the point estimation as;
[tex]\begin{gathered} \hat{p}=\frac{x}{n} \\ \hat{p}=\frac{180}{360}=0.60 \end{gathered}[/tex][tex]Z_{\frac{\alpha}{2}}=Z_{0.05}=1.96[/tex]Thus, the margin of error E is;
[tex]\begin{gathered} E=Z_{\frac{\alpha}{2}}\sqrt[]{\frac{\hat{p}(1-\hat{p})}{n}} \\ E=1.96\sqrt[]{\frac{0.60(0.40)}{300}} \\ E=1.96\sqrt[]{0.0008} \\ E=0.055 \end{gathered}[/tex]A 95% confidence interval for population proportion p is;
[tex]\hat{p}\pm E=0.60\pm0.055[/tex]The lower bound is;
[tex]0.60-0.055=0.545[/tex]The upper bound is;
[tex]0.60+0.055=0.655[/tex]Use diagram to find the following 1. m angle RVS = 2. M angle TVU =
The pie chart provides the following information;
[tex]\begin{gathered} m\angle RVS=(10x-10)^o \\ m\angle RVU=(8x-14)^o \\ m\angle UVT=8x^o \\ m\angle TVS=(5x+12)^o \end{gathered}[/tex]The sum of angles in a circle is 360 degrees.
Thus, we have;
[tex]\begin{gathered} (10x-10)^o+(8x-14)^o+8x^o+(5x+12)^o=360^o \\ 31x^o-12^o=360^o \\ 31x^o=360^o+12^o \\ 31x^o=372^o \\ x^o=\frac{372^o}{31} \\ x^o=12^o \end{gathered}[/tex]Then;
(a)
[tex]\begin{gathered} m\angle RVS=(10x-10)^o_{} \\ m\angle RVS=10(12)-10 \\ m\angle RVS=110^o \end{gathered}[/tex](b)
[tex]\begin{gathered} m\angle TVU=8x^o \\ m\angle TVU=8(12) \\ m\angle TVU=96^o \end{gathered}[/tex]what is 5.8x10² in standard notation?
Answer:
[tex]5.8\text{ }\times\text{ 10}^2[/tex]Explanation:
Here, we want to write the given number in standard notation
The form we have given, is the scientific notation
To write in the standard form, we consider the scientific notation as they are the same
We have the standard notation as:
[tex]5.8\text{ }\times\text{ 10}^2\text{ = 5.8 }\times\text{ 10}^2[/tex]One thermos of hot chocolate uses 2/3 cup of cocoa powder. How many thermoses can nalli make with 3 cups of cocoa powder?
In order to determine the number of thermos, divide by 3 by 2/3, as follow:
[tex]\frac{\frac{3}{1}}{\frac{2}{3}}=\frac{3\cdot3}{1\cdot2}=\frac{9}{2}=4.5[/tex]the previous result means that nalli can make four and one hal thermoses with 3 cups of cocoa powder.
(statistics) urgently need help with question 32, is it valid or not valid & is the argument sound or not?
From the Venn diagram shown above we notice that the conclusion is false. This comes from the fact that even if all queens are women not all women are quenss.
In ACDE, mZC = (4x – 16), m D = (6x - 1)", and mZE = (4x - 13). Find mZC.
Explanation:
We can do a diagram of triangle CDE:
The sum of the measures of the interior angles of any triangle is 180º. We can write an equation:
[tex]\begin{gathered} m\angle C+m\angle D+m\angle E=180º \\ (4x-16)+(6x-1)+(4x-13)=180 \\ (4x+6x+4x)+(-16-1-13)=180 \\ 14x-30=180 \end{gathered}[/tex]Solve for x:
[tex]\begin{gathered} 14x=180+30 \\ 14x=210 \\ x=\frac{210}{14} \\ x=15 \end{gathered}[/tex]And with x = 15, replace into the expression for the measure of angle C to find it:
[tex]m\angle C=4x-16=4\cdot15-16=60-16=44º[/tex]Answer:
m
What is the measurement of DC? How do you know ?
The vertices B, C and D form a right triangle.
Knowing 2 sides of the tright triangle, like BD and BC, we can find the length ofthe third side, DC, using the Pythagorean theorem: the sum of the squares of the length of the legs, DC and BC, is equal to the square of the length of the hypotenuse BD.
[tex]DC^2+BC^2=BD^2[/tex]Replacing with the values, we can calculate DC:
[tex]\begin{gathered} DC^2+60^2=100^2 \\ DC^2+3600=10000 \\ DC^2=10000-3600 \\ DC^2=6400 \\ DC=\sqrt[]{6400} \\ DC=80 \end{gathered}[/tex]Answer:
The correct options are
A: 80
B: Pythagorean theorem
Quadratic Functions in Standard FormCaroline wrote these steps to graph f(x) = 2x2 + 4x + 5 on note cards, but they gotmixed up. Help Caroline by re-writing the steps in the correct order. Use the notecards to complete the steps below.
1.- Determine the vertex...
2.- The axis of symmetry...
3.- The y-intercept...
4.- Plot a point...
5.- Plot another point...
The above is the correct order of the cards, now the reason for that first you have to find the vertex. Now, the axis of symmetry is a straight line that passes through the vertex. Later you have to find another 2 points reflected by the symmetry axis and finally construct the graph.
use the elimination to solve each system of equations exercise number 4)
To solve this system of linear equations using the elimination method, first, add both equations:
[tex]\begin{gathered} 8x+5y=38\Rightarrow\text{ Equation 1} \\ -8x+2y=4\Rightarrow\text{ Equation 2} \end{gathered}[/tex][tex]\begin{gathered} 8x+5y=38 \\ -8x+2y=4\text{ +} \\ --------- \\ 0x+7y=42 \\ 7y=42 \end{gathered}[/tex]Now solve for y dividing by 7 on both sides of the equation:
[tex]\begin{gathered} \frac{7y}{7}=\frac{42}{7} \\ y=6 \end{gathered}[/tex]Finally, replace the value of y in any of the initial equations, for example in equation 1
[tex]\begin{gathered} 8x+5y=38 \\ 8x+5(6)=38 \\ 8x+30=38 \\ \text{ Subtract 30 from both sides of the equation} \\ 8x+30-30=38-30 \\ 8x=8 \\ \text{ Divide by 8 from both sides of the equation} \\ \frac{8x}{8}=\frac{8}{8} \\ x=1 \end{gathered}[/tex]Therefore, the solution of the system of equations is
[tex]\begin{cases}x=1 \\ y=6\end{cases}[/tex]In professor Johnson's literature class there are 267 students. At a random check Prof.Johnson notices that 22 students among 59 students did not complete their essays.Can you estimate how many students in Prof. Johnson's class did not finish theiressay?Question 71 pts
We have a class of a total of 267 students.
The professor has a sample of 59 students, where 22 of them did not complete their essays.
This equals a proportion of:
[tex]p=\frac{22}{59}\approx0.373[/tex]If this sample is representative of the class, we can use this proportion to estimate how many students did not complete the essay.
To do that we multiply the total number of students by the proportion we have just calculated:
[tex]X=N\cdot p=267\cdot0.373\approx99.59\approx100[/tex]Answer: it can be estimated that approximately 100 students did not finish their essay.
which of the following graphs represents the equation Y -4 equals 3(x-1)?
Answer:
Explanation:
Given the equation:
[tex]y-4=3(x-1)[/tex]To determine its graph, check the graph that corresponds to the x and y-intercepts of this line.
When x=0
[tex]undefined[/tex]Write an equivalent expression by distributing the "-" sign outside the parentheses: -k-(-6.2m +1)
In order to get the required expression you take into account that when you eliminate a prenthesis preceded by a minus sign, terms inside the parenthesis change their sign.
Then, for the following expression, you have:
- k - (-6.2m + 1)
- k + 6.2m - 1 that is, signs inside the parenthesis have changed
Identify the slope and the y-intercept of each line and use them to write an equation of the graph
Notice that the line passes through the point (0,1) and the point (3,-1). Then, we have the following:
[tex]\begin{gathered} y-\text{intercept: (0,1)} \\ \text{slope:} \\ m=\frac{y_2-y_1}{x_2-x_1} \\ \Rightarrow m=\frac{-1-0}{3-0}=-\frac{1}{3} \\ m=-\frac{1}{3} \end{gathered}[/tex]now we can find the equation of the line using the slope and the y-intercept:
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ \Rightarrow y-1=-\frac{1}{3}(x-0) \\ \Rightarrow y=-\frac{1}{3}x+1 \end{gathered}[/tex]therefore, the equation of the line is y=-1/3x+1
how do you solve 0.27÷0.9?
Given:
[tex]0.27\div0.9[/tex]To divide the decimals, we must take care of the decimal points
So, we will divide it as follows:
[tex]0.27\div0.9=\frac{27}{100}\div\frac{9}{10}=\frac{27}{100}\times\frac{10}{9}=\frac{27}{9}\times\frac{10}{100}=3\times\frac{1}{10}=0.3[/tex]So, the answer will be 0.27 ÷ 0.9 = 0.3
I need help with this practice problem solving Make sure to read the instructions, answer by filling in the three boxes
Solution
[tex](-2\sqrt{3}-2i)^4[/tex]Therefore the correct answer is
The polar form of a complex number
[tex]128\text{ cis }\frac{2\pi}{3}[/tex]The rectangular form of a complex number
[tex]-128+128\sqrt{3}i[/tex]1. If ∠2 measures 120°, what is the measure of ∠1? Explain how you found the measure of ∠1.2. Think of the top and middle shelves as two lines cut by a transversal. What type of angles are ∠1 and ∠5?3. Use the relationship between ∠1 and ∠5 to decide whether the top and middle shelves are parallel.(Needs exterior angles)4. Is the bottom shelf parallel to the top shelf? Explain.5. Is the bottom shelf parallel to the middle shelf? Explain.
1.
The shelves can be assumed to be straight lines, and as straight lines have a 180° angle, then:
[tex]m\angle2+m\angle1=180\degree[/tex]We know the value of m∠2. Thus, we can replace it and solve for m∠1:
[tex]120\degree+m\angle1=180\degree[/tex][tex]m\angle1=180\degree-120\degree[/tex][tex]m\angle1=60\degree[/tex]2.
If we can suppose that the top and middle shelves are cut by a transversal, then ∠1 and ∠5 are corresponding angles.
3.
When two parallel lines are cut by a transversal, they form corresponding angles, and these are equal in measure. Therefore, as:
[tex]m\angle1=m\angle5=60\degree[/tex]Then we can say that the top and middle shelves are parallel.
4.
As m∠11 = m∠2, we can say that they are alternate exterior angles, which are formed when parallel lines are cut by a transversal. Therefore, the bottom shelf is parallel to the top shelf.
5.
Finally, we can see that as m∠11 = 120°, we are in the same situation as in question 1, for which we conclude that m∠9 = 60°. Now, we have the same situation as in question 2, in which m∠5 and m∠9 are corresponding. Thus the bottom shelf is parallel to the middle shelf.
In NOP, PNOP and m2O = 32. Find m P.
Solving Angle Problems.
[tex]PN\cong\text{ OP implies congruency, that is, length PN is the same as length OP.}[/tex]It follows therefore that
[tex]\begin{gathered} \angle NPO=\angle NOP=32^o\ldots.(\operatorname{Re}ason\colon\text{ Base angles of the isosceles triangle)} \\ \text{Hence}, \\ m\angle P=32^o \end{gathered}[/tex]The correct answer is the measure of angle P is 32 degrees
see, I got an answer but my teacher showed us the websites answer and I'm confused.
First let's remember what a Rational number is. A Rational number is that one that can be written in this form (as a fraction):
[tex]\frac{a}{b}[/tex]Where "a" is the numerator and "b" is the denominator.
Integers include negative numbers and, positive numbers and zero. For example, these are Integers:
[tex]4,2,-3,-8[/tex]An Integer is always a Rational number, because it can be written as a fraction with denominator 1:
[tex]\frac{4}{1},\frac{2}{1},\frac{-3}{1},\text{ }\frac{-8}{1}[/tex]Then:
A Rational number that is not an Integer is different from a Rational number that is an Integer, because the first one must be written with a denominator. For example:
[tex]\frac{1}{2}[/tex]but the second one can written showing only the numerator (because it is know that all Integers have denominator 1):
[tex]4=\frac{4}{1}[/tex]Therefore, all Integers are Rational numbers, but a Rational number is not always an Integer.
I need help with my math
SOLUTION:
Step 1:
An adult's ticket costs $11
A child's ticket costs $6
The number of Adult's tickets sold is x
The number of Children's tickets sold is y
The total number of tickets sold is 60
The total amount of sales made is $460
Step 2:
We need to form two equations based on the information given in the question;
[tex]undefined[/tex]The board of directors of a company must have select a president, a secretary and a treasurer in how many possible ways can this be accomplished if there are 22 members on the board
Given
Total number of members = 22
Find
Possible ways of selection of president, a secretary and a treasurer
Explanation
As we know , the number of possible ways of selection is given by
[tex]N=^nP_r[/tex]there are three members required so , r = 3
now , substitute the values in above equation
[tex]\begin{gathered} N=^{22}P_3 \\ N=\frac{22!}{(22-3)!} \\ \\ N=\frac{22!}{19!} \\ \\ N=22\times21\times20 \\ N=9240 \end{gathered}[/tex]Final Answer
Possible ways of selection of president, a secretary and a treasurer = 9240
Find -7/8 - 2 1/6. Write your answer as a mixed number in simplest form.
Answer:
3 1/24
Step-by-step explanation:
In 1960, the world record for the men's mile was 3.91 minutes. In 1980, the record time was 3.81 minutes. a, write the linear model that represents the world record (in minutes) for the men's mile as a function of the number of years, t , since 1960. y=___b, use the model to estimate the record time in 2000 and predict the record time in 2020.2000:___ minutes2020:___ minutes
To first answer this question, we need to find the slope of the linear equation. We have the following information:
x1 = 1960, y1 = 3.91
x2 = 1980, y2 = 3.81
Then
[tex]m=\frac{y_2-y_1}{x_2-x_1}=\frac{3.81-3.91}{1980-1960}=-0.005[/tex]Then, we have that the linear model will be:
[tex]y-y1=m\cdot(x-x1)\Rightarrow y-3.91=-0.005\cdot(x-1960)_{}[/tex]Or
[tex]y=-0.005\cdot(x-1960)+3.91\Rightarrow y=-0.005x+13.71[/tex]This is the linear model.
Then, to use the model to estimate the record time in 2000 and in 2020, we have:
[tex]y=-0.005\cdot(2000)+13.71\Rightarrow y=3.71[/tex]And
[tex]y=-0.005\cdot(2020)+13.71\Rightarrow y=3.61[/tex]Therefore, the linear model is y = -0.005x + 13.71.
The estimation for the record time in 2000 is 3.71 minutes.
The estimation for the record time in 2020 is 3.61 minutes.
This is a linear model.
What is the sum of 7/8 and 11/8
a boat is heading towards a lighthouse, whose beacon light is 117 feet above the water. the boats crew measures the angle of elevation to tye beacon 3. what is the ships horizontal distnace from the lighthouse( and the shore)? round your answer to the nearest hundreth of a foot if necessary.
So,
We could draw the situation of the problem as follows:
We want to find the horizontal distance, which we will call "x".
To find it, we could use the trigonometric ratio: tan(a).
This ratio relations the opposite side of the angle given (a) and its adjacent side. So, we could write:
[tex]\tan (3)=\frac{117}{x}[/tex]Now, if we solve for x:
[tex]x=\frac{117}{\tan (3)}[/tex]This is, x = 2232.49 ft
solve the equation -8y + 8 = 37y - 7
you must first get the variables on the same side of the equal sign. It yields,
[tex]-8y-37y+8=-7[/tex]if we also pass the constant 8 to the right hand side, we have
[tex]-8y-37y=-7-8[/tex]Hence, the left and right hand sides are equal to
[tex]-45y=-15[/tex]hence, we have
[tex]y=\frac{-15}{-45}[/tex]since minus times minus is plus, we obtain
[tex]y=\frac{15}{45}[/tex]and it can be reduced to
[tex]\begin{gathered} y=\frac{15}{15\cdot3} \\ y=\frac{1}{3} \end{gathered}[/tex]Finally, the answer is
[tex]y=\frac{1}{3}[/tex]Answer:
y= 1/3
Step-by-step explanation:
The point (-3, - 5) is on the graph of a function. Which equation must be true regarding the function? A. f(-3) = -5B. f(-3, -5) = -8C. f(-5) = -3D. f(-5, -3) = -2
SOLUTION
The correct option is A
Points with coordinates (x,y) on a graph can also be expressed thus:
[tex]f(x)=y[/tex]So with the above explanation, we can answer the question.
The point (-3,-5) on the graph means that x=-3 and y=-5
So it can be expressed as a function in the form:
[tex]\begin{gathered} f(x)=y \\ x=-3\text{ and y=-5} \\ f(-3)\text{ =-5} \end{gathered}[/tex]The correct option is A
Find the measure of Z CFD.СF5m + 116T3m + 80D
Martina created this box plot to represent the number of inches of snow that fell during the winter in several different cities. Snowfall Summary 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50 Number of inches (a) What was the least amount of snowfall in any of the cities? (b) In which quarter is the data most concentrated? Explain how you know. (c) In which quarter is the data most spread out? Explain how you know.
a)
The minimum happens at the end of the left whisker of the box plot, from the graph we notice that his happens at five. Therefore, the minium amount of snow in any of the cities was 5.
b)
The data is more concenrtated in the second quarter (from the median to the third quartile) this comes from the fact that the length of this part of the block is smaller compared to the second quarter.
c)
The data is more spread out in the second quarter (from the second quartile to the median); this comes from the fact that the length of that part of the box is larger than any other part of the plot
The area of the parallelogram below is square meters. 9 m 7 m 2m
Answer:
63 square meter
Explanation:
Area of the parallelogram = Base * Height
From the given diagram;
Base = 9m
Height = 7m
Area of the parallelogram = 9m * 7m
Area of the parallelogram = 63 square meter