We have the scores: 13, 7, 6, 6, 10, 12, 3, 1, 3.
We have to calculate its mean and standard deviation.
We will start with the mean:
[tex]\begin{gathered} M=\dfrac{1}{n}\sum ^n_{i=1}\, x_i \\ M=\dfrac{1}{9}(13+7+6+6+10+12+3+1+3) \\ M=\dfrac{61}{9} \\ M=6.78 \end{gathered}[/tex]And the standard deviation can be calculated as:
[tex]\begin{gathered} s=\sqrt[]{\dfrac{1}{n-1}\sum ^n_{i=1}\, (x_i-M)^2} \\ \\ s=\sqrt[]{\dfrac{1}{8}((13-6.78)^2+(7-6.78)^2+(6-6.78)^2+(6-6.78)^2+(10-6.78)^2+(12-6.78)^2+(3-6.78)^2+(1-6.78)^2+(3-6.78)^2)} \\ \\ s=\sqrt[]{\dfrac{139.56}{8}} \\ \\ s=\sqrt{17.44}=4.18 \end{gathered}[/tex]The sample mean is 6.78 hits.
The sample standard deviation is 4.18 hits.
Instructions: Use the given information to answer thequestions and interpret key features. Use any method ofgraphing or solving. Round to one decimal place, ifnecessary.The trajectory of a golf ball in a chip from the rough has aparabolic pattern. The height, in feet, of the ball is given bythe equation h(x) = -.25x² + 3.4x, where is thenumber of feet away from the golf club (along the ground)the ball is.The ball startsfeet above the ground.The ball reaches a+feet at a horizontal distance ofthe golf club it was hit with.The ball returns to the ground at aboutaway.height offeet away fromfeet
we have the equation
[tex]h(x)=-0.25x^2+3.4x[/tex]For x=0 -------> h(x)=0
so
The ball starts 0 feet above the ground
The equation represents a vertical parabola open downward
The vertex represents a maximum
Find out the vertex
Using a graphing tool
The vertex is the point (6.8,11.56)
so
The ball reaches a maximum height of 11.6 feet at a horizontal distance of 6.8 feet away from the golf club
The ball returns to the ground at about 13.6 feet away
Find the measure of each missing angle
Answer:
<1 109
<2 71
<3 109
<4 109
<5 71
<6 71
<7 109
Step-by-step explanation:
There are other relationships too
Angles 1 and 2 are supplementary angels. They add to 180.
Angles 1 and 3 are vertical angles they are equal.
Angles 71 and 2 are vertical angles.
If you translate angles 71, 1 ,2 and 3 down the transversal, they will land on 4, 5, 6,7. There are corresponding angels. Corresponding angles are equal.
Answer:
m<1= 109 degrees
m<2= 71 degrees
m<3= 109 degrees
m<4= 109 degrees
m<5= 71 degrees
m<6= 71 degrees
m<7= 109 degrees
Step-by-step explanation:
To find the measure of <1, you take 180 degrees (which is the degree of a straight line) minus 71. This is because you are trying to find what other number needs to be added to make the whole 180 degree line.
To find the measure of <2, opposite angles equal the same. This is also how you find m<3, m<6, and m<7.
The rest are hard to explain so look up "alternate interior angles" if you are interested.
Find the number of ways to arrange the letters in REPRESENT.
Solution
The Number of ways to arrange the letters in REPRESENT.
We count the number of the letters in REPRESENT
It is 9
We count the number of the repeated letters in REPRESENT
We have 3E and 2R
[tex]\begin{gathered} \text{The number of ways to arrange the letters in REPRESENT} \\ =\frac{9!}{3!2!} \\ =\frac{362880}{6\times2} \\ =\frac{362880}{12} \\ =30240\text{ ways} \end{gathered}[/tex]The number of ways to arrange the letters in REPRESENT is 30240ways
SCC Library150545866707462Test ScoresUse the Empirical Rule to answer the following questions.a. The mean isb. The standard deviation is% of the test scores are between 58 and 66.d.% of the test scores are between 54 and 70e.% of the test scores are between 50 and 74.f.% of the test scores are between 62 and 66.9.% of the test scores are less than 62h.% of the test scores are less than 66.Check Answer
a. Mean = (50+54+58+66+70+74+62)/ 7 = 62
b. Standard deviation is
c. Between 58 and 66 , are 68.3%
d. Between 54 and 70, are 34%
e. Between 62 and 66, Is 34%
f.
Is the statement true or false?The points (2,5) and (0,0) lie on the graph of 4x – 3y = 0.Is the statement true or false?O TrueO False
Given the points (2, 5) and (0, 0)
To determine if the points lie on the graph of
[tex]4x-3y=0[/tex]For point (2, 5)
Where x = 2
[tex]\begin{gathered} 4x-3y=0 \\ 4(2)-3y=0 \\ 8-3y=0 \\ 3y=8 \\ \text{Divide both sides by 3} \\ \frac{3y}{3}=\frac{8}{3} \\ y=2\frac{2}{3} \end{gathered}[/tex]Where y = 5
[tex]\begin{gathered} 4x-3y=0 \\ 4x-3(5)=0 \\ 4x-15=0 \\ 4x=15 \\ \text{Divide both sides by 4} \\ \frac{4x}{4}=\frac{15}{4} \\ x=3\frac{3}{4} \end{gathered}[/tex]From the deduction, point (2, 5) doesn't lie on the graph of 4x-3y=0
For point (0, 0)
Where x = 0
[tex]\begin{gathered} 4x-3y=0 \\ 4(x)-3y=0 \\ -3y=0 \\ y=0 \end{gathered}[/tex]Where y = 0
[tex]\begin{gathered} 4x-3y=0 \\ 4x-3(0)=0 \\ 4x=0 \\ x=0 \end{gathered}[/tex]From the deduction, point (0, 0) lie on the graph of 4x-3y=0
Since, only one of the points (0, 0) lie on the graph,
Hence, the statement is false.
Please Hurry). Cora is using successive approximations to estimate a positive solution to f (x) = g (x), where f (x) = x^2 + 13 and g (x) =3x + 14. The table shows her results for different input values of x.
First, we use the given functions to solve the equation f(x) = g(x)
[tex]x^2+13=3x+14[/tex]Now, we move all the terms to the left side
[tex]\begin{gathered} x^2-3x+13-14=0 \\ x^2-3x-1=0 \end{gathered}[/tex]Then, we use the quadratic formula
[tex]x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}[/tex]Where a = 1, b = -3, and c = -1.
[tex]\begin{gathered} x=\frac{-(-3)\pm\sqrt[]{(-3)^2-4\cdot(1)(-1)}}{2\cdot1} \\ x=\frac{3\pm\sqrt[]{9+4}}{2}=\frac{3\pm\sqrt[]{13}}{2} \\ x_1=\frac{3+\sqrt[]{13}}{2}\approx3.3 \\ x_2=\frac{3-\sqrt[]{13}}{2}\approx-0.3 \end{gathered}[/tex]Hence, the positive solution is 3.32. To break the school's record, the boys' time had to be faster than 2,2 1 / 2minutes. Estimate to decide if the boys broke the record. If so, howmuch faster were they? If not, how much slower were they? I only need question 2 answered
2) We would add the times of each boy. We have
2/3 + 11/12 + 5/6 + 7/12
The lowest common multiple of the denominator is 12. We would divide each denominator by 12 and multiply the numerator by the result. It becomes
(2*4 + 11*1 + 5*2 + 7*1)/12
= (8 + 11 + 10 + 7)/12
= 36/12
= 3 minutes
Since 3 is greater than 2 7/12, it means that the boys broke the record. The difference between the times is
3 - 2 7/12
Changeing 2 7/12 to improper fraction, it becomes 31/12
Difference = 3 - 31/12 = (3 * 12 - 31)/12 = (36 - 31)/12
Difference = 5/12
The boys were faster with 5/12 minute
does x+2y=2(y-4)+2 represent a function?
x+2y=2(y-4)+2 doesnot represent a function
Explanation:[tex]\begin{gathered} \text{Given:} \\ x+2y=2\mleft(y-4\mright)+2 \end{gathered}[/tex]To determine if it is a function, first we need to simplify the equation:
[tex]\begin{gathered} x\text{ + 2y = 2y - 8 + 2} \\ \text{collect like terms:} \\ x\text{ + 2y - 2y = -8 + 2} \\ x\text{ = -6} \\ \end{gathered}[/tex]For a relation, to be a function, each of its input must have only one output
For x = -6, this gives a vertical line.
This shows that irrespective of the value of y, the x coordinate will remain the same.
Each input of x = -6, has more than one y values as the y values changes but the x value remains the same.
As a result, the given relation is not a function
An automobile company is running a new television commercial in five cities with approximately the same population the following table shows the number of items the commercial is run on TV in each city and the number of car sales in hundreds find a linear Regression line for the data given in the table round any intermediate calculations to know less than six decimal places and round the coefficients to two decimal places
Using a linear regression calculator
The linear equation is given by
y=0.38x+1.29You have found the following ages (in years) of 5 zebras. Thosezebras were randomly selected from the 42 zebras at your localZOO:8, 11, 17,17, 7, 19Based on your sample, what is the average age of the zebras?What is the standard deviation? Round your answers to thenearest tenth.Average age:Get 3 of 4 questions to level up to FamiliarО о оCheck
We will have the following:
First, we will have that the apparent mean is:
[tex]\begin{gathered} x=\frac{8+11+17+17+7+19}{6}\Rightarrow x=\frac{79}{6} \\ \\ \Rightarrow x\approx13.2 \end{gathered}[/tex]Now, we calculate the standard deviation:
[tex]\begin{gathered} s=\sqrt{\frac{1}{N-1}\sum_{i=1}(x_i-x)^2} \\ \\ \Rightarrow s=\sqrt{\frac{1}{6-1}\sum(x_i-\frac{79}{6})^2}\Rightarrow s\approx5.2 \end{gathered}[/tex]So, the standard deviation is approximately 5.2.
The table below shows how many millilitres are on different numbers of liters Mark all of the true statements
the only true statement is
in 4 liters there are 4000 milliliters
What is the complementary And supplementary angle of 76 degree
Two complementary angles add up to 90 degrees.
Two supplementary angles add up to 180 degrees.
• To find the complement of an angle A, we subtract A from 90, or
90 - A• To find the supplement of an angle B, we subtract B from 180, or
180 - BNow,
We are given the angle 76°.
Let's use the formula/rule to find the complement and supplement of this angle.
The complement of 76°:[tex]\begin{gathered} 90-76 \\ =14\degree \end{gathered}[/tex]The supplement of 76°:[tex]\begin{gathered} 180-76 \\ =104\degree \end{gathered}[/tex]The length of a rectangle is 3 times its width. The perimeter of the rectangle is 80 cm. Use the equat Type your answer Previous
Given data:
The expression for length is L= 3b.
The perimeter of the rectangle is P = 80 cm.
The expression for the perimeter is,
[tex]P=2(L+b)[/tex]Substitute the given values in the above expression.
[tex]\begin{gathered} 80\text{ cm =2(3b+b)} \\ 80\text{ cm=8b} \\ b=10\text{ cm} \end{gathered}[/tex]The length of the rectangle is,
[tex]\begin{gathered} L=3(10\text{ cm)} \\ =30\text{ cm} \end{gathered}[/tex]Thus, the length of the rectangle is 30 cm, and width of the rectangle is 10 cm.
the graph of linear function g passes through the points (-7, -4) and (7, 6) as shownwhat are the slope and y-intercept of the graph of g? A) the slope is 5/7 and the y-intercept is -1B) the slope is 5/7 and the y-intercept is 1C) the slope is 7/5 and the y-intercept is -1 D the slope is 7/5 and the y-intercept is 1
To find the slope of the graph, we have to use the following formula:
[tex]m=\frac{y2-y1}{x2-x1}[/tex]Replace for the given coordinates:
[tex]m=\frac{6-(-4)}{7-(-7)}=\frac{10}{14}=\frac{5}{7}[/tex]When looking at the graph we can observe that the y intercept is 1.
It means that the answer is B) the slope is 5/7 and the y-intercept is 1.
Describe in words how the two quantities in each table are related.Table ATable BTable CTable D
0. Proportional Relationship: ,the number of laps is 400 times the number of meters
,1. Inversely Relationship ,as the number of meters from home ,increases ,the number of meters from school ,decreases
,2. The total expense in dollars is ,$400 more ,than the electricity bill.
,3. Each worker deposits ,$400, from their monthly salary.
Table A)
Let's pick two points and see how they are related. Namely: (0,0) and (1,400).
Notice that since the initial point is at the origin (0,0) we can state that this is a proportional relationship.
As the number of laps increases, the number of meters increases.
Table B)
Note that as the meters from home increases the meters from school decrease, so we have an inversely proportional relationship.
[tex]m=\frac{325-400}{75-0}=-1[/tex]Table C)
For this one as the electricity bills increase its cost, the total expenses in dollars increase as well:
[tex]\begin{gathered} m=\frac{524-485}{124-85}=1 \\ 485=1(85)+b \\ b=400 \end{gathered}[/tex]Note that the slope is 1, and the linear coefficient is 400 each time that there is an increase in the electricity bill the total expenses increase by $400
(85, 485), (124,524)
Table D)
Let's pick two points to find the slope, and the function to find out the relationship between those quantities:
[tex]\begin{gathered} m=\frac{598-472}{998-872}=1 \\ 472=1(872)+b \\ b=-400 \end{gathered}[/tex]So we can say that each worker deposits $400 from his salary.
3) Hence, the answers are:
0. Proportional Relationship: ,the number of laps is 400 times the number of meters
,1. Inversely Relationship ,as the number of meters from home ,increases ,the number of meters from school ,decreases
,2. The total expense in dollars is ,$400 more ,than the electricity bill.
,3. Each worker deposits ,$400, from their monthly salary.
last Keith week had $15 he washed cars over the weekend and now has $93 how much money did he make washing cars
Money Keith made from washing cars
= $93 - $15
= $78
There are seven nickels and five dimes in your pocket. Three times, you randomly pick a coin out of your pocket, return it to your pocket, and then mix-up the change in your pocket. All three times, the coin is a nickel. Find the probability of this occuring.A. 343/1728B. 1/8C. 25/546D. 1/22
The probability of an event happening is the ratio of the number of ways it can happen to the total number of outcomes.
The total number of coins is:
[tex]\begin{gathered} 7+5 \\ =12 \end{gathered}[/tex]Hence, the total number of outcomes is 12.
The number of nickels is 7. Hence, the number of possible outcomes is 7.
It follows that the probability of picking a nickel each time, since the coin is always returned is:
[tex]P(\text{nickel)}=\frac{7}{12}[/tex]Since each of the events (all three), does not depend on one another, it follows that they are independent and hence, the probability of all three occurring is the product of their probabilities:
[tex]\begin{gathered} \frac{7}{12}\times\frac{7}{12}\times\frac{7}{12} \\ =\frac{343}{1728} \end{gathered}[/tex]Hence, the correct option is option A.
Compute each sum below. If applicable, write your answer as a fraction.3 + 3(−3) + 3(−3)² + . . . + 3(-3)° = □Σ (3) - 0i = 1X
Part 1
we have the expression
[tex]\begin{gathered} 3+3(-3)+3(-3)^2+3(-3)^3+3(-3)^4+3(-3)^5+3(-3)^6 \\ 3-9+27-81+243-729+2,187 \\ 1,641 \end{gathered}[/tex]The answer Part 1 is 1,641Part 2
we have the expression
[tex]\begin{gathered} \sum_{i=1}^9(\frac{1}{4})^i=\frac{1}{4}+\frac{1}{4^2}+\frac{1}{4^3}+\frac{1}{4^4}+\frac{1}{4^5}+\frac{1}{4^6}+\frac{1}{4^7}+\frac{1}{4^8}+\frac{1}{4^9} \\ \\ =\frac{65,536+16,384+4,096+1,024+256+64+16+4+1}{262,144} \\ \\ =\frac{87,381}{262,144} \end{gathered}[/tex]The answer Part 2 is 87,381/262,144A chess club with 80 members is electing a new president. Rafael received 15 votes. What percentage of the club members voted for Rafael?
The percentage of the club members that voted for Rafael is 18.75%.
How to calculate the percentage?From the information given, it was stated that the
chess club with 80 members is electing a new president and Rafael received 15 votes.
The percentage that was voted by Rafael will be:
= Number of people that voted for Rafael / Number of members × 100
= 15 / 80 × 100
= 18.75%
The percentage is 18.75%.
Learn more about percentages on:
brainly.com/question/24304697
#SPJ1
4. Consider the following information about a group of 143 FCC students: Gender Right-handed Left-handed Total Female 63 15 78 Male 51 14 65 Total 114 29 143 If one person is randomly selected from the group, what is the probability that this student is female or left-handed?
Answer
The Probability that this student is female or left-handed is
[tex]\frac{92}{143}[/tex]Given
Total = 143
Total female = 78F
Total left handed =29
Female and left-handed =15
[tex]P(\text{female or left-handed)=}P(f)+P(L)-P(F\text{ and L)}[/tex][tex]\begin{gathered} P(f\text{ or L)=}\frac{78}{143}+\frac{29}{143}-\frac{15}{143} \\ P(\text{f or L )= }\frac{92}{143} \end{gathered}[/tex]If G is the incenter of ABC, find each measure.
3x + 4 = 5x - 8
collect like term
5x - 3x = 4 + 8
2x = 12
Divide both-side of the equation by 2
x = 6
substitute x=6 in the above
=[ 18 + 4 ] + [ 30 - 8]
= 22 + 22
= 44
m< ABC = 44°
m
m< ABC = 44°
We will find m
44° + 28° + m
m
= 108°
m = 1/2 of m
= 108°/2 =54°Therefore;m< ABC = 44°m =54°What is the radius, in centimeters, of a circle that has a circumference of 18 1/2
Circumference = 2πr
where c is the circumference and r is the radius
π = 22/7
[tex]18\text{ 1/2= 2}\times\frac{22}{7}\times r[/tex][tex]\frac{37}{2}=\frac{44r}{7}[/tex]cross-multiply
[tex]259=88r[/tex]Divide both-side by 88
r= 2.94 cm
What are the coordinates of the terminal determined by t = 20 3
As per given by the question,
There are given that the terminal point,
[tex]t=\frac{20\pi}{3}[/tex]Now,
To find the terminal point, there are use the refrence point,
[tex]t=\frac{2\pi}{3}[/tex]That means,
The given angle is equivalent to the angle ,
[tex]t=\frac{2\pi}{3}[/tex]Now,
According to the terminal point concept,
The radius of the unit circle at that point makes a right angle with the coordinates of the terminal point and,
There is also noted that the given terminal is on the 2nd quadrant of the cpordinate axis.
So,
The x value of the terminal point is negative and y value is positive.
Then,
There is use the relation,
[tex]-\cos (\pi-\frac{2\pi}{3})=\frac{x}{1}[/tex]Because the radius of the uit circle is 1.
Now,
[tex]\begin{gathered} -\cos (\pi-\frac{2\pi}{3})=\frac{x}{1} \\ -\text{cos(}\frac{\pi}{3})=x \\ x=-\frac{1}{2} \end{gathered}[/tex]Then,
Similarly to find the y-coordinate.
So,
Here, find the y-coordinate to relate the sine trigonometric function.
[tex]\begin{gathered} \sin (\pi-\frac{2\pi}{3})=\frac{y}{1} \\ \sin (\frac{\pi}{3})=y \\ y=\frac{\sqrt[]{3}}{2} \end{gathered}[/tex]The coordinate of the terminal point is,
[tex](x,\text{ y)=(-}\frac{1}{2},\text{ }\frac{\sqrt[]{3}}{2})[/tex]Hence, the option A is correct.
What are pairs of coplanar lines, I'm confused on how to find them
Coplanar is the line lieing in the same plane. We have two plane which are M and Q. AC and BE are coplanar pair of lines .
Suppose that your income is $33,900 per year and you receive a cost-of-living raise each year. If inflation is constant at 9.5% annually, in how many years will you bemaking $44,300 per year? Round your answer to the nearest whole number.
We can interpret this as a compounded interest. Remember that its formula is:
[tex]T=P(1+r)^n[/tex]Where:
• T, is the total amount after the investment. In this case, after the raise
,• P, is the principal. In this case, the intial salary
,• r, is the interest rate. In this case, the raise percentage
,• n, is the times the interest is compounded. In this case, the times the raise is compounded.
Using this and the data given, we'll have the following equations:
[tex]44300=33900(1+\frac{9.5}{100})^n[/tex]Solving for n,
[tex]undefined[/tex]mount Whitney is 3072m tall convert to kilometers
We have that 1000m are equivalent to 1km.
From this, we have that in order to find the equivalenci in km for 3072m we will divide 3072 by 1000:
[tex]\frac{3072}{1000}=3.072[/tex]From this, we have mount Whitney is 3.072 Km tall.
A polling firm wants to predict the success of a grocery store, and conducts surveys of randomly selected residents. The residents are asked whether they will shop for produce at the grocery store. The results are shown in the table. The actual percent of residents who will shop for produce at the grocery store is expected to be furthest away from which number?1)37.5%2)50.0%3)61.9%4)56.0%
The smaller the sample size, the greater the uncertainty in our estimate.
From the options, 37.5% is obtained from the smallest sample size (8) and thus the percent is expected to be furthest away from this value.
Answer: 37.5%.
The solids are similar. Find the volume V of the red solid. 7 mm 7 mm Volume 5292 mm
First we notice that the red solid is obtained by dividing by 3 the dimensions of the blue one.
Now we need to find the height of the blue solid to obtain the height of the red one. To do this we first need to remember that the volume of a pyramid is given by:
[tex]V=\frac{1}{3}Bh[/tex]where B is the area of the base, the are of the base of the blue solid is 21*21 (since it is a square). Plugging this value and the volume given we have:
[tex]5292=\frac{1}{3}(21^2)h[/tex]solving for h we have:
[tex]\begin{gathered} 5292=\frac{1}{3}(21^2)h \\ h=\frac{3\cdot5292}{21^2} \\ h=36 \end{gathered}[/tex]hence the height of the blue solid is 36 mm.
Now that we have the height of the blue solid we divide by 3 to find the height of the red one, then the height of the second pyramid is 12 mm.
Now that we have all the measurements we plug them in the formula for the volume:
[tex]\begin{gathered} V=\frac{1}{3}(7^2)(12) \\ =196 \end{gathered}[/tex]Therefore the volume of the red solid is 196 cubic milimeters.
what is the explicit formula of the geometric sequence?2, -8, 32, -128,...
EXPLANATION
Geometric Progression:
A geometric sequence has a constant ratio r and is defined by:
[tex]a_n=a_0\cdot r^{n-1}[/tex]Check wheter the ratio is constant: r=-4
2, -8 , 32, -128
Compute the ratios of all the adjacent terms:
-8/2= -4, 32/-8=-4, -128/32=-4
The ratio of all the adjacent terms is the same and equal to:
r=-4
The first element of the sequence is:
a_1=2
[tex]a_n=a_1\cdot r^{n-1}[/tex]Therefore, the nth term is computed by
r=-4,
[tex]a_n=2(-4)^{n-1}[/tex]18Pretest: Linear RelationshipsSelect the correct answer.Consider the graph of fx) given below.yf(x)2+612+-4--6-The function g(x) is a transformation of fx). If g(x) has a v-intercept at 3 which of the followingaNot64-2Not2xSubmit Te
Given the graphed function:
f(x)
The function g(x) is a transformation of the graphed function f(x). If g(x) has a y-intercept at 3, let's find the function which could represent g(x).
Using the graph, the function f(x) has a t-intercept at:
y = -1
Since g(x) is the transformation of f(x) and has a y-intercept of 3, it means there was a vertical translation from f(x) to g(x).
Now, let's find the units:
3 - (-1) = 3 + 1 = 4
This means there was a vertical translation 4 units upwards of the function f(x) to get the function g(x).
Now, apply the transformation rule for functions.
After a vertical translation 4 units upwards of f(x), the function g(x) will be:
g(x) = f(x) + 4
Therefore, the function which could represent g(x) is:
g(x) = f(x) + 4
ANSWER:
B. g(x) = f(x) + 4
