The median is defined as the sum of all the values divided by the total number of data, then in this case:
[tex]\begin{gathered} \mu=\frac{98+98+90+82+89+87}{6} \\ \mu=\frac{544}{6} \\ \mu=90.7 \end{gathered}[/tex]To find the median we need to order the data:
[tex]82,\text{ 87, 89, 90, 98, 98}[/tex]The median is the number that divides all the data in half, since we have an even number of data we need to take the mean between the middle data, that is, the median is:
[tex]\frac{89+90}{2}=89.5[/tex]The mode is the number that repeats itself more on the data set, then in this case we the mode is 98.
The range is the difference between the lowest and highest data, then:
[tex]98-82=16[/tex]Summing up we have:
mean: 90.7
median: 89.5
mode: 98
Range: 16
If the measures of two pair of complementary angles are added together then the sum is equal to the measures of two right anglestrue or false
ANSWER : FALSE
EXPLANATION : The sum of two complementary angles is 90°. Adding the measure of two right angles (right angles is a 90° angle) is equal to 180°.
Therefore, adding the two pairs of complementary angles is not equal to the sum of two right angles.
Hello please help I don’t know what I’m doing wrong
Explanation:
The domain of a function is the input value of any function for which the function exists.
For the function;
(f+g)(x) = 2x² + x
From the given function, we can see that the function will exist for all values of x i.e. the input variable exists on all real values.
The domain of the function in interval notation will be expressed as
(-∞, ∞)
For the function (f-g)(x) = x
Similarly for this function, the input variable exists on all real values.
The domain of the function in interval notation will be expressed as
(-∞, ∞)
For the function (fg)(x) =x^4 + x^3
Also for this function, the input variable exists on all real values.
The domain of the function in interval notation will be expressed as
(-∞, ∞)
For the function given as (f/g)(x) = 1 + 1/x
The function will not exist when x = 0. The function will be undefined at this point. The required domain of this function in interval notation will be:
[tex]D=(-\infty,0)U(0,\infty)[/tex]
Question 6 of 13Use a calculator to find the correlation coefficient of the data set.X13LO5y2014106916 4
Given
The data,
[tex][/tex]Use the Change-of-Base Formula and a calculator to evaluate the logarithm. Round your answer to three decimal places.
In order to solve this problem, we need to change the base of the logarithm function so we can use the calculator to solve it. One possible way to do it is by writing it in base 10.
We have:
[tex]\log _ba=\frac{\log _{10}a}{\log _{10}b}[/tex]In this problem, we have:
a = 47
b = 8.1
So, we can write
[tex]\log _{8.1}47=\frac{\log _{10}47}{\log _{10}8.1}[/tex]Now, using a calculator, we obtain:
[tex]\frac{\log_{10}47}{\log_{10}8.1}\cong1.841[/tex]Therefore, the last option is correct.
Assignment 10-1 A Triangle ABC = Triangle S B U
we know that
If two triangles are congruent, then its corresponding sides and corresponding angles are congruent
Remember that
Corresponding sides are named using pairs of letters in the same position on either side of the congruence statement
so
In this problem
ST=AB
SU=AC
UT=CB
therefore
Triangle
ABC=STUSelect the correct mapping of function f(x) to g(x), that represents a translation of 2 units to the right, and a horizontal compression of a factor of 3.
Given:
Translation of 2 units to the right.
A horizontal compression of a factor of 3.
[tex]f(x)=x^2\rightarrow g(x)=3(x-2)^2[/tex]Your employer promises after 6 months to give you a 15% pay raise in addition to your new pay. How much will your monthly income be after the 15% pay increase?
Lets assume that the actual pay is the 100%, if after 6 months you get a rais of 15% in addition of your new pay, then the monthly income after the raise will be the 115% of the actual pay
In a circle v, UTw =50 solve for X . If mUW= (9x-34)
Answer:
X=14.9
Step-by-step explanation:
mUW=2 . m <utw
so (9x - 34) = 2.50
9x - 34 = 100
x = 14.9
If v, = (2,4) and v2 = (-1,5), then w,-V is equal to which of the following?O 18O (-2. 20)O 22O (8.-5)
We are given the following matrix:
[tex]A=\begin{bmatrix}{4} & {-7} & {} \\ {-2} & {1} & {} \\ {} & {} & {}\end{bmatrix}[/tex]We are asked to determine the coefficients of:
[tex]A^{-1}[/tex]Which is the inverse matrix. To do that let's remember that the inverse of a 2 by 2 matrix of the form:
[tex]A=\begin{bmatrix}{a_1} & {a_2} & {} \\ {a_3} & {a_4} & {} \\ {} & {} & {}\end{bmatrix}[/tex]is:
[tex]A^{-1}=\frac{1}{\det A}\begin{bmatrix}{a_4} & {-a_2} & {} \\ {-a_3} & {a_1} & {} \\ {} & {} & {}\end{bmatrix}[/tex]The value of the determinant of A (det A) is given by:
[tex]\det A=a_1a_4-a_2a_3[/tex]Replacing we get:
[tex]A^{-1}=\frac{1}{a_1a_4-a_2a_3}\begin{bmatrix}{a_4} & {-a_2} & {} \\ {-a_3} & {a_1} & {} \\ {} & {} & {}\end{bmatrix}[/tex]Replacing the values:
[tex]A^{-1}=\frac{1}{(4)(1)-(-7)(-2)}\begin{bmatrix}{1_{}} & {7_{}} & {} \\ {2_{}} & {4_{}} & {} \\ {} & {} & {}\end{bmatrix}[/tex]Solving the operations:
[tex]A^{-1}=-\frac{1}{10}\begin{bmatrix}{1_{}} & {7_{}} & {} \\ {2_{}} & {4_{}} & {} \\ {} & {} & {}\end{bmatrix}[/tex]Or:
[tex]A^{-1}=\begin{bmatrix}{-\frac{1}{10}_{}} & {-\frac{7}{10}_{}} & {} \\ -{\frac{1}{5}_{}} & {-\frac{2}{5}_{}} & {} \\ {} & {} & {}\end{bmatrix}[/tex]Therefore, we have:
[tex]\begin{gathered} a=-\frac{1}{10} \\ b=-\frac{7}{10} \\ c=-\frac{1}{5} \\ d=-\frac{2}{5} \end{gathered}[/tex]Find the distance between the pair of points below to the nearest tenth, if necessary (-2,3), (6,9)
We can find the distance between the points by means of the distance formula:
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]where
[tex]\begin{gathered} (x_1,y_1)=(-2,3) \\ (x_2,y_2)=(6,9) \end{gathered}[/tex]By substituting these values into the distance formula, we have
[tex]d=\sqrt{(6-(-2))^2+(9-3)^2}[/tex]which gives
[tex]\begin{gathered} d=\sqrt{(6+2)^2+6^2} \\ d=\sqrt{8^2+36} \\ d=\sqrt{64+36} \end{gathered}[/tex]so we have
[tex]\begin{gathered} d=\sqrt{100} \\ d=10 \end{gathered}[/tex]Therefore, the distance between the two points is 10 units.
The coach is building shelves to store and organize the team’s collection of 175 game videos how many shelves will be needed if one shelf holds 28 videos?
7 shelves will need to store and organize the team's collection of 175 game videos.
Given:
The team’s collection of 175 game videos.
one shelf holds 28 videos.
Number of shelves = total videos/one shelf hold capacity.
= 175/28
= 6.25
since we cannot have 0.25 shelf we take it as 1.
So number of selves = 7 shelves.
Therefore 7 shelves will need to store and organize the team's collection of 175 game videos.
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a midwestern music competition awarded 40 ribbons. the number of blue ribbons awarded was 2 less than the number of white ribbons. the number of red ribbons was 3 more than the number of white ribbons. how many of each kind of ribbon was awarded
By the concept of basic equation there are 13 white ribbons, 11 blue ribbons and 16 red ribbons.
What are basic equation?When two expressions are connected with the equals sign (=) in a mathematical formula, it expresses the equality of the two expressions. An equation is an algebraic statement that demonstrates two mathematical expressions are equivalent in algebra, and this is how it is most usually used. In the equation 3x + 5 = 14, for instance, the two expressions 3x + 5 and 14 are separated by the symbol "equal." When two expressions are joined by an equal sign, a mathematical statement is called an equation. An equation is something like 3x - 5 = 16. By solving for x, we discover that x equals 7, which is the value for the variable.
r + w + b = 40
b = w - 2
r = w + 3
now we sub
(w + 3) + w + (w - 2) = 40
3w + 1 = 40
3w = 40 - 1
3w = 39
w = 39/3
w = 13
<=== 13 white ribbons
b = w - 2
13 - 2 = 11
<=== 11 blue ribbons
r = w + 3.
13 + 3 = 16
<=== 16 red ribbons
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Mantinum What is 92,119 rounded to the nearest thousand?
We will have that 92,119 rounded to the nearest thousand is:
[tex]92,119[/tex]This is since there are not smaller decimals on the number to be able to round it.
Place the numbers in order fromgreatest to least27, 62%, -0.062,65,0.
Answer
Explanation
To arrange this numbers in the required order, we need to simplify each of them and then compare them.
√3 = 1.732
172% = (172/100) = 1.72
-1.7 = -1.7
1 7/10 = 1 + 0.7 = 1.7
-0.7 = -0.7simplify each of them and then compare them.
So basically I have to reflect triangle STU across line ST and I need to find a valid reason of why the image of U will coincide with J. I need guidance please
Solution
- The reflection of an object across a line implies that the distance between the object and the reflection line is the same as the distance between the image and the reflection line.
- This implies that if the distance between the point U and the reflection line ST is x, then, the distance between the reflection line and the image of U must be a distance of x as well.
- This is illustrated below:
- From the above, we can see that distance x is a perpendicular distance from point U to reflection line ST.
- However, we must not just assume that distance x lands at point J.
- We can however show that this is the case because of the SSS congruency. That is,
[tex]\begin{gathered} SU\cong SJ\text{ \lparen Given in the question\rparen} \\ UT\cong TJ\text{ \lparen Given in the question\rparen} \\ ST\text{ is a common side for both triangles SUT and SJT} \end{gathered}[/tex]- Since both triangles are congruent, we can proceed to conclude that from line ST to point J is also a distance of x.
- Therefore, the image of U will coincide with J given that ST is the reflection line
A Little League baseball diamond has four bases forming a square whose sides measure 60 feet each. The pitcher's mound is 46 feet from home plate on a line joining home plate and second base. Find the distance from the pitcher's mound to third base. Round to the nearest tenth of a foot.
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data
Square
side = 60 feet
pitcher's mound from home plate = 46 feet
distance from the pitcher's mound to third base = ?
Step 02:
Diagram:
Step 03:
distance from the pitcher's mound to third base
side 1 = 60
side 2 = 46
angle 1 = 90 / 2 = 45
a ² = b ² + c ² - 2 * b * c* Cos A
a ² = 60² + 46² - 2(60)(46) Cos 45
a² = 1812.771
a = √1812.771
a = 42.576
The answer is:
The distance from the pitcher's mound to third base is 42.6 feet.
Can I please just get the answer I’m trying to get this class done before the 10th……
Given:
The batting averages are given in stemplot way.
The objective is to determine what batting average does 0.35│6 denotes.
Explanation:
In stemplot method, the stem represents all common digits other than one place value in the given set of data. The leaf represents the variation of once place for the respective stem data.
Then the given expression 0.35│6 represents the stem value as 0.35 and 6 as the leaf value.
Thus. one occurence of batting average is 0.356.
Hence, option (B) is the correct answer.
Mr mustard bought a bag of citrus tree fertilizer. He used 1/5 of the bag for his orange tree and 2/3 of the bag for his lemon tree. About how much of the fertilizer does he have left?A. 0.5 B. 0.8 C. 0 D. 0.1
Problem
Mr mustard bought a bag of citrus tree fertilizer. He used 1/5 of the bag for his orange tree and 2/3 of the bag for his lemon tree. About how much of the fertilizer does he have left?
Solution
For this problem we know that the total bag represent 1 and since he used 1/5 for the orange tree and 2/3 for the lemon tree we can do the following operation to find the remaining space:
[tex]1-\frac{1}{5}-\frac{2}{3}[/tex]And after solve the operation we got:
[tex]\frac{4}{5}-\frac{2}{3}=\frac{2}{15}[/tex]And if we convert to decimals we got 2/15= 0.133
Then the best approximation for this case would be:
D. 0.1
12) Determine if the number is rational (R) or irrational (I)
Given
[tex]number=\sqrt{17}[/tex]Find
Determine if the number is rational or irrational.
Explanation
It cannot be expressed in the form of p/q , where q is not equal to 0.
so , it is irrational number.
Final Answer
Therefore , the number is irrational.
I need help with number 5. Here is the problem:Injured runners train on a special track at a rehabilitation center. The track is a square with a half circle on its left and right sides. The area of the square is 128 square feet. What is the length of the track? Use the table to help you answer the questions.
To have a pictorial representation of this problem (the track), we will have the figure below:
To find the length of the track, we will sum up the length of two sides of the square and the circumference of the two half semicircles.
We will find the length of the square thus:
[tex]\begin{gathered} A=l^2 \\ 128=l^2 \\ \sqrt[]{128}=l \\ 11.314ft=l \\ \text{Each side of the square is 11.314ft} \end{gathered}[/tex]Now we will find the circumference of a half-circle:
[tex]=\frac{\pi D}{2}[/tex]Since the length of the square is also the diameter of the half circle:
[tex]\begin{gathered} D=l=11.314 \\ \text{Circumference of half-circle:} \\ =\frac{\pi(11.314)}{2} \\ =17.772ft \end{gathered}[/tex]The length of the track will be calculated with this expression:
[tex]=\text{length of two sides of the square + circumference of two half-circles}[/tex][tex]\begin{gathered} =2(11.312ft)+2(17.772ft) \\ =22.624ft+35.544ft \\ =58.168ft \\ \text{The length of the track is 58.168ft} \end{gathered}[/tex]I am trying to place the second point at 12.5. My graph only extend to -10.
We have to graph the line y = -2/5*x-5.
To do that, we need two points that belong to the line.
We can give two arbitrary values to x and calculate y using the equation of the line.
For example, for x=0, we get:
[tex]x=0\Rightarrow y(0)=-\frac{2}{5}\cdot0-5=-5[/tex]Then, the point is (0,-5).
Now, if we make x = 5, we can calculate y as:
[tex]x=5\Rightarrow y(5)=-\frac{2}{5}\cdot5-5=-2-5=-7[/tex]Then, we get the point (5, -7).
Using this two points we can graph the line as:
NOTE: In the case that the graph is limited to certain intervals in x or y, we have to try with different values of x until we find two points within the range shown by the graph.
In this case, (0,-5) and (5,-7) will be located within the range shown.
3. Brust is riding his bicycle north away from an intersection at a rate of 15 miles per hour. Sully is driving his car towards the intersection from the west at a rate of 30 miles per hour. If Brust is 0.4 miles from the intersection, and Sully is 1 mile from the intersection, at what rate is the distance between the two of them increasing or decreasing?
The graph shows the situation of Brust and Sully. The distance between them is d
If x is the distance from Sully to the intersection and y is the distance from Brust to the intersection, the distance d is
[tex]d=\sqrt[]{x^2+y^2}[/tex]The rate of change of d in time is computed by taking the derivative:
[tex]d^{\prime}=\frac{xx^{\prime}+yy^{\prime}\text{ }}{\sqrt[]{x^2+y^2}}[/tex]We have the following parameters:
x=1, y=0.4, x'=-30, y'=15
Substituting:
[tex]d^{\prime}=\frac{(1)(-30)+(0.4)(15)\text{ }}{\sqrt[]{1^2+0.4^2}}[/tex]d' = -22.3 miles per hour
Since d' is negative, the distance is decreasing
Need help with number 2 not sure how to solve it all
B(x) will be given by:
[tex]B(x)=100x-5[/tex]Part 1:
x = 9
[tex]B(9)=100(9)-5=900-5=895[/tex]Part 2:
x = 10.34
[tex]B(10.34)=100(10.34)-5=1034-5=1029[/tex]Part 3:
[tex]B(9)+B(10.34)=895+1029=1924[/tex]Question 25 of 27Which of the following is an example of independent events?OA. Rolling a 6 on a number cube and spinning a 7 on a spinnerB. Drawing a jack from a standard deck of cards and then drawing a2 without replacing the jackC. Selecting a green marble from a bag of 10 different coloredmarbles and then selecting a second green marble without puttingthe first backOD. Owning cows and living on a dairy farm
Independent events are events where one event occurring or not does not affect whether the other one happens.
Pulling two cards out of a deck of cards, when you don't replace the first card, or pulling two marbles from a bag, where you don't replace the first marble, are not independent. By removing the first card/marble, you've change the situation for the second draw.
Using a spinner and rolling a die are totally independent, since they are different objects and what happens on one does not impact what will happen on the other.
And if you live on a dairy farm, that creates a better chance of being involved with dairy production and cows, so those are not independent.
Option A has two independent events.
100 divided by 72,144
Answer:0.00138611665
Step-by-step explanation:
A chemist wishes to mix a solution that is 6% acid. She has on hand 14 liters of a 4% acid solution and wishes to add some 10% acid solution to obtain the desired 6% acid solution. How much 10% acid solution should she add?
she should add 7 liters of 10% acid solution
Explanation
Step 1
set the equation:
a) let X represents the amount os solution that is 4% acid
let Y represents the amount os solution that is 10% acid
so
I)
[tex]\begin{gathered} \frac{4}{100}X+\frac{10}{100}Y=\frac{6}{100}(x+y) \\ \end{gathered}[/tex]if he has 14 liters of 4% acid solution
[tex]x=14[/tex][tex]\begin{gathered} \frac{4}{100}X+\frac{10}{100}Y=\frac{6}{100}(X+Y) \\ \frac{4}{100}*14+\frac{10}{100}Y=\frac{6}{100}(X+Y) \\ 0.56+0.1Y=0.06(14+Y) \\ 0.56+0.1Y=0.84+0.06Y \\ \end{gathered}[/tex]Step 2
solve the equation :
[tex]\begin{gathered} 0.56+0.1Y=0.84+0.06Y \\ subtract\text{ 0.06Y in both sides} \\ 0.56+0.1Y-0.06Y=0.84+0.06Y-0.06Y \\ 0.56+0.04Y=0.84 \\ subtract\text{ 0.56 in both sides} \\ 0.56+0.04Y-0.56=0.84-0.56 \\ 0.04Y=0.28 \\ divide\text{ both sides by 0.04} \\ \frac{0.04Y}{0.04}=\frac{0.28}{0.04} \\ Y=7 \end{gathered}[/tex]therefore,
she should add 7 liters of 10% acid solution
I hope this helps you
10b-2x+6 True or False is the expression contains 3 terms
It is true because they are not similiar.
Question 9 of 10If bis an explanatory variable and cis the corresponding response variable,which of these would be represented by the vertical axis on a scatterplot?O A. b БB. Neither b nor cOC. Both band cD. CSUBMIT
The response variable is dependent variable , and depends on the explanatory variable. The explanatory variable is independant variable and always represented on the horizontal axis.
The dependent variable (or response varaible) is represented on the vertical axis. So C is represented on the vertical axis of scatter plot.
Simplify the following expression by distributing and combining like terms.-5(k+6) + 7(k-4)
The given expression is
[tex]-5(k+6)+7(k-4)[/tex]To solve this, first, we use the distributive property.
[tex]-5(k+6)+7(k-4)=-5k-30+7k-28[/tex]Then, we reduce like terms.
[tex]2k-58[/tex]Therefore, the simplest form of the given expression is 2k - 58.A physical education teacher plans to divide the seventh graders at Wilson Middle School into teams of equal size for a year-ending mock Olympic event. He wants each team to have between 6 and 10 students, and all teams need to have the same number of students. The seventh grade at Wilson consists of three classes; one with 20 students, one with 33 , and one with 26 . How many students should be on each team?
First let's find the total number of students:
[tex]S=20+33+26=79[/tex]Now, let's divide this total by 6, 7, 8, 9 and 10, and check if the result has no remaining (that is, the result is a whole number):
[tex]\begin{gathered} \frac{79}{6}=13.167 \\ \\ \frac{79}{7}=11.286 \\ \\ \frac{79}{8}=9.875 \\ \\ \frac{79}{9}=8.778 \\ \\ \frac{79}{10}=7.9 \end{gathered}[/tex]Since none of the results is a whole number, it's impossible to divide these students in teams with the same number of students.
Therefore the correct option is the second one.