A data set has these values: 8, 10, 10, 12, 12, 12, 12, 14, 14, 16. The histogramof the distribution is shownWhich statement does not describe the data set?O A. It has a mode of 12.O B. It is symmetricO c. It has a range of 17OD. It has a mean of 12.
Answers
Given a data set has these values: 8, 10, 10, 12, 12, 12, 12, 14, 14, 16.
It is clear that the frequency of 12 is the greatest of all. So, the mode of the data is 12.
From the graph it is clear that, it is symmetric.
The range of the data is Max - Min = 16 - 8 = 8. Thus, range is 8.
The mean of a data is:
[tex]\text{Mean}=\frac{\text{ sum of all observation}}{\text{ total number of observation}}[/tex]For the given data:
[tex]\begin{gathered} \text{Mean}=\frac{8+10+10+12+12+12+12+14+14+16}{10} \\ =\frac{120}{10} \\ =12 \end{gathered}[/tex]Thus, the mean of the data is 12.
Thus, the statement that does not describe the data set is c.
Related Questions
Sanjay is making punch. He uses 1/3 cup of pineapple juice for every 3/4 cup of orange juice. How many cups of pineapple juice does he need if he uses 3 cup of orange juice.
Answers
Step
The question involve a direct proportion because when quantity inrease, the other increase.
Concept:
Find the constant of proportionality by dividing one quantity by the other.
Step 2
Find constant of proportionality K for 1/3 cup of pineapple juice for every 3/4 cup of orange juice.
[tex]\begin{gathered} k\text{ = }\frac{1}{3}\text{ }\frac{.}{.}\text{ }\frac{3}{4} \\ k\text{ = }\frac{1}{3}\text{ }\times\text{ }\frac{4}{3} \\ k\text{ = }\frac{4}{9} \end{gathered}[/tex]Step 3
Use can use the direct proportion method
Let P represent the number of cups of pineapple juice
[tex]\begin{gathered} \frac{\frac{1}{3}}{\frac{3}{4}}\text{ = }\frac{P}{3} \\ \text{Cross multiply} \\ \frac{3}{4}P\text{ = }\frac{1}{3}\text{ }\times\text{ 3} \\ \frac{3P}{4}\text{ = 1} \\ 3P\text{ = 4} \\ P\text{ = }\frac{4}{3} \end{gathered}[/tex]Final answer
[tex]\begin{gathered} \frac{4}{3}\text{ cups of pineapple juice is n}eeded\text{ for 3 cups of orange juice.} \\ \frac{4}{3}\text{ cups of Pineapple juice} \end{gathered}[/tex]The annual interest rate for Jack's savings account increased from 2.1% to 3.2%. Complete parts (a) and (b) below.a. Describe the change as an absolute change in terms of percentage pointsThe annual interest rate increased by percentage points.(Type an integer or decimal rounded to the nearest tenth as needed.)b. Describe the change as a relative change in terms of a percentageThe annual interest rate increased by %.(Type an integer or decimal rounded to the nearest tenth as needed.)
Answers
Step 1
Given;
[tex]\begin{gathered} \text{Initial annual interest;2.1\%} \\ \text{Current annual interest=3.2\%} \end{gathered}[/tex]Step 2
Describe the change as an absolute change in terms of percentage points. Absolute change is given as;
[tex]\text{Current annual interest}-\text{Initial annual interest}[/tex][tex]\begin{gathered} 3.2-2.1=1.1\text{ \%}^{} \\ \end{gathered}[/tex]The annual interest rate increased by 1.1 percentage points.
Step 3
Describe the change as a relative change in terms of a percentage.
[tex]Relative\text{ change in \%=}\frac{Absolute\text{ c}hange}{\text{initial annual interest}}\times100[/tex][tex]\begin{gathered} Relative\text{ change in \%=}\frac{1.1}{2.1}\times100=52.38095 \\ Relative\text{ change in \%}\approx52.4 \end{gathered}[/tex]The annual interest rate increased by 52.4 % to the nearest tenth.
Use the diagram as a reference to answer the question below
Answers
Let us draw out the triangle below:
Given that
[tex]\arctan \frac{\sqrt[]{3}}{3}=\beta[/tex]Using the trigonometric identity for tan 30, where
[tex]\tan 30=\frac{\sqrt[]{3}}{3}[/tex]Therefore,
[tex]\beta=30\degree[/tex]The sum of angles in a triangle is 180°.
Therefore,
[tex]\begin{gathered} \alpha+\beta+90=180\degree \\ \therefore \\ \alpha+30+90=180 \\ \alpha=180-90-30 \\ \alpha=60\degree \end{gathered}[/tex]To get the sides of the triangle, let us apply the Trigonometric ratios:
Using the Sine Trig. ratio,
[tex]undefined[/tex]Caculate the arc length of GH in terms of pie
Answers
Here, we want to calculate the arc length GH in terms of pi
What we will do here is to use the formula for the length of an arc
However, looking at the central angle, we can see it is 60
60 is actually 1/6 of the angle at the center which is 360
Thus, we have the arc length as 1/6 of the length of the circumfrence of the circle
Mathematically, we have this as;
[tex]\begin{gathered} GH\text{ = }\frac{1}{6}\text{ }\times\text{ 2}\times\text{ }\pi\times\text{ r} \\ \\ r\text{ is radius = 10}mm \\ \\ GH\text{ = }\frac{1}{6}\times2\times\pi\times10 \\ \\ GH\text{ = }\frac{10}{3}\pi\text{ mm} \end{gathered}[/tex]Determine the value of each variable in the figure below. Keep answers in simplest
rodicol form
c
42
30°
609
Answers
The triangles is the bigger triangle are both right angled
Considering the triangle by the left:
when angle = 60°
opposite = d
hypotenuse = 42
To get d, we will use sine ratio:
[tex]\begin{gathered} \sin \text{ 60}\degree\text{ = }\frac{opposite}{hypotenuse} \\ \sin \text{ 60}\degree\text{= }\frac{d}{42} \\ d\text{ = 42 }\times\text{ sin 60}\degree\text{ } \\ In\text{ radical form sin60}\degree\text{ = }\frac{\sqrt[]{3}}{2} \\ d\text{ =42 }\times\frac{\sqrt[]{3}}{2} \\ d\text{ = }21\text{ }\sqrt[]{3} \end{gathered}[/tex]To get a, we will use cosine ratio:
[tex]\begin{gathered} \cos \text{ 60}\degree\text{ = }\frac{adjacent}{hypotenuse} \\ \cos \text{ 60}\degree\text{in radical form = }\frac{1}{2} \\ \text{adjacent = a} \\ \cos \text{ 60}\degree\text{ = }\frac{a}{42} \\ a\text{ = 42(}\cos \text{ 60}\degree)\text{ }=\text{ 42(}\frac{1}{2}) \\ a\text{ = }21 \end{gathered}[/tex]Considering the triangle by the right:
opposite = d = 21√3
angle = 30°
hypotenuse = c
To get c, we will use sine ratio:
[tex]\begin{gathered} \sin \text{ 30}\degree\text{ = }\frac{opposite}{hypotenuse} \\ \sin \text{ 30}\degree\text{ = }\frac{21\surd3}{c} \\ c\text{ = }\frac{21\surd3}{\sin \text{ 30}\degree}\text{ ; }\sin \text{ 30}\degree\text{ = 1/2 } \\ c\text{ = }\frac{21\surd3}{\frac{1}{2}}=\text{ }21\surd3\text{ }\times\text{ 2} \\ c\text{ = 42 }\sqrt[]{3} \end{gathered}[/tex]b = adjacent
To get b, we will use cosine ratio:
[tex]\begin{gathered} \cos \text{ 30}\degree\text{ = }\frac{adjacent}{\text{hypotenuse}}\text{= }\frac{b}{c} \\ \cos \text{ 30}\degree\text{ }=\frac{b}{42\text{ }\sqrt[]{3}} \\ \cos \text{ 30}\degree\text{ in radical form = }\frac{\sqrt[]{3}}{2} \\ b\text{ = }42\text{ }\sqrt[]{3}\text{ }\times\text{ }\cos \text{ 30}\degree\text{ = }42\text{ }\sqrt[]{3}\text{ }\times\frac{\sqrt[]{3}}{2} \\ b\text{ = }\frac{42(3)}{2} \\ b\text{ = 63} \end{gathered}[/tex]How would I solve this problem, and with which theorem would it be solved with?
Answers
Given:
[tex]\begin{gathered} m\text{ }\angle RST=(3x-2)^0 \\ m\text{ }\angle TSK=(2x+22)^0 \end{gathered}[/tex]The angles form a linear pair.
Required:
[tex]m\angle RST\text{ = ?}[/tex]From the linear pair theorem:
The Linear Pair Theorem states that two angles that form a linear pair are supplementary; that is, their measures add up to 180 degrees.
Applying this theorem, we have:
[tex]m\text{ }\angle RST\text{ +m }\angle TSK\text{ = 180}[/tex]Substituting we have:
[tex]\begin{gathered} (3x-2)\text{ + (2x + 22) = }180 \\ \text{Collect like terms} \\ 3x\text{ + 2x -2 + 22 = 180} \\ 5x\text{ = 180-20} \\ 5x\text{ = 160} \\ \text{Divide both sides by }5 \\ \frac{5x}{5}=\frac{160}{5} \\ x\text{ = 32} \end{gathered}[/tex]The required angle is:
[tex]\begin{gathered} m\angle RST\text{ = 3x -2} \\ \text{Substituting} \\ =\text{ 3(32)-2} \\ =\text{ }96-2 \\ =\text{ 94} \end{gathered}[/tex]Name of the theorem: linear pair theorem:
A sample of 394 people is selected. The people are classified according to place of residence ("urban", "suburban", or "rural"). They are also classified accordingto highest educational degree earned ("no college degree", "two-year degree", "Your-year degree", or "advanced degree“). The results are given in thecontingency table below.No college degree Two-year degree Four-year degree Advanced degreeUrban50152045Suburban23481543Rural46272240
Answers
Class: Place of residence is rural
Class frequency: (46+27+22+40) =135
n: 394 people is selected
Relative frequecy of people in the sample whose place of residence is rural:
[tex]=\frac{135}{394}\approx0.34[/tex]Help please and based on the answer that I’m supposed to get would it have the same solution?
Answers
Solution
To get equation B from A
Distributive property
a(b + c) = ab + ac
=>3(x + 2) = 18
=>3x + 6 = 18.
D. Rewrite one side (or both) using the distributive property.
Using the slope formula, find the slope of the line through the given points(12,0) and (2,-4)is the slope defined?
Answers
The slope is 2/5, and defined
Explanation:The slope is:
[tex]\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ \\ =\frac{-4-0}{2-12} \\ \\ =\frac{-4}{-10} \\ \\ =\frac{2}{5} \end{gathered}[/tex]The slope is defined
Which of the following represents another way to write the function rule f(x) = 3 +11.f(1) = 4 2.f(y) = 3x + 1 3.y - 3x+1 4.x=3y+1
Answers
A common notation which is used to represent functions is the following:
[tex]y=f(x)[/tex]Then, the function f(x)=3x+1 can also be written as:
[tex]y=3x+1[/tex]Therefore, the answer is that of the 3rd option.
what is the probability of landing on a 5 and then later on a 5 as a fraction or whole number
Answers
probabilities of landing on 5 = favorable outcome / total outcomes
total outcomes = 3 ( 5 , 4 and 3)
Favourable outcomes = 1 ( 5)
P = 1/3
Probability of of landing on 5 two times
1/3 x 1/3 = 1/9
in each figure find the measure of the angles and the lengths of the sides
Answers
According to the problem, angles E and F are equal. Angles D and G are equal.
Also, if the trapezoid is isosceles, then FG = DE by definition. So, we express the following
[tex]\begin{gathered} FG=DE \\ 11=a-4 \end{gathered}[/tex]Let's solve for a
[tex]\begin{gathered} 11+4=a \\ a=15 \end{gathered}[/tex]We already know that the sum of all the interior angles is 360°.
[tex]c+c+4c-20+4c-20=360[/tex]Let's solve for c
[tex]\begin{gathered} 10c-40=360 \\ 10c=360+40 \\ c=\frac{400}{10}=40 \end{gathered}[/tex]Then, we find each angle using the value of c
[tex]\begin{gathered} D=c=40 \\ G=c=40 \\ E=4c-20=4\cdot40-20=160-20=140 \\ F=4c-20=4\cdot40-20=160-20=140 \end{gathered}[/tex]Hence, angles D and G measure 40°, angles E and F measure 140°.Hi I will be late ⏰ if we are ok weQuestion 5
Answers
SOLUTION:
Case: Differentiation
Method:
[tex]\begin{gathered} h(t)=10+50t+\frac{1}{2}at^2 \\ h^{\prime}(t)=50+2\times\frac{1}{2}at^{2-1} \\ h^{\prime}(t)=50+at \\ But \\ h^{\prime}(1.25)=9.75 \\ h^{\prime}(1.25)=50+1.25a \\ 9.75=50+1.25a \\ 1.25a=9.75-50 \\ 1.25a=-40.25 \\ a=\frac{-40.25}{1.25} \\ a=-32.2ft\text{ /}s^2 \end{gathered}[/tex]Final answer:
a = -32.2 ft per sq seconds
What is the domain of y = cos x? ?- [-1,1]- [0,pi] - [-pi/2, pi/2]- (-♾, ♾)
Answers
We have the following:
[tex]y=\cos x[/tex]The domain of a function are the input values that the function can take or the values of the x-axis.
In this case, the x-axis can take any value, that is, the domain would be
[tex](-\infty,\infty)[/tex]From negative infinity to positive infinity, that is, all numbers
it takes Abbas 12 minutes to eat a pizza, and it takes Mashi 6 minutes to eat the same size pizza. Working together, how many of these pizzas could they polish off in 24 minutes if they can continue eating pizza at the same rate?
Answers
Given:
Abbas takes 12 minutes to eat a pizza and Mashi takes 6 minutes to eat same size pizza.
Abbas will eat 2 pizza in 24 minutes and Mashi eats 4 pizza in 24 minutes .
[tex]\text{Total number of pizza they polish off in 24 minutes }=2+4[/tex][tex]\text{Total number of pizza they polish off in 24 minutes }=6[/tex]need help on questions
Answers
we have that
300 votes represent 60% of all votes
so
Applying proportion
Find out the total students that represent 100%
so
300/60=x/100
solve for x
x=(300/60)*100
x=500
answer is 500 students2/3x - 9 = 6explain work
Answers
Here, we are to solve for the value of x in the given euation;
2/(3x-9) = 6
We can solve this by making a cross multiplication
2/(3x-9) = 6/1
The cross-multiplication would yield;
2 * 1 = 6 * (3x-9)
2 = 6(3x-9)
opening the bracket, we have
2 = 18x - 54
Collect like terms;
54 + 2 = 18x
18x = 56
divide both sides by 18
18x/18 = 56/18
x = 28/9
x = 3 1/9
Can I get an answer please? (also let me know if you need more than this image)
Answers
A' ( 0,0)
B' (4,0)
C' (4, 8)
D' (0,8)
Given the transformation rule, we want to get the coordinates of the transformed point
The transformation rule is that;
(x,y) to (x,2y)
Thus we have;
A (0,0) to (0 , 2(0))
A' (0,0)
For B (4,0)
WE have
(4, 2(0)) = (4,0)
For C (4,4)
WE have;
(4, 2(4)) = (4,8)
For (0,4)
We have
(0, 2(4)) = (0,8)
2L + 2W =PSolve for w
Answers
Answer:
[tex]W=\frac{P}{2}-L[/tex]Explanation:
Given the equation
[tex]2L+2W=P[/tex]To solve for W, first subtract 2L from both sides
[tex]\begin{gathered} 2L+2W-2L=P-2L \\ \\ 2W=P-2L \end{gathered}[/tex]Next, divide both sides by 2
[tex]\begin{gathered} \frac{2W}{2}=\frac{P-2L}{2} \\ \\ W=\frac{P}{2}-L \end{gathered}[/tex]Describe the effect of the transformation (x,y) → (x,y+4)
Answers
The image's been translated 4 units up.
Since this Geometric Transformation, described is a Translation.
Then We can say that the Image moved 4 units up, for it is +4 and this figure has not been translated horizontally.
Pre-Image Image
(x,y) (x, y+4)
If terminal side of angle t goes through (-5/13,12/13) what is sin(t)
Answers
Given the point P(-5/13,12/13)
the angle t is
then
since we know x and y values (-5/13,12/13) we can solve theta
where
Opp = -5/13
Adj = 12/13
[tex]tan(\theta)=\frac{Opp}{Adj}[/tex][tex]tan(\theta)=\frac{\frac{-5}{3}}{\frac{12}{13}}[/tex][tex]tan(\theta)=\frac{-5*13}{3*12}[/tex][tex]tan(\theta)=\frac{-65}{36}[/tex][tex]\theta=ArcTan(\frac{-65}{36})[/tex][tex]\theta=61.02°[/tex]Adding the 90° of the first quadrant
The angle t is
[tex]t=61.02+90[/tex][tex]t=151.02[/tex]to rads
[tex]t=\frac{151.02\pi}{180}[/tex]then sin t
[tex]sin(t)=0.48450[/tex]1. congruent circles2. tangent circles3. concentric circleswhat best describes the circles shown
Answers
A.) Two circles are congruent if they have the same size. The size can be measured as the radius, diameter or circumference. They can overlap.
Among the given figures, this best describes what congruent circles are,
B.) When two circles touch one another at exactly one point, then we say that the two circles are tangent to one another.
Among the given figures, this best describes what tangent circles are.
C.) Concentric circles are circles with a common center.
Among the given figures, this best describes what concentric circles are,
Evaluate the expression using the order of operations.A. 31B. 34C. 19D. 14
Answers
Answer: B. 34
Find the area of a regular hexagonwith a side length of 8 cm. Round tothe nearest tenth.а8 cm[?] cm2
Answers
We are asked to determine the area of a regular hexagon given a side of 8 cm. To do that we will use the following formula:
[tex]A=\frac{3\sqrt[]{3}}{2}a^2[/tex]Where:
[tex]\begin{gathered} A=\text{ area} \\ a=\text{ length of the side} \end{gathered}[/tex]Now, we plug in the values:
[tex]A=\frac{3\sqrt[]{3}}{2}(8cm)^2[/tex]Solving the operations:
[tex]A=166.3cm^2[/tex]Therefore, the area of the hexagon is 166.3 square centimeters.
A test is graded on a scale from O to 100. Your friend says that if you score a 78, your percentile rank must be 78. Is your friend correct?
Answers
Percentile rank refers to the percentage of scores that are equal to or less than a given score.
A percentile rank of 78 means that 78% of the scores fall at or below a given score.
Then, if if you score a 78 in a test graded from 0 to 100, it doesn't mean that the percentile rank is 78; to find the percentile rank you need to compare your score with the score of the other students that presented the test.
Answer: Your friend is not correctArianna filled up her car with gas before embarking on a road trip across the country. Let G represent the number of gallons of gas remaining in her gas tank after driving for t hours. A graph of G is shown below. Write an equation for G then state the x- intercept of the graph and determine its interpretation in the context of the problem.
Answers
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data
G = gallons remaining in the tank
t = hours
equation = ?
x- intercept of the graph = ?
Step 02:
We must analyze the graph to find the solution.
point 1 ( 0 , 15) x1 = 0 y1 = 15
point 2 (12 , 0) x2 = 12 y2 = 0
slope formula
[tex]m\text{ = }\frac{y2\text{ -y1}}{x2-x1}=\frac{0-15}{12-0}=\frac{-15}{12}=-1.25[/tex]slope-intercept form of the line
y = mx + b
m = -1.25
b = y-intercept = 15
G = -1.25x + 15
x- intercept of the graph = 12
After 12 hours there is no gas left in the tank.
The answer is:
G = -1.25x + 15
x- intercept of the graph = 12
After 12 hours there is no gas left in the tank.
What is the scientific notation of the following number? 367 x 10^-3 *
Answers
the given number is
367 x 10^-3
the scientific notation of this number will be
3.67 x 10^-1
thus, the answer is 3.67 x 10^-1
a grocery store sells chicken for $3.30 per pound. what would be the cost of 2 1/2 pounds of chicken
Answers
hello
the store sells chicken for $3.30 per pound
1 pound = $3.30
would would be the cost of 2 1/2 pound
let x represent the cost of 2 1/2 pound
[tex]\begin{gathered} 1\text{ pound = \$3.30} \\ 2\frac{1}{2}pound\text{ }=\text{ x} \\ \text{1 pound = \$3.30} \\ \frac{5}{2}\text{ pound = x} \\ cross\text{ multiply and make x the subject of formula} \\ 2.5\text{ }\times\text{ 3.30 }=\text{ 1 }\times\text{ x} \\ x\text{ = 8.25} \end{gathered}[/tex]the cost of 2 1/2 pound chicken is $8.25
Efgh is a rectangle . EA is 12 inch. Find the length of the diagonal EH
Answers
ANSWER
line EH is 24 in (option B)
EXPLANATION
Since EF || GH, and EG || FH
line EH = EA + AH
But EA and AH are equal
Then, EH = 12 + 12 = 24 in
Hence, line EH is 24 in
how to solve 5u+27+4u=9
Answers
Given equation is
[tex]5u+27+4u=9[/tex]Now, we keep all the terms with u in the left hand side and the terms without u in the right hand side. It follows
[tex]\begin{gathered} 5u+4u=9-27 \\ 9u=-18 \\ u=-2 \end{gathered}[/tex]Hence, the solution is u=-2.