Answers
In order to create a boxplot of the Area 1 dataset, first let's put the dataset in crescent order:
[tex]12,24,30,32,35,44,45,56,57,59,61,65,68,92,100.[/tex]Since the set has 15 elements, the median is the 8th element, so the median is 56.
The median will divide the set into two smaller sets with 7 elements each. The first interquartile (IQ1) is the median of the first subset (so it will be the 4th element), and the third interquartile (IQ3) is the median of the second subset (so it will be the 12th element).
So the first interquartile is 32 and the third interquartile is 65.
Now we need the lower and upper limit of the set.
The lower limit is 12 and the upper limit is 100.
Now, creating the boxplot, we have:
Related Questions
Robert is paid $12.00 per hour to chop firewood he chops 40% of the pile of firewood in 3/4 of an hour at this rate how much will Robert be paid to chop the entire pile of firewood?
Answers
Robert chops 40% of the pile of firewood in 3/4 of an hour.
Then, we would chop 80% of the pile of firewood in 2*(3/4)=3/2 hours.
where 3/2 = 1.5 hours
Also, he would chop the missing 20% in (3/4)/2=3/8.
The full work is for 3/8+3/2 =15/8 hours
Now, if one hour is paid $12.00, we can use the rule of three to know how much is paid for 15/8 hours:
1h-----------$12.00
15/8 h -------- $x
where x=(12.00*5/8)/1
x=22.50
Hence, Robert will be paid $22.50 to chop the entire pile of firewood.
tan (θ) cot (θ)=1Trig: use trigonometric identities to transform the left side of the equation into the right side
Answers
1) Let's prove this identity
Since tan (θ) = sin(θ)/cos((θ)
And cot((θ) = cos ((θ)/sin((θ)
2) Let's plug it into:
[tex]\begin{gathered} \tan \text{ (}\theta)\cot \text{ (}\theta)\text{ =1} \\ \frac{\sin (\theta)}{\cos (\theta)}\cdot\frac{\cos (\theta)}{\sin (\theta)}=1 \\ 1=1 \end{gathered}[/tex]Simplifying (dividing) sin(θ) on the numerator, with sin (θ) on the denominator and similarly cos (θ) with cos(θ) we'll get to 1 over 1 time 1 over 1 = 1
Then 1=1
Find the sum of the first 16 terms in an arithmetic series where a1 = 2, and the common difference is d=2.A) 306B) 272C) 240D) 360
Answers
B)272
Explanation
An arithmetic sequence is defined as a series of numbers, in which each term (number) is obtained by adding a fixed number to its preceding term.
[tex]Sum=\frac{n}{2}\mleft[2a+(n-1)d\mright],[/tex]
where 'a' is the first term, 'd' is the common difference between two numbers, and 'n' is the number of terms.so
Step 1
Let
[tex]\begin{gathered} a=2 \\ d=2 \\ n=16 \end{gathered}[/tex]replace,
[tex]\begin{gathered} Sum=\frac{n}{2}\lbrack2a+(n-1)d\rbrack, \\ Sum=\frac{16}{2}\lbrack2\cdot2+(16-1)2\rbrack, \\ Sum=8\lbrack4+(15)2\rbrack \\ Sum=8\lbrack4+30\rbrack \\ Sum=8\lbrack34\rbrack \\ Sum=272 \end{gathered}[/tex]therefore, the answer is
B)272
I hope this helps you
I need help with 17 pls I need an answer in explanation
Answers
Step 1
2n = 70
divide both sides by 2
[tex]\begin{gathered} \frac{2n}{2}=\frac{70}{2} \\ n\text{ = 35} \end{gathered}[/tex]Step 2
Make a conclusion based on step 1
If n = 3.5
Then substituting for n = 3.5 in the equation
[tex]\begin{gathered} 2(3.5)\text{ =7} \\ 7\text{ is not equal to 70} \end{gathered}[/tex]Therefore n = 3.5 is not a solution of the equation 2n = 70
0.4(5x-15)=2.5(x+3) solution is it infinitely or no solution or one solution
Answers
There is one solution to the equation
Here, we want to check the nature of the solution to the equation
We can start this by evaluating the equation;
[tex]\begin{gathered} 0.4(5x-15)\text{ = 2.5(x+3)} \\ 2x\text{ - 6 = 2.5x + 7.5} \\ 2.5x-2x\text{ = -6-7.5} \\ 0.5x\text{ = -13.5} \\ x\text{ = }\frac{-13.5}{0.5} \\ x\text{ = -27} \end{gathered}[/tex]As we can see, only a single solution exists for the equation
Test ContentQuestion 110 PointsA box is 36 inches long, 18 inches wide, and 6 inches deep. How many cubic feet are in the box?A 5 cubic feetB4.5 cubic feet© 3 cubic feetD2.25 cubic feet
Answers
The box is 2.25 cubic feet (option D)
Explanation:length of the box = 36 inches
width = 18 inches
depth = height = 6 inches
To get the volume of the box in cubic feet, we need to first convert the dimensions from iches to feet to make it easy to solve.
conversion from iches to ft:
12 inches = 1 ft
36 inches = 36/12
= 3 ft
18 inches = 18/12
width = 18 inches = 3/2 ft
6 inches = 6/12
height = 6 inches = 1/2 ft
The box is a rectangular prism
Volume of rectangular prism = length × width × height
[tex]\begin{gathered} \text{Volume of the rectangular prism = 3 ft }\times\text{ }\frac{3}{2}\text{ ft }\times\text{ }\frac{1}{2}\text{ ft} \\ \text{Volume of the rectangular prism = 9/4 ft}^3\text{ = }2.25ft^3 \\ \\ \\ Volume\text{ of the box = 2.25 cubic f}eet\text{ (option D)} \end{gathered}[/tex]You have from 9:30 pm to 11 pm to do a project. A) at 10 pm what fraction of the time remains?B) at 10:50 pm what fraction of time remains?
Answers
We were told that you have from 9:30 pm to 11 pm to do a project. This means that you have an hor and 30 minutes to do the project. Recall,
1 hour = 60 minutes
1 hour and 30 minutes would be 60 + 30 = 90 minutes
A) At 10pm, the amount of time that you have left is 1 hour(between 10pm and 11 pm)
This is equal to 60 minutes. The fraction of time left would be
time left/total number of hours
fraction of time that is remaining = 60/90 = 2/3
B) At 10:50 pm, the number of minutes left before 11 pm is 10 minutes. Thus,
Fraction of time that is remaining = 10/90 = 1/9
identify the correct graph of the circle. (x + 3)² + (y + 1) = 16I have to send the graphs in message
Answers
The general form of a equation of a circle is:
[tex](x-h)^2+(y-k)^2=r^2[/tex]Where:
r is the radius of the circle
(h,k) are the coordinates of the center of the circle
Then, the given equation:
[tex](x+3)^2+(y+1)^2=16[/tex]The radius and the coordinates of the center are:
[tex]\begin{gathered} r=4 \\ h=-3 \\ k=-1 \\ \\ \mleft(-3,-1\mright) \end{gathered}[/tex]Then, the graph for this circle is: Photo number 2
The equation we used today to represent a line is called _______ formFor the equation y=mx+b, m is the ______For the equation y=mx+b, b is the _______
Answers
1) The equation we used today to represent a line is called :
The slope-intercept form
In this form, y=mx +b
2) For the equation y=mx+b, m is the slope
It measures how steep is the line.
3) For the equation y=mx+b, b is the line coefficient
This is the point where the line intercepts the y coordinate.
what is a equation to find interest.
Answers
The formula to find the simple interest is the following:
[tex]A=P(1+rt)[/tex]Where P is the principal amount, r is the interest rate, t is the time and A is the Future value
Events A and B are independent. Find the indicated Probability.P(A) = 0.4P(B) =P(A and B) = 0.2
Answers
From the statement, we know that:
• P(A) = 0.4,
,• P(A and B) = 0.2.
Because A and B are independent events, the probability of A and B is the product of the individual probabilities:
[tex]P(A\text{ and }B)=P(A)*P(B)\Rightarrow P(B)=\frac{P(A\text{ and }B)}{P(A)}.[/tex]Replacing the data of the problem, we get:
[tex]P(B)=\frac{0.2}{0.4}=0.5.[/tex]AnswerP(B) = 0.5
what two consecutive whole numbers that 12 lie between [tex] \sqrt{12} [/tex]
Answers
Simplify the number to obtain the value in decimal.
[tex]\begin{gathered} \sqrt[]{12}=\sqrt[]{2\cdot2\cdot3} \\ =2\sqrt[]{3} \\ =2\cdot1.732 \\ =3.464 \end{gathered}[/tex]The value 3.464 lies between 3 and 4, which are also consecutive whole number.
So answer is 3 and 4.
1. A car has a 16-gallon fuel tank. When driven on a highway, it has a gasmileage of 30 miles per gallon. The gas mileage (also called "fuel efficiency")tells us the number of miles the car can travel for a particular amount of fuel(one gallon of gasoline, in this case). After filling the gas tank, the driver got ona highway and drove for a while.
Answers
Given:
Capacity of the car's fuel tank = 16 gallons
Gas mileage of car = 30 miles per gallon
Given that the driver filled the tank and got on a highway, let's solve for the following:
• (a) How many miles has the car traveled if it has the following amounts of gas left in the tank:
Use the expression:
[tex](16-g)\times30[/tex]Where g reresents the amount of gas left.
• 15 gallons:
If the car has 15 gallons left, to calculate the distance traveled, we have:
[tex]\begin{gathered} (16-15)\times30 \\ \\ =(1)\times30 \\ \\ =30\text{ miles} \end{gathered}[/tex]If the car has 15 gallons left, it has traveled for 30 miles.
• 10 gallons:
For 10 gallons, we have:
[tex]\begin{gathered} (16-10)\times30 \\ \\ =(6)\times30 \\ \\ =180\text{ miles} \end{gathered}[/tex]If the car has 10 gallons left, it has traveled for 180 miles.
• 2.5 gallons:
[tex]\begin{gathered} (16-2.5)\times180 \\ \\ =13.5\times180 \\ \\ =405\text{ miles} \end{gathered}[/tex]If the car has 2.5 gallons left, it has traveled for 405 miles.
• Part b.
Let's write an equation that shows the relationship between the distance traveled (d), and the amount of gas left in the tank in gallons(x).
To write the equation, we have:
[tex]d=(16-x)30[/tex]• Part C.
Let's find the amount of gallons left in the tank when the car has traveled the following distances:
• 90 miles:
[tex]\begin{gathered} x=16-\frac{90}{30} \\ \\ x=16-3 \\ \\ x=13\text{ gallons} \end{gathered}[/tex]If the car has traveled 90 miles, it will have 13 gallons left in the tank.
• 246 miles:
[tex]\begin{gathered} x=16-\frac{246}{30} \\ \\ x=16-8.2 \\ \\ x=7.8\text{ gallons} \end{gathered}[/tex]If the car has traveled for 246 miles, it will have 7.8 gallons left in the tank.
• Part d.
To write the equation, we have:
[tex]x=16-\frac{d}{30}[/tex]Answer:
Step-by-step explanation:
For 90 :
90/x = 30
x=90/30
x=3 gallons
For 246 :
246/x=30
x=246/30
x=8.2 gallons
In exercises 3 and 4 , find the values of x and y.
Answers
Trigonometry and Triangles
To solve the problem, we need to recall the following:
* The sum of the interior angles in a triangle is 180°
* The sum of two supplementary angles is 180°
* The tangent of an acute angle in a right triangle is defined as:
[tex]\tan \theta=\frac{\text{opposite side}}{adjacent\text{ side}}[/tex]We included a new variable z to help solve the problem. Details below:
Angle 59° and angle z° are supplementary because they are a linear pair, thus:
z + 59 = 180
Solving for z:
z = 121
Now we focus on the left triangle with interior angles of 45°, z°, and x°. The sum of all three must be 180°, thus:
45 + 121 + x = 180
Solving for x:
x = 180 - 45 - 121
x = 14
Now focus on the bigger triangle (the one that contains two smaller triangles).
This triangle is right (it has one interior angle of 90°) and it's also an isosceles triangle because it also has one interior angle of 45°.
Any right triangle
the measure of an inclined angle between two sides is 45° and the measure of the sides are 5m and 8m. find the measure of the third side.
Answers
EXPLANATION
We can represent the states in the following picture:
We can apply a Trigonometric ratio in order to get the value of the third side, assuming that it is called x:
[tex]\sin45=\frac{Opposite\text{ cathetus}}{Hypotenuse}=\frac{x}{8}[/tex]Multiplying both sides by 8:
[tex]8*\sin45=x[/tex]Switching sides:
[tex]x=8*\sin45[/tex]Multiplying terms:
[tex]x=4\sqrt{2}[/tex]In conclusion, the measure of the third side is approximately equivalent to 4√2 or 5.65
What diameter must a circular piece of stock be to mill a hexagonal shape with a side length of 2.7 in.?
Answers
Given:
A circular piece of stock be to mill a hexagonal shape with a side length of 2.7 in.
Required:
We need to find the diameter of hexagon.
Explanation:
now use the sin function
[tex]\begin{gathered} sin30=\frac{1.35}{r} \\ \\ \frac{1}{2}=\frac{1.35}{r} \\ \\ r=2.7 \end{gathered}[/tex]so by r
[tex]d=2r=5.4\text{ in}[/tex]Final answer:
Diameter of hexagon is 5.4 in
Please help me figure out how to solve the problem X squared to the Y square root 18 X to the fifth Y to the second
Answers
To solve this problem, we will use the following property of exponents:
[tex]x^nx^m=x^{n+m}.[/tex]
Now, notice that:
[tex]x^5=x^{2+3}=x^2x^3\text{.}[/tex]Therefore, we can rewrite the given expression as follows:
[tex]x^2y\sqrt[]{18x^2y^2x^3}.[/tex]Recall that:
[tex]\sqrt[]{ab}=\sqrt[]{a}\sqrt[]{b}.[/tex]Therefore, we can split the root as follows:
[tex]x^2y\sqrt[]{18x^2y^2x^3}=x^2y\sqrt[]{18}\sqrt[]{x^2y^2}\sqrt[]{x^3}\text{.}[/tex]Simplifying we get:
[tex]x^2y\sqrt[]{18}\sqrt[]{x^2y^2}\sqrt[]{x^3}=x^2y\sqrt[]{9\cdot2}\sqrt[]{x^2}\sqrt[]{y^2}\sqrt[]{x^3}=x^2y3\sqrt[]{2}xy\sqrt[]{x^2x}.[/tex]Multiplying like terms, we get:
[tex]x^2yxy\sqrt[]{18x^3}=x^4y^2\sqrt[]{18x}=x^4y^2\sqrt[]{(9\cdot2)x^2}=3x^4y^2\sqrt[]{2x}.[/tex]Answer:
[tex]3x^4y^2\sqrt[]{2x^3}\text{.}[/tex]Example:
Simplify
[tex]2x^2y^3\sqrt[]{9x^3y^2}.[/tex]First, we notice that:
[tex]\begin{gathered} x^3=x^2x, \\ 9=3^2. \end{gathered}[/tex]Therefore, we can rewrite the expression as:
[tex]2x^2y^3\sqrt[]{3^2x^2xy^2}=2x^2y^3\sqrt[]{3^2x^2y^2}\sqrt[]{x}=2x^2y^3(3xy)\sqrt[]{x}.[/tex]Simplifying we get:
[tex]6x^3y^4\sqrt[]{x}.[/tex]what is the distance between (-7,2) and (1,-6)
Answers
The distance between two points is the length of the path connecting them. The shortest path distance is a straight line. In a 2 dimensional plane, the distance between points (X1, Y1) and (X2, Y2) is given by the Pythagorean theorem:
[tex]d=\sqrt[]{(x2-x1)^2+(y2-y1)^2}[/tex][tex]\begin{gathered} d=\sqrt[]{(1-(-7))^2+(-6-2)^2} \\ d=\sqrt[]{8^2+8^2} \\ d=\sqrt[]{64+64} \\ d=\sqrt[]{128} \\ d=11.31 \end{gathered}[/tex]The answer would be d = 11.31
7x+2=58 it wants you to solve
Answers
7x +2=58
7x = 58-2
7x = 56
x = 56/7
x = 8
Is -13, -6, 1, 8 arithmetic?
Answers
Given the following sequence
[tex]\lbrace-13,-6,1,8,\ldots\rbrace[/tex]We want to know if this sequence is arithmetic. The general term of an arithmetic sequence is given by
[tex]a_n=a_1+(n-1)d[/tex]Where d represents the common ratio. An arithmetic sequence increases by the same value every term(this value is the common ratio). If the difference between neighbor terms is the same for all of our terms, this sequence can be written as an arithmetic sequence.
Let's calculate the difference between the terms
[tex]\begin{gathered} a_2-a_1=-6-(-13)=-6+13=7 \\ a_3-a_2=1-(-6)=1+6=7 \\ a_4-a_3=8-1=7 \end{gathered}[/tex]Since the difference is the same, this sequence is Arithmetic.
I need help with this practice Having troubleIf you can, use Desmos to graph the function
Answers
In general, given a function g(x)
[tex]undefined[/tex]Seventh gradeS.1 Which x satisfies an equation? DJSWhat value of x is a solution to this equation?14 + x = 25x = 11x = 12
Answers
The given equation is
[tex]14+x=25[/tex]Remember that the value which satisfies an equation must give the same equality. For example, in this case, we have to get 25 on both sides of the equation.
Observe that x = 11 will satisfy the equation
[tex]\begin{gathered} 14+11=25 \\ 25=25 \end{gathered}[/tex]Hence, the right answer is x = 11.Graph y = (1/2)|x + 2| – 1 using transformations
Answers
First let's start with the graph of y = x:
Then, let's apply the "absolute value" operator: y = |x|
Then, we have an horizontal translation of 2 units to the left: y = |x + 2|:
Then, a vertical stretch by a factor of 1/2: y = (1/2)|x + 2|:
Finally, a vertical translation of 1 unit down: y = (1/2)|x + 2| - 1:
Step 2 of 2: Use the discriminant b ^ 2 - 4ac to determine the number of solutions of the given quadratic equationThen solve the quadratic equation using the tormuisx = (- b plus/minus sqrt(b ^ 2 - 4ac))/(2a)
Answers
ANSWER
The value of x is 4
EXPLANATIONS;
Given that
[tex]\text{ -x}^2\text{ = - 8x + 16}[/tex]Re-write the quadratic function
[tex]-x^2\text{ + 8x - 16 = 0}[/tex]Recall, that the general form of quadratic function is given as
[tex]\text{ ax}^2\text{ + bx + c = 0}[/tex]Relating the two functions together
a = -1
b = 8
c = - 16
Determine the number of solutions first using the discriminant
[tex]\begin{gathered} \text{ D = b}^2\text{ - 4ac} \\ \text{ D = \lparen8\rparen}^2\text{ - 4 }\times(-1\text{ }\times\text{ -16\rparen} \\ \text{ D = 64 - 4\lparen16\rparen} \\ \text{ D= 64 - 64} \\ \text{ D = 0} \end{gathered}[/tex]Since D = 0 , then , the quadratic function has one real solution
Solve the equation using the general quadratic formula
[tex]\begin{gathered} \text{ x = }\frac{-b\text{ }\pm\sqrt{b^2\text{ - 4ac}}}{2a} \\ \\ \text{ x = }\frac{-8\text{ }\pm\sqrt{8^2\text{ - 4\lparen-1 }\times\text{ -16\rparen}}}{2\times-1} \\ \\ \text{ x }=\frac{-8\text{ }\pm\sqrt{64-\text{ 4\lparen16\rparen}}}{-2} \\ \\ \text{ x = }\frac{-8\text{ }\pm\sqrt{64\text{ - 64}}}{-2} \\ \text{ x = }\frac{-8\pm\sqrt{0}}{-2} \\ \\ \text{ x = }\frac{-8\pm0}{-2\text{ }} \\ \text{ x }=\text{ }\frac{-8\text{ - 0}}{-2\text{ }}\text{ or }\frac{-8\text{ + 0 }}{-2} \\ \text{ x = 4 or 4} \end{gathered}[/tex]Hence, the value of x is 4
The graph of the function y=f(x) is given. Find the domain of f(x).Using the graph given.
Answers
Given
Graph of the function y = f(x)
Find
domain of f(x)
Explanation
As we know domain of a function is all the values of x that makes the function defined.
here in the graph , the function is defines for x values 0 to 5
since , the point 0 and 5 is in open interval , so , the graph does not include the points 0 and 5
hence , the domain is (0 , 5)
Final Answer
Therefore , the domain of the given function is (0 , 5)
the sum of the first two terms of an arit
Answers
SOLUTION:
We are told that;
[tex]\begin{gathered} a+a+d=15 \\ a+2d+a+3d=43 \end{gathered}[/tex]Rewriting, we have;
[tex]\begin{gathered} 2a+d=15 \\ 2a+5d=43 \end{gathered}[/tex]Subtracting the first and second equations, we have;
[tex]\begin{gathered} 4d=28 \\ d=7 \end{gathered}[/tex]and;
[tex]\begin{gathered} 2a+7=15 \\ 2a=8 \\ a=4 \end{gathered}[/tex]Thus, the first four terms of the sequence are;
[tex]4,11,18,25[/tex]Kevin has money into savings accounts. One rate is 7% and the other is 8%, If he has $150 more than the 8% account and the total interest is $51 how much is invested in each savings account?
Answers
Let x be the total invested in at the 7% account and y the total invested at the 8% account.
Since he has $150 more than the 8% account, it implies that x + y = y + 150 and, therefore, x = $150
Since the total interest is $51, we have:
0.07x + 0.08y = 51
0.07*150 + 0.08y = 51
10.5 + 0.08y = 51
0.08y = 40.5
y = 40.5/0.08 = $506.25
Kevin has $150 at the 7% account and 506.25 at the 8% account.
plot the point on the line with the x-coordinate x = -9
Answers
Substituting x=-9 in the given equation we get:
[tex]-4(-9)+y-38=0.[/tex]Simplifying the above result, we get:
[tex]\begin{gathered} 36+y-38=0, \\ y-2=0. \end{gathered}[/tex]Adding 2 to both sides of the equation, we get:
[tex]\begin{gathered} y-2+2=0+2, \\ y=2. \end{gathered}[/tex]Therefore, the coordinates of the point with x=-9 are:
[tex](-9,2)\text{.}[/tex]Answer:
1 plus 1 my little sister needs help
Answers
Answer:
[tex]1+1=2[/tex]Step-by-step explanation:
If you have one apple and you buy another one, you will have 2 apples. Therefore,
[tex]1+1=2[/tex]Triangle ABC is reflected across the y-axis and then dilated by a factor of 1/2 centered at the origin. Which statement correctly describes the resulting image, triangle DEF?
Answers
There are a number of transformations that can be used to alter the size and position of a shape. These include dilation, translation, reflection, and rotation.
Dilation can be either an enlargement, which results in an image that is larger than the original figure, or a reduction, which results in an image that is smaller than the original figure. If a dilation operation is performed on a shape, we will have a change in the lengths of the shape or the area covered. However, the angles of the shape remain the same since all the sides change by the same factor.
A reflection is a transformation that preserves both size and shape of a polygon or object. All that happens in a reflection is a change in the position and orientation of the shape.
If triangle ABC is dilated and reflected, any change in the side lengths is from the dilation. The angles are preserved, however, both by dilation and reflection.
The correct option is OPTION C.