A hospital conducted a random sample of its patients by asking each to report the number of colds they had experienced over the last year. The results are shown in the bocks plot and the histogram
Answers
We are given a boxplot and a histogram of the number of colds patients had experienced over the last year.
Let us analyze each of the given statements.
Statement 1: Both displays show the data is skewed right.
The above statement is correct.
Notice that the peak of the histogram is at 2 and the long tail of values is to the right of the peak.
Hence, the histogram is skewed right.
Now, notice the boxplot, the whisker is longer on the right side of the box.
Hence, the distribution of the boxplot is skewed right.
Statement 2: Both displays show the data is skewed left.
The above statement is incorrect. (because statement 1 is correct)
Statement 3: Only the histogram indicates the number of patients in the sample.
The above statement is correct.
You can calculate the total number of patients in the sample by adding up the heights of all bars in the histogram.
On the other hand, there is no indication of the number of patients in the boxplot.
Statement 4: The box plot shows the mean number of colds was 2.
The above statement is incorrect because a box plot gives us the median value, not the mean.
Statement 5: The box plot shows the median number of colds was 2.
The above statement is correct.
The median of the box plot is the middle value of the box which is exactly 2.
Hence, the median of the box plot is 2.
Summary:
Statements 1, 3, and 5 are correct.
Related Questions
There is no time help quickly please
Answers
The piece-wise function graphed is defined as follows:
f(x) = 2x - 5, if x > 1.f(x) = 4x - 3, if x ≤ 1.The parameters are as follows:
a = 1.b = -5.c = 4.d = -3.What is a piecewise-defined function?A piecewise-defined function is a function that has different definitions, depending on the input of the function.
In this problem, the graphed function has to definitions, as follows:
To the left and equals to x = 1.To the right(greater) than x = 1.To the left of x = 1, the linear function has:
Intercept of -3, as it crosses the y-axis at y = -3.Slope of 4, as when x increases by 1, y increases by 4.Thus the definition is:
f(x) = 4x - 3, if x ≤ 1.
Thus the parameters are c = 4 and d = -3.
To the right of x = 1, the linear function has:
Slope of 2, as when x increases by 1, y increases by 2.Intercept of -5, as when x = 1, y = -3, considering the slope, when x = 0, y = -5.Thus the definition is:
f(x) = 2x - 5, if x > 1.
The parameters are a = 2 and b = -5.
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find the point-slope equation . use first point in your equation
Answers
Given:
[tex]The\text{ given points are \lparen-10,-20\rparen and \lparen1,-9\rparen.}[/tex]Required:
We need to find the point-slope equation of the line that passes through the given points.
Explanation:
Consider the point-slope form of the equation.
[tex]y-y_1=m(x-x_1)[/tex]Consider the slope formula.
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex][tex]Substitute\text{ }y_2=-9,y_1=-20,x_2=1,\text{ and }x_1=-10\text{ in the slope formula.}[/tex][tex]m=\frac{-9-(-20)}{1-(-10)}[/tex][tex]m=\frac{-9+20}{1+10}[/tex][tex]m=\frac{11}{11}[/tex][tex]m=1[/tex]Use the first point (-10,-20) in the point-slope equation.
[tex]Substitute\text{ }m=1,\text{ }x_1=-10,\text{ and }y_1=-20\text{ in the point-slope form of equation}[/tex][tex]y-(-20)=(1)(x-(-10))[/tex]Final answer:
[tex]y-(-20)=(1)(x-(-10))[/tex]a circle circumference is approximately 76 cm. estimate the radius, diameter and area of the circlethe only answers we have to choose from are 440, 460 and 480
Answers
the area of the circle is 460 cm²
Explanation:circumference of a circle = 2πr
r = radius
let π = 3.14
circumference of the circle = 76cm
76 = 2 × 3.14 × r
76 = 6.28× r
76 = 6.28r
76/6.28 = 6.28r/6.28
r = radius = 12.1cm
Diameter = 2 × 12.1cm = 24.2cm
Area of a circle = πr²
Area = 3.14 × (12.1)²
Area = 459.7 cm²
Approximately to the nearest whole number, the area of the circle is 460 cm²
Which of the following does not describe the graph below?A. The y-intercept is (0, -3).B. The x-intercept is (6, 0).C. The slope is 1/2.D. The change in the y-values is 6, & the change in the x-values is 3.
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D.
1) Looking attentively at the graph
The following option does not describe
Let's check the slope
The option that does not describe is
D.
Because the
A, B and C are true.
And the change in the y values is -3, and the change in x- value is 6.
Translate the figure 2 units right and 2 units down.
Plot all of the points of the translated figure.
You may click a plotted point to delete it.
Answers
Answer:
Look at the picture attached.
Un avión de pasajeros hizo un viaje de ida y vuelta a Las Vegas. En el viaje de ida voló a 432 mph y en el viaje de regreso a 480 mph. ¿Cuánto tiempo tomó el viaje allí si el viaje de regreso tomó nueve horas?
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The time taken for the trip if the return trip was 9 hours is 17 hours.
How to calculate the time?The outward journey used 432 mph. The return journey was 480 mph and this was for 9 hours.
Let the time taken for the initial trip be x. This will be:
x/9 = 432 / 48
Cross multiply
480x = 432 × 9
x = (432 × 9) / 480
x = 8
Therefore, the initial trip was 8 hours.
The time taken for the whole trip will be:
= Outward trip + Return trip
= 8 hours + 9 hours
= 17 hours.
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The width of a rectangle is 3 less than twice the length, x. If the perimeter of the rectangle is 36 feet. Find length and width.
Answers
The length of the rectangle is given to be x.
The width of a rectangle is 3 less than twice the length. This can be written mathematically to be:
[tex]\begin{gathered} \text{Twice the length }\Rightarrow2x \\ \text{Three less }\Rightarrow2x-3 \end{gathered}[/tex]Therefore, we will have the rectangle to look as shown below:
The formula to calculate the perimeter of a rectangle is given to be:
[tex]P=2(l+w)[/tex]Given that we have the following parameters:
[tex]\begin{gathered} P=36 \\ l=x \\ w=2x-3 \end{gathered}[/tex]Substituting these values, we can get the value of x as shown below:
[tex]\begin{gathered} 36=2(x+2x-3) \\ 36=2(3x-3) \\ 36=6x-6 \\ 6x=36+6 \\ 6x=42 \\ x=\frac{42}{6} \\ x=7 \end{gathered}[/tex]Given that the length has been calculated, we can get the width to be:
[tex]\begin{gathered} w=2(7)-3 \\ w=14-3 \\ w=11 \end{gathered}[/tex]ANSWER
The length of the rectangle is 7 feet and the width of the rectangle is 11 feet.
Find the volume of the sphere. Round your answers to the nearest tenth ifnecessary. Use 3.14 for pi.A. 5.6 inB. 4.2 inC. 1.6 inD. 6.3 in1 in.
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1) Given that the volume of the spherehe volume of the sphere
Does [4/7 8/14] have an inverse? Why or why not?
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Solution:
The matrix is given below as
[tex]\begin{bmatrix}{4} & {8} \\ {7} & {14}\end{bmatrix}[/tex]Calculate the determinant of the matrix below
The determinant of the matrix is
[tex]\begin{gathered} (14\times4)-(8\times7) \\ =56-56 \\ =0 \end{gathered}[/tex]The inverse of a matrix is calculated using the formula below
[tex]\begin{gathered} A^{-1}=\frac{adjA}{|A|} \\ |A|=0 \end{gathered}[/tex]Hence,
The final answer is
NO,THE DETERMINANT IS ZERO
OPTION D is the right answer
Choose the method (graphing, substitution, or elimination) that is best to solve each system.
Answers
Solution:
We will solve the system of equation by substitution method
[tex]\begin{gathered} y=3-x------------(1) \\ 5x+3y=-1-----------(2) \end{gathered}[/tex][tex]\begin{gathered} Substitute\text{ y=3-x into equation \lparen2\rparen} \\ 5x+3(3-x)=-1 \\ 5x+9-3x=-1 \\ 2x+9=-1 \\ 2x=-1-9 \\ 2x=-10 \\ x=-\frac{10}{2} \\ x=-5 \end{gathered}[/tex]Substitute x = -5 into equation (1)
[tex]\begin{gathered} y=3-(-5) \\ y=3+5 \\ y=8 \end{gathered}[/tex]Thus, x = -5, y= 8
Hello my answer was wrong. Can I have some help
Answers
The perpendicular line is
x = 4
Explanation:Parameters:
Line: y = -3
Point: (4, -6)
If two lines are perpendicular, then the slope of one is the negative reciprocal of the slope of the other.
The slope of the line:
y = -3
is zero
The negative reciprocal of 0 is -1/0, which is undefined.
Hence, we say the perpendicular line is:
x = k
Where k is any real number.
Examples of the perpendicular lines are:
x = 1, x = 2, x = 1/2, etc
Now, given the point (4, -6), we put x = 4 in the line x = k, so that
k = 4.
Therefore, the required perpendicular line is:
x = 4
Graph:
The graph of y = -3 is a horizontal straight line that cuts through -3 on the y-axis
The graph of x = 4 is a vertical straight line that cuts through 4 on the y-axis.
Question found in screenshot, it's only one question however, NOT 3.
Answers
Step 1
Given the function f defined in the question
Required: To find a relationship between a and b so that f is continuous at x=2
Step 2
[tex]\lim _{x\rightarrow2^-}f(x)\text{ = }a(2)^2+b(2)[/tex][tex]\lim _{x\rightarrow2^-}f(x)=4a+2b[/tex][tex]\lim _{x\rightarrow2^{+^{}}}f(x)=5(2)-10=0[/tex]Step 3
For f to be continuous
[tex]\lim _{x\rightarrow2^-}f(x)=\lim _{x\rightarrow2^+}f(x)_{}[/tex]Hence,
[tex]\begin{gathered} 4a+2b=0 \\ \text{Subtract 2b from both sides} \\ 4a+2b-2b=0-2b \\ \text{simplify} \\ 4a=-2b \\ or \\ -2b=4a \end{gathered}[/tex][tex]\begin{gathered} \text{Divide through by -2} \\ \frac{-2b}{-2}=\frac{4a}{-2} \\ b=-2a \end{gathered}[/tex]Hence, the relationship between a and b so that f(x) is continuous at x= 2 is seen below as;
b=-2a
A player threw a ball from point P to 3rd Base. How far did the player throw the ball? Round the answer to the nearest foot.A).210ftB).150ftC).127ftD).79ft
Answers
Answer:
B).150ft
Explanation:
The distance from homeplate to 1st Base = 90 feet
Therefore: distance from homeplate to point P is:
[tex]90+30=120ft[/tex]The distance from homeplate to 3rd base is 90 feet.
We see that the problem forms a right-triangle where the distance from point P to 3rd Base is the Hypotenuse.
Using Pythagoras Theorem:
[tex]\begin{gathered} \text{Distance}^2=120^2+90^2 \\ Dis\tan ce=\sqrt[]{120^2+90^2} \\ =\sqrt[]{22500^{}} \\ =150ft \end{gathered}[/tex]The player threw the ball a distance of 150 feet.
Find the equation of a line that goes through the point ( 1,- 6 ) and is perpendicular to the line: y = (1 / 8)x - 9
Answers
Step 1
Given;
[tex]\begin{gathered} y=\frac{1}{8}x-9 \\ with\text{ points \lparen1,-6\rparen} \end{gathered}[/tex]Required; Find the equation of a line that goes through the point ( 1,- 6 ) and is perpendicular to the line: y = (1 / 8)x - 9
Step 2
For perpendicular lines, the relationship between the slopes is;
[tex]m_1=-\frac{1}{m_2}[/tex][tex]\begin{gathered} m_1=\frac{1}{8} \\ \frac{1}{8}=-\frac{1}{m_2} \\ m_2=-8 \end{gathered}[/tex]The y-intercept is found thus;
[tex]\begin{gathered} y=-8x+b \\ b=y-intercept \\ y=-6 \\ x=1 \\ -6=-8(1)+b \\ b=-6+8=2 \end{gathered}[/tex]Answer; The required equation will be;
[tex]y=-8x+2[/tex]Hello! I need some assistance with this homework question, pleaseQ3
Answers
difference quotient (option B)
Explanation:[tex]\frac{f(x\text{ + h) - f(x)}}{h}[/tex]The above shows the rate of change over an interval a, b:
[tex]\begin{gathered} \frac{f(b\text{) - f(a)}}{b\text{ - a}} \\ \text{where f(b) = f(x + h)} \\ f(x)\text{ = f(a)} \\ h\text{ = b - a} \end{gathered}[/tex]The term that is used to refer to the rate of change over an interval is difference quotient (option B)
The following figure shows ABC with side links to the nearest 10th find m
Answers
We have to find the measure of angle at vertex B.
We can use the Law of sines, that let us write proportions between the sine of an angle of the triangle and the sides.
This law tells us that the quotient between the sine of an angle of the triangle and the length of the opposite side is equal for each of the three angles of the triangle.
So in this case we can write:
[tex]\frac{\sin(C)}{AB}=\frac{\sin (B)}{AC}[/tex]We can replace the values we already know and calculate the measure of B as:
[tex]\begin{gathered} \sin (B)=\frac{AC}{AB}\cdot\sin (C) \\ \sin (B)=\frac{10}{14}\cdot\sin (59\degree) \\ \sin (B)\approx\frac{10}{14}\cdot0.857 \\ \sin (B)\approx0.612 \\ B\approx\arcsin (0.612) \\ B\approx37.75\degree \end{gathered}[/tex]Answer: B = 37.75°
Subtracting a positive and adding a negative number are completely different operations. O True O False
Answers
subtracting a positive number
4 - 2 = 2
Adding a negative number
4+ (-2) = 4 - 2 = 2
So they are not completely different operations.
Answer : FALSE
Round to the nearest whole number if needed and look at the picture for accurate description
Answers
The total side area of the figure is 72.8 square inches and the volume is 32 cubic inches.
To solve this, first lets calculate the area of one of the rectangular sides of the object:
Since it's a rectagle of base 2' and height 7', the area is:
[tex]2^{\prime}\cdot7^{\prime}^{}=14in^2[/tex]There are 4 side like this, so we need to multiply it by 4:
[tex]14in^2\cdot4=56in^2[/tex]Next we can calculate the area of the square base. It's a square of side 2', then:
[tex](2^{\prime})^2=4in^2[/tex]Finally, we need to calculate the area of the piramid on top. Let's find out the area of each triangle.
SInce s = 3.2' is the slant height of the pyramid, that's the height of the triangle, and the base is the same as the whole object: 2'
Then we can use the formula for the area of a triangle:
[tex]A=\frac{h\cdot b}{2}[/tex]Thus:
[tex]\frac{3.2^{\prime}\cdot2^{\prime}}{2}=3.2in^2[/tex]Before add all, we calculated the area of just one triangle, since there is 4 in the object, we need to multiply by 4:
[tex]3.2in^2\cdot4=12.8in^2[/tex]And now we can add all:
[tex]56in^2+4in^2+12.8in^2=72.8in^2[/tex]Now for the volume, we can calculate first the volume of the pyramid:
[tex]Volume\text{ of a pyramid=}\frac{b^2h}{3}[/tex]The base of the pyramid is 2' and the height is 3', then:
[tex]\frac{(2in)^2\cdot3in}{3}=4in^3[/tex]For the rectangular prism, we need to multiply the base times the width times the height.
[tex]7^{\prime}\cdot2^{\prime}\cdot2^{\prime}=28in^3[/tex]Added:
[tex]23in^3+4in^3=32in^3[/tex]Then the final answer is 72.8 square inches for the total area and 32 cubic inches for the total volume
Kurt earns $6 a week for doing chores. How many weeks will it take him toearn50 if he has already earned $10? Explain how you found your answer
Answers
Kurt already has $10 and he earns $6 per week.
Then, the number n of weeks that it will take to Kurt earn reach $50 is given by:
n = (50 - 10)/6 = 40/6 = 20/3 = 6.67
If we round this result to a whole number, we will find that it will take 7 weeks to Kurt earn $50.
graph the circle which is centered at (-1,0.5) and has a radius of 3.5 units
Answers
Step 1. Find the center
Step two
Graph a circle
Remember the radius is 3.5 units in order to know that, we need to have a point of 3.5 units of the center to the left, to the right, up and down and then we can obtain the graph of the circle
Find the value of X, Given that OP II NQ
Answers
Given that:
ON = 9, PQ = x, OP = y, NM = 18, QM = 20
From the figure, the triangles OPM and NQM are similar. Hence their sides are proportional, that is,
[tex]\frac{NM}{OM}=\frac{QM}{PM}[/tex]Plug the given values into the equation.
[tex]\frac{18}{27}=\frac{20}{20+x}[/tex]Cross-multiply and simplify to find x.
[tex]\begin{gathered} 20+x=20\cdot\frac{27}{18} \\ =30 \\ x=30-20 \\ =10 \end{gathered}[/tex]Hence the value of x is 10.
Mr. Goldstein is driving to Houston. The equation y = -45x + 270 represents the numbers of miles that he still has to travel after driving for x hours. What is the slope of the line and what does it represent in this situation
Answers
The slope is -45, and it represents the number of driving miles per hour.
Explanation:The given equation is:
y = -45x + 270
The slope is -45, and it represents the number of driving miles per hour.
if p(x)=3x^2+5x-8 then find p(-2)
Answers
P(x) = P(-2)
P(-2) = 3(-2)^2 + 5(-2)-8
= 3(4) + (-10) - 8
= 12 + (-10 -8)
= 12 + (-18)
= 12 - 18
= - 6
P(-2) = -6
(divided on both sides by -2)
Answer:
P = 3
(btw i am not sure if this is the answer you are looking for. Please clarify ths objective of this equation. What are we looking for? Are we solving for "P" ?)
Write the equation of the line passing through point (-5, -4) and parallel to y = -3
Answers
A line parallel to a horizontal line is also horizontal.
The equation of the line parallel to
[tex]y=-3[/tex]is of the form
[tex]y=b[/tex]Since, the line passes through (-5,-4), the value of b is -4
So, the required equation is
[tex]y=-4[/tex]Hence, the correct option is (c)
A. Step 1B. Step 1C. Step 3D. Olga did not make a mistake
Answers
SOLUTION
Let's solve the question and see where Olga made a mistake
The question is
[tex]\frac{1}{4}(\frac{1}{3}k+9)=6[/tex]Solving this we have
[tex]\begin{gathered} \frac{1}{4}(\frac{1}{3}k+9)=6 \\ \\ multiplying\text{ both sides by 4} \\ \\ \frac{1}{4}(\frac{1}{3}k+9)\times\frac{4}{1}=6\times4 \\ \\ (\frac{1}{3}k+9)=24 \end{gathered}[/tex]Next step we move 9 to meet 24, we have
[tex]\begin{gathered} (\frac{1}{3}k+9)=24 \\ \\ \frac{1}{3}k=24-9 \\ \\ \frac{1}{3}k=15 \end{gathered}[/tex]Now multiply 3 to both sides
[tex]\begin{gathered} \frac{1}{3}k\times3=15\times3 \\ \\ k=45 \end{gathered}[/tex]Therefore k = 45 and not 5. So Olga made a mistake in the last step, which is step 3. So the answer is step 3
If u3i + 7j and v=8i + 1j, find the angle between them.
Answers
STEP 1
Establish the problem.
We need to find the angles the vectors given make with the horizontal.
The vectors are given in unit vector form and will require diagrammatic representation as well.
u = 3i + 7j means vector u goes 3 units along the x asis and 7 units along the y axis
v = 8i + j means vector u goes 8 units along the x asis and 1 units along the y axis
We now get the plot.
STEP 2:
Get angles that the two vectors make with the horizontal and subtract to get answer.
Angle u to the horixontal is given as:
[tex]\begin{gathered} \text{Tan }\theta=\frac{y\text{ coordinate}}{x\text{ coordinate}} \\ \text{Tan u}=\frac{7}{3} \\ u=tan^{-1}(\frac{7}{3})=66.8\text{ degrees} \end{gathered}[/tex]Angle v to the horixontal is given as:
[tex]\begin{gathered} \text{Tan }\theta=\frac{y\text{ coordinate}}{x\text{ coordinate}} \\ \text{Tan u}=\frac{1}{8} \\ u=tan^{-1}(\frac{7}{3})=7.1\text{ degrees} \end{gathered}[/tex][tex]\text{Therefore, the angle between the two is given as }\theta=\text{ 66.8 - 7.1 = 59.7 degrees}[/tex]Find the length of the size not given when the hypotenuse is c and the legs are a and b
Answers
Take into accoun that the Pythagorean theorme is given by:
c² = a² + b²
8.
a = ?, b = 18, c = 30
solve the equation for a:
c² = a² + b²
a² = c² - b²
a = √(c² - b²) replace the values of c and b
a = √(30² - 18²)
a = √(900 - 324)
a = √(576)
a = 24
9.
c= ?, a = 5, b = 12
replace the values of b and a:
c = √(a² + b²)
c = √(5² + 12²)
c = √(25 + 144)
c = √(169)
c = 13
10.
b = ?, a = 6, c = 10
solve the equation for b:
b = √(c² - a²)
b = √(10² - 6²)
b = √(100 - 36)
b = √(64)
b = 8
Question attached as screenshot below, it's hard calculus please only accept if you are capable.
Answers
The given position vector is
[tex]S(t)=\frac{t^3}{3}-\frac{15t^2}{2}+50t[/tex]N0w the velocity will be
[tex]v(t)=t^2-15t+50[/tex]Now,
[tex]\begin{gathered} v(t)\ge0,0\leq t\leq5,10\leq t\leq12 \\ v(t)<0,5So if the initial direction of the particle is towards the right, then in the interval 5And if the initial direction of the particle is towards the left then the particle will move towards the right in the interval 5
The graph shows the function y = q*
a) Give the coordinates of the point of intersection
of the curve with the y-axis.
b) Find the value of q.
50-
q=
c) Work out the value of y when x = 10
y =
40-
30-
20-
10-
N
3
4X
Answers
The answers to the graph that shows the function y = q* are solved and stated above.
What is exponential function?The exponential function is a mathematical function denoted by the expression as - f(x) = eˣReal exponential function is commonly defined by the following power series as -[tex]$e^{x} =\sum _{k=0}^{\infty }{\frac {x^{k}}{k!}}=1+x+{\frac {x^{2}}{2}}+{\frac {x^{3}}{6}}+{\frac {x^{4}}{24}}+\cdots }[/tex]
Given is a exponential graph as shown in the image.
( 1 ) -The coordinates of the point of intersection of the curve with the y-axis is (0, 1).
( 2 ) -The function is -
y = qˣ
At x = 1, y = 4. So, we can write -
4 = q
q = 4
( 3 ) -y = 4ˣ
y = 4¹⁰
y = 64 x 64 x 64 x 4
y = 1048576
Therefore, the answers to the graph that shows the function y = q* are solved and stated above.
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simplify: 2a^6 b^6)(3a^-5 b^-7)
Answers
Use power properties to simplify the expression:
[tex]\begin{gathered} a^{-5}=\frac{1}{a^5} \\ b^{-7}=\frac{1}{b^7} \end{gathered}[/tex][tex]\begin{gathered} (2a^6b^6)(3a^{-5}b^{-7}) \\ (2a^{6^{}}b^6)(\frac{3}{a^5b^7}) \\ 6\cdot\frac{a^6}{a^5}\cdot\frac{b^6}{b^7} \\ \frac{6a}{b} \end{gathered}[/tex]