a) What were the ranges of typing speeds for the two groups?Group 1: Group 2:b) Which group had more typing speed in the 40s1) Group 1 2)Group 2 3) Each had the samec) Which group had the greater median typing speed?1) Group 1 2)Group 2 3) Each had the same
Answers
The given stem and leaf plot shows the typing speeds of two groups of students.
Group 1 has n1= 20 students
Group 2 has n2= 19 students
The stem and leaf plot is two sided, meaning that they share the same stem.
The observed values are the number of words per minute.
In the steam the ten of each value is placed and in the leafs you find the units:
This way you can determine the observations for both samples. I'll do so and arrange them form least to greatest:
Group 1:
33, 34, 37, 42, 44, 44, 45, 47, 48, 49, 49, 50, 51, 52, 52, 55, 55, 63, 66, 67
Group 2:
33, 36, 41, 42, 44, 46, 46, 51, 52, 52, 52, 53, 53, 56, 59, 60, 66, 67, 69
Part a
The range is calculated as the difference between the maximum and minimum observations of a sample. To determine those values you need the sample ordered from least to greatest.
For group 1:
Minimum value: 33 words/min
Maximum value: 67 words/min
Range= maximum-minimum=67-33=34words/min
For group 2:
Minimum value: 33words/min
Maximum value: 69 words/min
Range: 69-33=36words/min
→ the range for group 1 is 34words/min while the range for group 2 is 36words/min
Part b
To determine which group had more typing speeds in the fourties you have to count said observations for both of them.
You can do it directly from the stem and leaf plot, go to the row correpsonding to the 4 in the plot and count or use the values:
For group 1: in the second row there are 8 leafs, corresponding to the observations: 42, 44, 44, 45, 47, 48, 49, 49,
For group 2: in the second row there are 5 leafs, corresponding to the observations: 41, 42, 44, 46, 46
→There are more typing speeds in the 40s in group 1.
Part c:
The median is a measure of center that divides the sample in two halves. To calculate it you have to determine its position and then look for the corresponding value in the sample that was previously ordered from least to greatest.
To determine the position of the mean you have to use the following fomula:
For even samples: n/2
For odd samples: (n+1)/2
Median of group 1
n1=20 students
The sample is even, calculate its position using the first formula:
Position: n/2 = 20/2= 10
The median is in the tenth position, look in the sample for the tenth observation:
33, 34, 37, 42, 44, 44, 45, 47, 48, 49, 49, 50, 51, 52, 52, 55, 55, 63, 66, 67
→The median typing speed for group 1 is 49 words/min
Median of group 2
n2=19 students
The sample is odd, you have to use the second formula to find its position:
Position: (n+1)/2= (19+1)/2= 20/2= 10
The median of this group is the 10th observation:
33, 36, 41, 42, 44, 46, 46, 51, 52, 52, 52, 53, 53, 56, 59, 60, 66, 67, 69
→The median typing speed for group 2 is 52 words/min
→Group 2 has the greater median typing speed.
Related Questions
A length measure can never be more than one half unit in error. why is this the case?can someone please answer this question.
Answers
Answer:
This is because the degree of accuracy is half a unit each side of the unit of measure
[tex]\text{When an instrument measures in '1' s any value betwe}en\text{ 6}\frac{1}{2}\text{ and 7}\frac{1}{2\text{ }}\text{ is measured as 7}[/tex]
Use a 30 - 60 - 90 triangle to find the tangent of 60 Degrees
Answers
Let's put more details in the given figure to better understand the solution:
Let's now determine the Tangent of 60 degrees:
[tex]\text{ Tangent (60}^{\circ})\text{ = }\frac{\text{ Opposite}}{\text{ Adjacent}}[/tex][tex]\text{ = }\frac{\text{ }\sqrt[]{3}}{1}[/tex][tex]\text{ Tangent (60}^{\circ})\text{ = }\sqrt[]{3}[/tex]Therefore, the tangent of 60 degrees is √3.
The answer is Option 1 : √3
Suppose a binomial trial has a probability of success of 0.3 and 450 trials are performed. What is the standard deviation of the possible outcomes?6.3614.8511.629.72
Answers
The standard deviation of a binomial distribution with n trials and a probability of success of p is given by the formula:
[tex]\sigma=\sqrt[]{n\cdot p\cdot(1-p)}[/tex]From the problem, we identify:
[tex]\begin{gathered} n=450 \\ p=0.3 \end{gathered}[/tex]Then:
[tex]\begin{gathered} \sigma=\sqrt[]{450\cdot0.3\cdot(1-0.3)}=\sqrt[]{450\cdot0.3\cdot0.7} \\ \sigma\approx9.72 \end{gathered}[/tex]1. Given the points Al-1, 2) and B(7, 8), find the coordinates of the polnt P on the directed line segment JB that partitions AB in the ratio 1:3. Plot P along with segment AB. 10 B 6 (x,y) = (x1+k(x2 - x2),y. +k(y2-y) 2 210182632 2 68 110 2 24 6 8 -10 2. Find the coordinates of P so that P partitions AB in the ratio 5.1 with A(2, 4) and B(8, 10). L 3. Find the coordinates of P so that P partitions AB in the ratio 1 to 3 with A(-5, 4) and B(7,-4). 4. Find the coordinates of P so that P partitions AB in the ratio 3:4 with A(-9, -9) and B(5,-2).
Answers
We can find the point with help of the end points and the ratio so:
[tex]\begin{gathered} x=-1+\frac{1}{1+3}(7-(-1)) \\ x=-1+\frac{1}{4}8 \\ x=-1+2 \\ x=1 \end{gathered}[/tex]now for y:
[tex]\begin{gathered} y=2+\frac{1}{1+3}(8-2) \\ y=2+\frac{1}{4}6 \\ y=3.5 \end{gathered}[/tex]So now we can graph it so:
POSThe expression(-4)(x) is equivalent to the expression x”. What is the value of n?n =
Answers
given expression:
[tex]\mleft(-4\mright)\mleft(x\mright)=x^n[/tex]To find the value of n.
[tex]\begin{gathered} \ln \mleft(\mleft(-4\mright)x\mright)=n\ln \mleft(x\mright) \\ n=\frac{\ln\left(-4x\right)}{\ln\left(x\right)} \end{gathered}[/tex]What is the difference between the decimal forms of rational numbers and the decimal forms of irrational numbers?
Answers
The decimal forms of rational numbers can be finite, i.e. have a non infinite number of digits. In case they have infinite digits then these are periodic. This means that there's a patron of digits that is repeated infinitely.
Irrational numbers on the other hand can only have infinite digits on their decimal form and they are not periodic.
Simplify: 8z + 5y + 6z + Зу * O 14z + 8y 13y + 9z O 22y 22z
Answers
Answer:
14z + 8y
Explanation:
Given the equation 8z + 5y + 6z + Зу
first is to collect the like terms;
8z + 5y + 6z + Зу
= (8z + 6z) + (5y + 3y)
= 14z + 8y
Hence the simplified form is 14z + 8y
Aline has a slope of -3/4 and a y-intercept of 5. Write an equation insiope-intercept for that could represent this situation."
Answers
Here, we want to write an equation in the slope-intercept form
Mathematically, we have this as;
[tex]y\text{ = mx + b}[/tex]b is the slope and m is the y-intercept
Thus, substituting the values we have in the question;
m = -3/4 and b = 5
Thus, we have the equation as;
[tex]y\text{ = -}\frac{3}{4}x\text{ + 5}[/tex]determine whether or not each equation is a linear equation in two variables. if so, identify a b and c a. 2x =5 + yb. y = 5x + 3
Answers
Given:
Linear equation in x and y:
An equation of the form y = mx + c or ax + by +c =0 is a linear equation as the degree of both variables x and y is one.
(a) 2x = 5 + y:
The equation can be written as:
[tex]y=2x-5\text{ or 2x-y-5=0}[/tex]This is of the form of ax+by+c=0 so it is linear.
Here, a=2, b= 1, c= - 5
(b) y = 5x + 3:
[tex]y=5x+3\text{ or 5x-y+3=0}[/tex]This is already in the form of ax + by+ c=0 so it also linear.
Here, a= 5 , b = - 1, c= 3
33<=105/p what is the answer
Answers
The answer is p≤35/11.
From the question, we have
33≤105/p
⇒p≤105/33
⇒p≤35/11
Inequality:
The mathematical expression with unequal sides is known as an inequality in mathematics. Inequality is referred to in mathematics when a relationship results in a non-equal comparison between two expressions or two numbers. In this instance, any of the inequality symbols, such as greater than symbol (>), less than symbol (), greater than or equal to symbol (), less than or equal to symbol (), or not equal to symbol (), is used in place of the equal sign "=" in the expression. Polynomial inequality, rational inequality, and absolute value inequality are the various types of inequalities that can exist in mathematics.
When the symbols ">", "", "", or "" are used to connect two real numbers or algebraic expressions, that relationship is known as an inequality.
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Please help me I don’t know if I’m right or missing any other to select.
Answers
The given equations are
[tex]-x+4y=7[/tex][tex]6x-3y=42[/tex]To find the answer we need to cancel out x or y.
so we have to find the LCM of the coefficients of the corresponding variable.
consider the coefficients of x is -1 in the first equation and 6 in the second equation .
Lcm of -1 and 6 is 6.
Multiplying the first equation by 6.
consider the coefficients of y is 4 in the first equation and -3 in the second equation .
Lcm of 4 and 3 is 12
Multiplying the first equation by 3 and the second equation by 4.
Either one of these is the first step to eliminate variables.
Amswer os
[tex](x + 4)x + 5)[/tex]write the equivalente expression
Answers
given that (x+4) (x+5) and they are asking for equivalent form.
at first both terms are in multiplication form,so multiply x with (x+5) so we get that
[tex](x+4)(x+5)=x^2+5x+4x+20=x^2+9x+20[/tex]Select all inputs for which f (x)=2A:x=-7B:x=0C:x=4D:none of the above
Answers
To answer this question, we need to see the graph of the function carefully.
For x = -7, we can see that the function is equal to 2, that is:
[tex]f(-7)=2[/tex]For x = 0, we have that the function is equal to -1, that is:
[tex]f(0)=-1[/tex]For x = 4, we have that the function is equal to -2, that is:
[tex]f(4)=-2[/tex]We need to find the value of x. Then, we have to find the point where we "touch" the function, and then find the y-value of the function.
Therefore, in summary, we have that the only input for which f(x) = 2 is when x = -7 (option A).
Complete the ratio table of the median price of renting a two-bedroom apartment by finding the value of x and y. Round answers to two decimal places. Norfolk $951 Richmond $1,042 1 X Х 100 у To solve the values set up and solve a a. Bar Chart b. Ratio c. Proportion d. Weighted Average x = y =
Answers
2+4=6 is true
7*8=56 is true
So the statement 2+4=6 AND 7*8=56 is also true
So the answer for question #36 is a) the statement is true because both proporsitions are true
One thermos of hot chocolate uses 2/3 cup of cocoa powder. How many thermoses can nalli make with 3 cups of cocoa powder?
Answers
In order to determine the number of thermos, divide by 3 by 2/3, as follow:
[tex]\frac{\frac{3}{1}}{\frac{2}{3}}=\frac{3\cdot3}{1\cdot2}=\frac{9}{2}=4.5[/tex]the previous result means that nalli can make four and one hal thermoses with 3 cups of cocoa powder.
state the solution for the quadratic equation depicted in the graph.
Answers
For this problem, we were provided with the graph of a quadratic equation, and we need to determine the solutions for this graph.
The solutions of a quadratic equation are the values of "x" that make the expression equal to "0". Therefore, we need to look at the graph for the values at which the graph crosses "y=0".
We have two points for this problem. The first one is approximately -5, and the second is 6.
Find the area of each circle. Round to the nearest tenth.Only 1 and 2
Answers
Explanation
The area a circle can be expressed in two forms;
[tex]\begin{gathered} \text{Area}=\pi r^2 \\ \text{Area}=\pi(\frac{d}{2})^2 \\ \end{gathered}[/tex]Where r and d are the radius and the diameter of the circle.
Therefore;
For number 1, r =21 yards,
[tex]\text{Area}=\pi\times21^2=1385.4\text{square yards}[/tex]Answer: 1385.4 square yards
For number 2, d= 0.4 km
[tex]\text{Area}=\pi\times(\frac{0.4}{2})^2=\pi\times0.2^2=0.1km^2[/tex]Answer:0.1 square kilometres
Given the table below, write a linear equation that defines the dependent variable, c, in terms of the independent variable, a.
Answers
For a linear equation, the first step is to find the slope.
Based on the table, I see that every time "t" increases by 1, then "k" increases by 4.
Since we're told k is the dependent variable, the slope will be
[tex]\dfrac{\text{change in }k}{\text{change in }t}} = \dfrac{4}{1} = 4[/tex]
The slope is always [tex]\dfrac{\text{change in dependent variable}}{\text{change in independent variable}}[/tex].
Once you have the slope, you need the vertical (We'd normally call this this y-intercept, but there's no "y" here. You could call it the "k" intercept in this example.)
From the table, we again see that t=0 has k=2, so that 2 is the value we need.
This gives us our equation: k = 4t + 2.
(This all is really just the slope-intercept form with x's now being called "t" and y's now being called "k".)
An animal shelter provides a bowl with 1.35 liters of water for 6 cats.About how much water will be left after the cats drink their average daily amount of water?Water ConsumptionAverage Amount(Liters per day)AnimalCanada Goose0.24Cat0.15Mink0.10Opossum0.30Bald Eagle0.16liter(s) of water will be left after the cats drink their average daily amount of water.
Answers
Data
1.35 litres of water
6 cats
0.15 litres per day
Procedure
Amount of water taken by the 6 cats
[tex]0.15\cdot6=0.9[/tex]Left
[tex]1.35-0.9[/tex]0.45 litres of water will be left
Write the following decimal numbers as a fraction: • One hundred and twenty four hundredths • Five tenths 5/10 Twenty seven thousandths Fifty two and nine hundredths
Answers
ANSWER:
10024/100
5/10
27/1000
5209/100
STEP-BY-STEP EXPLANATION:
The first thing is to convert the writing into a decimal number and then convert it into a fraction, just like this:
One hundred and twenty four hundredths:
100.24 = 10024/100
Five tenths
0.5 = 5/10
Twenty seven thousandths
0.027 = 27/1000
Fifty two and nine hundredths
52.09 = 5209/100
Need immediate help on 2 questions for my test tomorrow
Answers
The data that can be determined from the box plots are
a)
This is because the line in the middle of the box plot is the median of the box plot.
b)
The upper quartile of a box plot is the part of the box plot that is to the right of the line. In this case the median line is at the same location and the upper quartile ends at the same location.
and
The data that can not be determined is
c)
The reason this can not be determined is because the median is the average of the grades. This could mean some students scored in the higher levels and more scored below the median, which in turn drags it down.
d)
Would be following the same reason as C. It can be determined that there was a larger range lower grades in period 5 over period 3, but it can't be determined how many.
Solve by substitution method. a) x + y = 8 and x - y = 4
Answers
Answer:
x = 6
y = 2
Step-by-step explanation:
x + y = 8 ---> (1)
x - y = 4 ---> (2)
First, let us find the value of x.
For that, add both equations.
(1) + (2)
x + y + ( x - y ) = 8 + 4
Solve the brackets.
x + y + x - y = 8 + 4
2x = 12
Divide both sides by 2.
x = 6
Now let us find the value of y.
For that, let us use equation 1 and replace x with 6.
x + y = 8
6 + y = 8
Subtract 6 from both sides.
y = 8 - 6
y = 2
M Find the range of possible diagonal lengths in a parallelogram with the given side lengths. 4. 3 and 12 5. x and 2x 6. x and x 812a, 25) F C12a + 2c, 25) The area of a parallelogram is given by the formula A=bh, where A is the area, b is the length of a base, and h is the height perpendicular to the base. ABCD is a parallelogram. E, F, G, and Hare the midpoints of the sides. 7. Show that the area of EFGH is half the area of ABCD. G A(0,0) D(200)
Answers
Here, we want to find the range of the diagonal length of a parallelogram measuring x by x units
From what we have, we can see that the sides are equal and what this mean is that we have a square with equal diagonal length from any of the sides
So to get the diagonal length, we use the Pythagoras' theorem since the dsigonal splits the square into two equal parts
Thus, we have;
[tex]\begin{gathered} d^2=x^2+x^2 \\ \\ d^2=2x^2 \\ \\ d\text{ = x}\sqrt[]{2} \end{gathered}[/tex]If you don’t need further explanation on this question, we can end the session. I’d really appreciate you letting me know how I did by rating our session after you exit. Thanks and have a great day!
A bag contains 25 cookies. There are 15 chocolate chip cookies, 7 peanut butter cookies, and the rest are oatmeal raisin cookies. What is the probability of randomly choosing a chocolate chip or peanut butter cookie from the bag? (Write your answer as a whole percent)
Answers
SOLUTION:
Case: Probability
Method:
Total= 25 cookies
Chocolate chip (C)= 15
Peanut butter (P)= 7
Oatmeal raisin (O)= 25 - 15 - 7
Oatmeal raisin= 3
The probability of randomly choosing a chocolate chip or peanut butter cookie from the bag.
[tex]\begin{gathered} Pr(CorP)=\frac{15+7}{25} \\ Pr(CorP)=\frac{22}{25} \end{gathered}[/tex]As a percentage, the percentage equivalence is:
[tex]\begin{gathered} Pr(CorP)=\frac{22}{25}\times100 \\ Pr(CorP)=22\times4 \\ Pr(CorP)=88 \end{gathered}[/tex]Final answer:
88%
Find the exponential function f(x)=Ca^x whose graph is given below.
Answers
Answer:
f(x) = 2[tex](\frac{1}{3}) ^{x}[/tex]
Step-by-step explanation:
exponential in the form
f(x) = C[tex]a^{x}[/tex]
to find C and a use points from the graph
using (0, 2 ) , then
2 = C[tex]a^{0}[/tex] ( [tex]a^{0}[/tex] = 1 ) , so
C = 2
f(x) = 2[tex]a^{x}[/tex]
using (2, [tex]\frac{2}{9}[/tex] )
[tex]\frac{2}{9}[/tex] = 2a² ( divide both sides by 2 )
[tex]\frac{1}{9}[/tex] = a² ( take square root of both sides )
[tex]\sqrt{\frac{1}{9} }[/tex] = a ⇒ a = [tex]\frac{1}{3}[/tex]
f(x) = 2 [tex](\frac{1}{3}) ^{x}[/tex] ← exponential function
Indenting the zeros and state their multiplicities describe the effect on the graph
Answers
Answer:
6) The given equation is,
[tex]f(x)=(x+7)^2(2x+1)(x-4)^3[/tex]we know that,
The number of times a given factor appears in the factored form of the equation of a polynomial is called the multiplicity.
we get,
Zero Multiplicity Effect
-7 2 Touches the x axis at x=-7
-1/2 1 Passese through the x axis at x=-1/2
4 3 Passes through the point and the curve bend at x=4
Lisa's rectangular living room is 20 feet wide. If the length is 5 feet less than twice the width, what is the area of her living room?
Answers
1) Let's gather all the data
Width: 20'
Length: 2w-5
2) Now we can plug that into the formula for the are of a rectangle, like this
[tex]\begin{gathered} A=wl \\ A=20\cdot(2(20)-5) \\ A=20\cdot(40-5) \\ A=20\cdot35 \\ A=700ft^2 \end{gathered}[/tex]Notice that we have plugged into that the width w=20. Therefore the area of the living room is 700ft²
Can someone pls help me with my homework I have to go to sleep so pls be fast
Answers
Okay, here we have this:
Let's calculate the slope (using the points: (2, 58.5) and (4, 107.5)):
m=(107.5-58.5)/(4-2)=49/2=24.5
Finally we obtain that the slope is 24.5, so this means that option III is incorrect.
And considering that the y intercept represents the value of y when x equals 0 (0 tickets sold), If a person does not buy any ticket, they should not pay anything, this means that the option IV isn't right.
So, finally we are only left with option I and II let's check them:
Replacing in function:
Total value = (number of tickets * cost per ticket) + service charge
2 Tickets:
58.5=(2*24.5)+9.5
58.5=49+9.5
58.5=58.5
4 Tickets:
107.5=(4*24.5)+9.5
107.5=98+9.5
107.5=107.5
8 Tickets:
205.5=(8*24.5)+9.5
205.5=196+9.5
205.5=205.5
12 Tickets:
303.5=(12*24.5)+9.5
303.5=294+9.5
303.5=303.5
20 Tickets:
499.5=(20*24.5)+9.5
499.5=490+9.5
499.5=499.5
Finally we obtain that the correct answer is the option A. Statements I and III.
A plater holds 24 strawbers,2 aplles,16 oranges.What fraction of all the fruits are strawberiias?Fracion of apples?Fraction of oranges?
Answers
The fraction for strawberries, apples, and oranges is 12/21, 1/21, and 8/21 respectively.
What are fractions?A fraction depicts a portion of an entire. This entire could be a location or a group of things. The Latin word "fraction," which means "to break," is where the word "fraction" comes from. In mathematics, a fraction is represented by a numerical value that designates a portion of an entire. The numerator displays how many pieces the whole has been divided into. It is positioned at the top of the fraction, beneath the fractional bar is the denominator.
Given,
Number of strawberries = 24
Number of apples = 2
Number of oranges = 16
So, the total number of fruits is given as
= 24 + 2 + 16
= 42
The fraction for strawberries = 24/42
=12/21
The fraction for apples = 2/42
= 1/21
The fraction for oranges = 16/42
=8/21
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Help me please so i can see if i’m on the rights track. if csc (θ) = 13/12 and 0° < θ < 90°, what is cos (θ)? write the answer in simplified, rationalized form.
Answers
Given in the question is:
[tex]\csc (\theta)=\frac{13}{12}[/tex]Recall the trigonometric identity:
[tex]\csc (\theta)=\frac{1}{\sin (\theta)}[/tex]Therefore, we have that
[tex]\sin (\theta)=\frac{12}{13}[/tex]Recall the trigonometric ratio:
[tex]\begin{gathered} \sin (\theta)=\frac{\text{opp}}{\text{hyp}} \\ \cos (\theta)=\frac{\text{adj}}{\text{hyp}} \end{gathered}[/tex]and, using the Pythagorean Theorem:
[tex]hyp^2=opp^2+adj^2[/tex]From the sin value, we have:
[tex]\begin{gathered} opp=12 \\ hyp=13 \\ \therefore \\ 13^2=12^2+adj^2 \\ 169=144+adj^2 \\ adj^2=169-144=25 \\ adj=\sqrt[]{25} \\ adj=5 \end{gathered}[/tex]Therefore, the value of cos(θ) is:
[tex]\sin (\theta)=\frac{5}{13}[/tex]