Answer:
Step-by-step explanation:
a) Number of variables in the data set : 5
b) A quantitative variable is the one which can be quantitatively measured. i.e. it is a numerical value.
A categorical variable is the one that can take one value from a limited number of fixed values.
Exchange is a Categorical Variable. Price/Earnings Ratio is a Quantitative Variable. Gross Profit Margin (%) is a Quantitative Variable.
c. Out of the 25 stocks, AMEX is the exchange for 5 stocks. So percent frequency is 5/25 = 0.2 = 20%.
NYSE is the exchange for 3 stocks. So percent frequency is 3/25 = 0.12 = 12%.
OTC is the exchange for 17 stocks. So percent frequency is 17/25 = 0.68 = 68%.
These percentages are correctly shown in graph a. So the answer is a.
d) The frequency distribution is
Gross Profit Margin Frequency
0-14.9 2
15-29.9 6
30-44.9 8
45.59.9 6
60.74.9 3
As we come across the Gross Profit Margin values in the table, we add a | next to its respective interval and build the above table. E.g. the first value in the table under Gross Profit Margin is 36.7 which lies in the interval 30–44.9. So we add one | in fromt of that interval and so on until we cover the entire table. The number of | shows the frequency distribution of the values.
The correct histogram is A.
e. The average price/earnings ratio is found by adding all the 25 values in the table and dividing the answer by 25.
= 505.40/25
= 20.2Graph the equation below by plotting the
y-intercept and a second point on the
line. When you click Done, your line will
appear
Answer:
Plot the y-intercept at (0, 2). Plot your second point at (-1, -1).
Step-by-step explanation:
I attached an image of what the finished graph should look like when you press done. *rotate the image so the grey is on the bottom*
The company produces two types of goods in quantities of x and y, with market prices of €40 and 80€, respectively. If the production cost is given by function C(x,y) =2x^2+5y^2+120 and is not exceeding €250. What is the max profit obtained?
Answer:
€ 270
Step-by-step explanation:
Since the production cost C(x,y) = 2x² + 5y² + 120 is less than or equal to 250, we have 2x² + 5y² + 120 ≤ 250
The selling price S(x,y) = 40x + 80y
The profit P(x,y) = S(x,y) - C(x,y) = 40x + 80y - 2x² - 5y² - 120
Using the principle of lagrange multipliers, we want to maximize the profit P(x,y) under the condition that C(x.y) ≤ 250.
So, dP/dx = 40 - 4x , dC/dx = 4x, dP/dy = 80 - 10y , dC/dy = 10y
dP/dx + λdC/dx = 0
40 - 4x + 4λx = 0 (1)
4λx = 4x - 40
λ = (x - 10)/x
dP/dy + λdC/dy = 0
80 - 10y + 10λy = 0 (2)
substituting λ into (2), we have
80 - 10y + 10(x - 10)y/x = 0
multiplying through by x, we have
80x - 10xy + 10xy - 100y = 0
80x - 100y = 0
80x = 100y
x = 100y/80
x = 5y/4
substituting x into C(x,y) ≤ 250, we have
2(5y/4)² + 5y² + 120 ≤ 250
25y²/8 + 5y² + 120 ≤ 250
25y² + 40y² + 960 ≤ 2000
65y² ≤ 2000 - 960
65y² ≤ 1040
y² ≤ 1040/65
y² ≤ 16
y ≤ ±√16
y ≤ ± 4 since its quantity, we take the positive value.
So x = 5y/4 = 5(± 4)/4 = ± 5
So, x ≤ ± 5
For the maximum value for the profit, P(x,y), we take the maximum values of x and y which are x = 5 and y = 4. Substituting these values into P(x,y), we have
P(5,4) = 40(5) + 80(4) - 2(5)² - 5(4)² - 120
= 200 + 320 - 50 - 80 - 120
= 520 - 250
= 270
So, the maximum profit obtained is € 270
Roxie is picking out some movies to rent, and she is primarily interested in horror films and documentaries. She has narrowed down her selections to 66 horror films and 1515 documentaries. Step 2 of 2 : How many different combinations of 33 movies can she rent if she wants at least two documentaries?
Answer:
1,085
Step-by-step explanation:
The calculation of number of different combinations of 3 films she can rent if she needs at least two documentaries is shown below:-
[tex]= N\times (2 \times documentaries\ and\ 1\ horror \ movies)+N\times (3\ documentaries)[/tex]
[tex]=(6C_1)\times (15C_2)+(6C_0)\times (15C_3)[/tex]
= 630 + 455
= 1,085
Therefore for calculating the number of different combinations of 3 films she can rent if she needs at least two documentaries we simply applied the above formula and here we consider one number in the question as it shows the double number.
You need to haul a load of patio bricks to a job site. Each brick weighs 4 pounds 14 ounces. Truck can carry a 3/4 - ton load. How many bricks can the truck carry in a full load?
Answer:
339 bricks.
Step-by-step explanation:
We have the weight of each brick and what the truck can support. Therefore what we must do is pass all to the same unit of measurement to calculate the quantity of bricks.
In this case we will pass everything to pounds.
We have that a 1 pound is 16 ounces, therefore 14 would be:
14 ounces * 1 pound / 16 ounces = 0.875 pounds
In addition we have that 1 ton is 2204.62 pounds, therefore 3/4 would be:
3/4 ton * 2204.62 pounds / 1 ton = 1653.467 pounds
Therefore, in total the brick weighs 4,875 pounds (4 + 0.875) and the truck can support 1653,467 pounds, the number of bricks would be:
1653.467 / 4.875 = 339.17
In other words, it can support about 339 bricks.
A survey was sent out to compare the proportion of adults who use their car horns when driving for two age populations (1=younger adults, defined as between 20 and 39 years old and 2 =older adults, defined as over 60 years old). The following data was obtained from those who responded.
Calculate the 90% confidence interval using the standard normal distribution. Note that 1 =0.52. P2= 0.35, and s.e.(P1-P2) =0.0338. Round to the fourth decimal point. Please enter you answer in the following format: (lower value, upper value)
Use the horn Use the horn
Group Yes No Total
1= younger adults 261 240 501
2= older adults 123 229 352
Answer:
The 90% confidence interval for the difference between proportions is (0.115, 0.228).
As the value 0 is not included in the interval, we can conclude that there is significant difference in the proportion of youger adults that use the horn and older adults that use the horn.
Step-by-step explanation:
We want to calculate the bounds of a 90% confidence interval.
For a 90% CI, the critical value for z is z=1.645.
The sample 1 (younger adults) , of size n1=501 has a proportion of p1=0.521.
[tex]p_1=X_1/n_1=261/501=0.5210[/tex]
The sample 2 (older adults), of size n2=352 has a proportion of p2=0.3494.
[tex]p_2=X_2/n_2=123/352=0.3494[/tex]
The difference between proportions is (p1-p2)=0.1715.
[tex]p_d=p_1-p_2=0.5210-0.3494=0.1715[/tex]
The pooled proportion, needed to calculate the standard error, is:
[tex]p=\dfrac{X_1+X_2}{n_1+n_2}=\dfrac{261+123}{501+352}=\dfrac{384}{853}=0.4502[/tex]
The estimated standard error of the difference between means is computed using the formula:
[tex]s_{p1-p2}=\sqrt{\dfrac{p(1-p)}{n_1}+\dfrac{p(1-p)}{n_2}}=\sqrt{\dfrac{0.4502*0.5498}{501}+\dfrac{0.4502*0.5498}{352}}\\\\\\s_{p1-p2}=\sqrt{0.0005+0.0007}=\sqrt{0.0012}=0.0346[/tex]
Then, the margin of error is:
[tex]MOE=z \cdot s_{p1-p2}=1.645\cdot 0.0346=0.0569[/tex]
Then, the lower and upper bounds of the confidence interval are:
[tex]LL=(p_1-p_2)-z\cdot s_{p1-p2} = 0.1715-0.0569=0.115\\\\UL=(p_1-p_2)+z\cdot s_{p1-p2}= 0.1715+0.0569=0.228[/tex]
The 90% confidence interval for the difference between proportions is (0.115, 0.228).
What is the value of expression below? 7/2-4.5x3+8
Answer:-2
Step-by-step explanation:
Ok so I’m assuming the x stands for the multiplication sign
7/2-4.5*3+8
Use pemdas
Multiplication first
7/2-4.5*3+8
-4.5*3
7/2-13.5+8
Then addition
-13.5+8
Lastly subtraction
7/2-5
-2
Find the value of x in the figure below. Round to the nearest tenth.
Answer:
16
Step-by-step explanation:
We can find x using tan 40° which can be represented as x/20. tan 40° is also equal to about 0.8 so that means x / 20 = 0.8 and x = 16.
Help asap giving branlist!!!
Answer:
Option 2
Step-by-step explanation:
The question states "the width of the rectangle is 4 less than half the length." Since we are looking for the value of w, w will be equal to the expression we create. We start with half the length and than subtract 4 from it. This is because it says 4 less than half the length, not half of 4-length or another variation. In many of these problems the best way to solve them is by working backwards.
Answer:
Option 2
Step-by-step explanation:
Translating these words into math, we get w = 1/2l - 4 which is Option 2.
Please answer this correctly
Answer:
First we need to calculate 1 part.
Calculate big part first
13*15 = 195
7*12 = 84
195+84=279
279
279 is answer
Answer: 279 yd^2
Step-by-step explanation:
Separate this into two separate rectangles: the larger top rectangle (13 yd x 15 yd) and the smaller bottom rectangle (12 yd x 7 yd).
area of rectangle 1 + area of rectangle 2 = total area of figure
b1(h1) + b2(h2) = total area
13(15) + 7(12) = total area
195 + 84 = total area
279 yd^2 = total area
. Suppose that only 20% of all drivers come to a complete stop at an intersection having flashing lights in all directions when no other cars are visible. What is the probability that, of 15 randomly chosen drivers coming to an intersection under these conditions,
Answer:
a. P(x≤9)=0.9999
b. P(x=6)=0.0430
c. P(x≥6)=0.0611
Step-by-step explanation:
The question is incomplete:
a.At most 9 will come to a complete stop?
b.Exactly 6 will come to a complete stop?
c.At least 6 will come to a complete stop?
d.How many of the next 20 drivers do you expect to come to a complete stop?
The amount of drivers from the sample that will come to a complete stop can be modeled by a binomial random variable with n=15 and p=0.2.
The probability that exactly k drivers from the sample come to a complete stop is:
[tex]P(x=k) = \dbinom{n}{k} p^{k}q^{n-k}[/tex]
a. We have to calculate the probability that at most 9 come to a complete stop:
[tex]P(x\leq9)=\sum_{k=0}^9P(x=k)\\\\\\P(x=0) = \dbinom{15}{0} p^{0}q^{15}=1*1*0.0352=0.0352\\\\\\P(x=1) = \dbinom{15}{1} p^{1}q^{14}=15*0.2*0.044=0.1319\\\\\\P(x=2) = \dbinom{15}{2} p^{2}q^{13}=105*0.04*0.055=0.2309\\\\\\P(x=3) = \dbinom{15}{3} p^{3}q^{12}=455*0.008*0.0687=0.2501\\\\\\P(x=4) = \dbinom{15}{4} p^{4}q^{11}=1365*0.0016*0.0859=0.1876\\\\\\P(x=5) = \dbinom{15}{5} p^{5}q^{10}=3003*0.0003*0.1074=0.1032\\\\\\P(x=6) = \dbinom{15}{6} p^{6}q^{9}=5005*0.0001*0.1342=0.043\\\\\\[/tex]
[tex]P(x=7) = \dbinom{15}{7} p^{7}q^{8}=6435*0*0.1678=0.0138\\\\\\P(x=8) = \dbinom{15}{8} p^{8}q^{7}=6435*0*0.2097=0.0035\\\\\\P(x=9) = \dbinom{15}{9} p^{9}q^{6}=5005*0*0.2621=0.0007\\\\\\P(x\leq9)=0.0352+0.1319+0.2309+0.2501+0.1876+0.1032+0.043+0.0138+0.0035+0.0007\\\\P(x\leq9)=0.9999[/tex]
b. We have to calculate the probability that exactly 6 will come to a complete stop:
[tex]P(x=6) = \dbinom{15}{6} p^{6}q^{9}=5005*0.0001*0.1342=0.043\\\\\\[/tex]
c. We have to calculate the probability that at least 6 will come to a complete stop:
[tex]P(x\geq6)=\sum_{k=6}^{15}P(x=k)\\\\\\P(x=6) = \dbinom{15}{6} p^{6}q^{9}=5005*0.0001*0.1342=0.043\\\\\\P(x=7) = \dbinom{15}{7} p^{7}q^{8}=6435*0*0.1678=0.0138\\\\\\P(x=8) = \dbinom{15}{8} p^{8}q^{7}=6435*0*0.2097=0.0035\\\\\\P(x=9) = \dbinom{15}{9} p^{9}q^{6}=5005*0*0.2621=0.0007\\\\\\P(x=10) = \dbinom{15}{10} p^{10}q^{5}=3003*0*0.3277=0.0001\\\\\\P(x=11) = \dbinom{15}{11} p^{11}q^{4}=1365*0*0.4096=0\\\\\\P(x=12) = \dbinom{15}{12} p^{12}q^{3}=455*0*0.512=0\\\\\\[/tex]
[tex]P(x=13) = \dbinom{15}{13} p^{13}q^{2}=105*0*0.64=0\\\\\\P(x=14) = \dbinom{15}{14} p^{14}q^{1}=15*0*0.8=0\\\\\\P(x=15) = \dbinom{15}{15} p^{15}q^{0}=1*0*1=0\\\\\\P(x\geq6)=0.043+0.0138+0.0035+0.0007+0.0001+0+0+0+0\\\\P(x\geq6)=0.0611[/tex]
What is the circumference of the circle? Use 3.14 for Pi. A circle with diameter 33 centimeters.
Answer:
207.24cm
Step-by-step explanation:
Circumference=2pi*r
=2 (3.14)(33)
=207.24cm
The circumference of the circle is 103.62 cm².
Given that, a circle with diameter of 33 cm.
Radius=d/2=16.5 cm.
What is the formula to find the circumference of the circle?The formula to find the circumference of the circle is 2πr.
Now, 2×3.14×16.5=103.62 cm².
Therefore, the circumference of the circle is 103.62 cm².
To learn more about the circumference of the circle visit:
https://brainly.com/question/27177006.
#SPJ2
The equation h = 7m + 8 models the growth of a plant after it was put into a flowerbed. If
m is the number of months since it was planted and h is the plant's height in
centimeters, which statement is valid?
The vertical axis on a graph would
represent the number of months the plant
has been in the flowerbed.
The height of the plant is the dependent
variable.
The domain of the function represents the
height of the plant.
The variable m could be represented as
f(h).
Answer:
2
Step-by-step explanation:
the vertical axis would be h, the plant's height, and the horizontal axis would be m, the number of months. This would make statement 2 the only valid statement.
statement 1: Incorrect, as the vertical axis is the height
statement 2: correct, as h depends on m
statement 3: incorrect, as the domain is the horizontal and represents the number of months
statement 4: incorrect, as h = f(m)
What’s the correct answer for this?
Answer:
(0,2)
Step-by-step explanation:
2:4 means one part is 2/(2+4)=1/3 of AB and the other part is 2/3 of AB
Add 1/3 of the distance from -2 to 4. (1/3)(4+2)=2. -2+2=0 The x coordinate is 0
Subtract 1/3 of the distance from 6 to -6, (1/3)6+6)=4 6-4=2 The y coordinate is 2
The point is (0,2)
Runners are always talking about minutes per mile. This is the inverse of distance divided by time. Like, on my morning jogs I shoot for 11 minutes per mile. Next month, I'm doing a 10k (that's 10 kilometer) run with my daughter. I'm going to average 11 minutes per mile. Calculate, in minutes how long it will take me to complete the run averaging 11 minutes per mile.
Answer:
around 68 minutes 31 seconds.
Step-by-step explanation:
10km = miles = 6.21x11 = 68.31
Sally earns $12.50 an hour cleaning houses. If she works from 8:00am to 6:00pm, how much money will she make?
Answer:
She will make 125 dollars
Step-by-step explanation:
First figure out how many hours are in between 8 AM and 6PM
Second multiply that number by the salary she makes per hour. In this case its 12.50*10
Lastly Get the answer and add a dollar sign :D
In each of the following situations, data are obtained by conducting a research study. Classify each Experimental or Correlational.
Research Study
1. A researcher is interested in whether listening to different types of music or no music while taking a test affects test scores. Students are randomly assigned to one of three groups: The first group takes a test without listening to an iPod, the second group takes the same test while listening to classical music on an iPod, and the third group takes the test while listening to rock music on an iPod. The researcher compares the test scores across the three groups.
2. A psychologist is interested in gender and cognition. She collects data on a large sample of siblings, recording their gender, birth order, and IQ.
3. A professor of ophthalmology is interested in developmental precursors of vision disorders. He collects data from a sample of teenagers on right-eye vision, left-eye vision, and whether the bedroom light was kept off or on as they slept during the night as babies.
Answer:
1. Experimental
2. Correlational
3. Experimental.
Step-by-step explanation:
1. Experimental.
Researches are interested on finding the effects of music on a test.
2. Correlational
Researchers are interested on finding the correlation of the gender and cognition from different samples
3. Experimental
The Researcher wants to know the effects of bedroom light.
What is the equation of a line with a slope of -2 that passes through the point(6,8)
Step-by-step explanation:
work is shown and pictured
Determine whether the underlined number is a statistic or a parameter. In a study of all 1700 professors at a college, it is found that 35% own a computer Choose the correct statement below. O Parameter because the value is a numerical measurement describing a characteristic of a sample. Statistic because the value is a numerical measurement describing a characteristic of a population. O Statistic because the value is a numerical measurement describing a characteristic of a sample. Use the given minimum and maximum data entries, and the number of classes, to find the class width, the lower class limits, and the upper class limits minimum = 21, maximum = 120, 8 classes (Type a whole number.) Choose the correct lower class limits below .
A. 21, 33, 47, 59, 72, 86, 98, 112
B. 21.34, 47, 60, 73, 86, 99. 112
Answer:
The first option is correct.
Parameter because the value is a numerical measurement describing a characteristic of population.
Class width = 12.375
B. 21.34, 47, 60, 73, 86, 99. 112 is the lower class limit
Step-by-step explanation:
The first option is correct.
Parameter because the value is a numerical measurement describing a characteristic of population.
Parameter is a measure that describes the entire population.
Statistic basically describes a sample of the population.
From the given information , the entire 1700 professors at a college is the population and only 35 % own a television is a characteristic, called parameter, of population.
Another objective we are to find here is:
Use the given minimum and maximum data entries, and the number of classes, to find the class width, .
Class width = Maximum - Minimum /No of classes
Given that :
Maximum = 120
Minimum = 21
number of classes = 8
Then;
Class width = 120 - 21 /8
Class width = 12.375
From the given information :
B. 21.34, 47, 60, 73, 86, 99. 112 is the lower class limit
Drivers who are members of the teamsters Union earn an average of $17.15 per hour (U.S. News & World Report). Assume that available data indicate wages are normally distributed with a standard deviation of $2.25. 1) What is the probability that wages are between $15.00 and $20.00 per hours?
Answer:
[tex]P(15<X<20)=P(\frac{15-\mu}{\sigma}<\frac{X-\mu}{\sigma}<\frac{20-\mu}{\sigma})=P(\frac{15-17.15}{2.25}<Z<\frac{20-17.15}{2.25})=P(-0.96<z<1.27)[/tex]
And we can find the probability with this difference and using the normal standard table:
[tex]P(-0.96<z<1.27)=P(z<1.27)-P(z<-0.96)= 0.898-0.169 = 0.729[/tex]
Step-by-step explanation:
Let X the random variable that represent the wages, and for this case we know the distribution for X is given by:
[tex]X \sim N(17.15,2.25)[/tex]
Where [tex]\mu=17.15[/tex] and [tex]\sigma=2.25[/tex]
We want to find this probability:
[tex]P(15<X<20)[/tex]
And we can use the z score formula given by:
[tex]z=\frac{x-\mu}{\sigma}[/tex]
Using this formula we have:
[tex]P(15<X<20)=P(\frac{15-\mu}{\sigma}<\frac{X-\mu}{\sigma}<\frac{20-\mu}{\sigma})=P(\frac{15-17.15}{2.25}<Z<\frac{20-17.15}{2.25})=P(-0.96<z<1.27)[/tex]
And we can find the probability with this difference and using the normal standard table:
[tex]P(-0.96<z<1.27)=P(z<1.27)-P(z<-0.96)= 0.898-0.169 = 0.729[/tex]
In October of 2012, Apple introduced a much smaller variant of the Apple iPad, known at the iPad Mini. Weighing less than 11 ounces, it was about 50% lighter than the standard iPad. Battery tests for the iPad Mini showed a mean life of 10.25 hours (The Wall Street Journal, October 31, 2012). Assume that battery life of the iPad Mini is uniformly distributed between 8.5 and 12 hours.
a. Give a mathematical expression for the probability density function of battery life.
b. What is the probability that the battery life for an iPad Mini will be 10 hours or less (to 4 decimals)?
c. What is the probability that the battery life for an iPad Mini will be at least 11 hours (to 4 decimals)?
d. What is the probability that the battery life for an iPad Mini will be between 9.5 and 11.5 hours (to 4 decimals)?
e. In a shipment of 100 iPad Minis, how many should have a battery life of at least 9 hours (to nearest whole value)?
Answer:
a. [tex]f_X(x) = \dfrac{1}{3.5}8.5<x<12[/tex]
b. the probability that the battery life for an iPad Mini will be 10 hours or less is 0.4286 which is about 42.86%
c. the probability that the battery life for an iPad Mini will be at least 11 hours is 0.2857 which is about 28.57 %
d. the probability that the battery life for an iPad Mini will be between 9.5 and 11.5 hours is 0.5714 which is about 57.14%
e. 86 should have a battery life of at least 9 hours
Step-by-step explanation:
From the given information;
Let X represent the continuous random variable with uniform distribution U (A, B) . Therefore the probability density function can now be determined as :
[tex]f_X(x) = \dfrac{1}{B-A}A<x<B[/tex]
where A and B are the two parameters of the uniform distribution
From the question;
Assume that battery life of the iPad Mini is uniformly distributed between 8.5 and 12 hours
So; Let A = 8,5 and B = 12
Therefore; the mathematical expression for the probability density function of battery life is :
[tex]f_X(x) = \dfrac{1}{12-8.5}8.5<x<12[/tex]
[tex]f_X(x) = \dfrac{1}{3.5}8.5<x<12[/tex]
b. What is the probability that the battery life for an iPad Mini will be 10 hours or less (to 4 decimals)?
The probability that the battery life for an iPad Mini will be 10 hours or less can be calculated as:
F(x) = P(X ≤x)
[tex]F(x) = \dfrac{x-A}{B-A}[/tex]
[tex]F(10) = \dfrac{10-8.5}{12-8.5}[/tex]
F(10) = 0.4286
the probability that the battery life for an iPad Mini will be 10 hours or less is 0.4286 which is about 42.86%
c. What is the probability that the battery life for an iPad Mini will be at least 11 hours (to 4 decimals)?
The battery life for an iPad Mini will be at least 11 hours is calculated as follows:
[tex]P(X\geq11) = \int\limits^{12}_{11} {\dfrac{1}{3.5}} \, dx[/tex]
[tex]P(X\geq11) = {\dfrac{1}{3.5}} (x)^{12}_{11}[/tex]
[tex]P(X\geq11) = {\dfrac{1}{3.5}} (12-11)[/tex]
[tex]P(X\geq11) = {\dfrac{1}{3.5}} (1)[/tex]
[tex]P(X\geq11) = 0.2857[/tex]
the probability that the battery life for an iPad Mini will be at least 11 hours is 0.2857 which is about 28.57 %
d. What is the probability that the battery life for an iPad Mini will be between 9.5 and 11.5 hours (to 4 decimals)?
[tex]P(9.5 \leq X\leq11.5) =\int\limits^{11.5}_{9.5} {\dfrac{1}{3.5}} \, dx[/tex]
[tex]P(9.5 \leq X\leq11.5) ={\dfrac{1}{3.5}} \, (x)^{11.5}_{9.5}[/tex]
[tex]P(9.5 \leq X\leq11.5) ={\dfrac{1}{3.5}} (11.5-9.5)[/tex]
[tex]P(9.5 \leq X\leq11.5) ={\dfrac{1}{3.5}} (2)[/tex]
[tex]P(9.5 \leq X\leq11.5) =0.2857* (2)[/tex]
[tex]P(9.5 \leq X\leq11.5) =0.5714[/tex]
Hence; the probability that the battery life for an iPad Mini will be between 9.5 and 11.5 hours is 0.5714 which is about 57.14%
e. In a shipment of 100 iPad Minis, how many should have a battery life of at least 9 hours (to nearest whole value)?
The probability that battery life of at least 9 hours is calculated as:
[tex]P(X \geq 9) = \int\limits^{12}_{9} {\dfrac{1}{3.5}} \, dx[/tex]
[tex]P(X \geq 9) = {\dfrac{1}{3.5}}(x)^{12}_{9}[/tex]
[tex]P(X \geq 9) = {\dfrac{1}{3.5}}(12-9)[/tex]
[tex]P(X \geq 9) = {\dfrac{1}{3.5}}(3)[/tex]
[tex]P(X \geq 9) = 0.2857*}(3)[/tex]
[tex]P(X \geq 9) = 0.8571[/tex]
NOW; The Number of iPad that should have a battery life of at least 9 hours is calculated as:
n = 100(0.8571)
n = 85.71
n ≅ 86
Thus , 86 should have a battery life of at least 9 hours
Do the measures of center make sense? A. Only the mode makes sense since the data is nominal. B. All the measures of center make sense since the data is numerical. C. Only the mean, median, and midrange make sense since the data is nominal. D. Only the mean, median, and mode make sense since the data is numerical.
Answer:
A. Only the mode makes sense since the data is nominal.
Step-by-step explanation:
Hello!
The objective of the study was to determine if deficiency of carbon dioxide in the soil affects the phenotype of peas.
The variable of study is X: Phenotype of a pea grown in soil with carbon dioxide deficiency.
Possible values of Phenotype codes:
1= smooth-yellow
2= smooth-green
3= wrinkled-yellow
4= wrinkled-green
The absolute frequencies for each phenotype are:
f(1)= 3
f(2)= 4
f(3)= 6
f(4)= 1
n= 14
a) Mean:
X[bar]= (∑xifi)/n= [(1*3)+(2*4)+(3*6)+(4*1)]/14= 33/14= 2.357= 2.36
The average value is always within range of definition of the variable but it does not necessarily correspond to an observation.
b) Median:
To determine the value that corresponds to the median you have to calculate its position:
For even samples the position is:
PosMe= n/2= 14/2= 7
Then you have to arrange the data from least to greatest, in this case, starting from the first category, you have to determine where the seventh observation is within the observed absolute frequencies. The phenotype that corresponds to the 7th observation is 2= smooth-green.
Me= 2= smooth-green.
c) Mode:
The mode corresponds to the most observed category/ value of the variable, i.e. the category with the most observations is 3= wrinkled-yellow
Md= 3= wrinkled-yellow
d) Midrange: (1 + 4)/2= 2.5
e)
As you can see the variable is qualitative and categorical. Even if all central tendency measurements can be calculated, truth is that the only one that shows any valuable information regarding the data set is the mode.
I hope this helps!
Find the sample space for picking a number from 1 to 3 and choosing red or white
Answer:
The event of picking a number from 1 to 3 consists of:
Pick number 1
Pick number 2
Pick number 3
The event of choosing red or white card consists of:
Choose a red card
Choose a white card
=> The sample space for picking a number from 1 to 3 and choosing red or white card:
Pick number 1 and choose a red card
Pick number 1 and choose a white card
Pick number 2 and choose a red card
Pick number 2 and choose a white card
Pick number 3 and choose a red card
Pick number 3 and choose a white card
Hope this helps!
:)
The lengths of text messages are normally distributed with a population standard deviation of 6 characters and an unknown population mean. If a random sample of 21 text messages is taken and results in a sample mean of 30 characters, find a 80% confidence interval for the population mean. Round your answers to two decimal places. z0.10 z0.05 z0.04 z0.025 z0.01 z0.005 1.282 1.645 1.751 1.960 2.326 2.576
Answer:
The 80% confidence interval for the population mean is between 28.32 characters and 31.68 characters.
Step-by-step explanation:
We have the standard deviation for the population, so we can use the normal distribution. If we had the standard deviation for the sample, we would have to use the t-distribution.
We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:
[tex]\alpha = \frac{1-0.8}{2} = 0.1[/tex]
Now, we have to find z in the Ztable as such z has a pvalue of [tex]1-\alpha[/tex].
So it is z with a pvalue of [tex]1-0.5 = 0.9[/tex], so [tex]z = 1.282[/tex]
Now, find the margin of error M as such
[tex]M = z*\frac{\sigma}{\sqrt{n}}[/tex]
In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.
[tex]M = 1.282*\frac{6}{\sqrt{21}} = 1.68[/tex]
The lower end of the interval is the sample mean subtracted by M. So it is 30 - 1.68 = 28.32 characters.
The upper end of the interval is the sample mean added to M. So it is 30 + 1.68 = 31.68 characters.
The 80% confidence interval for the population mean is between 28.32 characters and 31.68 characters.
Zareen has 24 minutes to work on her math homework in each problem is taking her 2/3 of a minute on average to complete which expression can be used to determine the number of my problem she will be able to complete in the time she has
Answer:
Hey mate , here is your answer. Hope it helps you
Step-by-step explanation:
Given Zareen has 24min to work on her math homework, and each problem is taking her 2/3 of a minute
As give one problem takes
24*(2/3) minutes = 16
Hence
2/3 divided by 24
what is the radius diameter of the following circle?
Answer:
radius=7
diameter =2×radius
d=2×7
diameter=14
Answer:
Hello!
The answer is-
Radius: 7
Diameter: 14
Step-by-step explanation:
Diameter:
2*(radius)
d=2(7)
Diameter is 14
Ryan remembers numbers using images that look somewhat like each number: 0 is a ball, 1 is a stick, 2 is a hanger, 3 is a comb, 4 is a kite, etc. Ryan remembered a 4-digit phone extension with this story: A person uses a hanger to pop a ball, then flies two kites. What number is Ryan likely remembering? (1) 2044 or (2) 2042 (3) 2004 or (4) 2204
Answer:
2044
Step-by-step explanation:
just follow the story
a person uses a
hanger (2)
to pop a
ball (0)
then flies
two kites (44)
Answer:
1). 2044
Step-by-step explanation:
The story includes: a hanger, a ball, and two kites (in that order)
From the information given, a hanger is 2, a ball is 0, and a kite is 4.
So it would be 2044.
Which point is a solution to y>2X-1
Answer:
Step-by-step explanation:
Answer:
B) (0,2)
Step-by-step explanation:
2 ≥ 2(0)-1
2 ≥ 0-1
2 ≥ -1
Which is true about the polynomial-8m3+11m
Answer:
“It is a binomial with a degree of 3”
Step-by-step explanation:
Since it has just two different coefficients, it would be considered “binomial” for that reason. As you can notice, the highest degree is 3. So match those up and the correct answer would be the second choice “It is a binomial with a degree of 3”
Answer:
B
Step-by-step explanation:
Given AB intersects DE at point C. prove: DCB = ECA. What is the missing reason in step 5
Answer: the answer is linear pair
Step-by-step explanation:
Answer:
Linear pair postulate
Step-by-step explanation:
Please help me please I’m stuck please
[tex]answer \\ 9 \\ please \: see \: the \: attached \: picture \: for \: full \: solution \\ hope \: it \: helps[/tex]
Answer:
9
Step-by-step explanation:
The ratio of 5 to 5+3 is equivalent to the ratio of 15 to 15+x. This is because when you have a triangle inside of a triangle and both of them share two of the same sides and the third sides are parallel to each other, the side ratios of the triangles are always proportionate.
[tex]\frac{5}{5+3} =\frac{15}{15+x}[/tex] Starting equation
[tex]\frac{5}{8} =\frac{15}{15+x}[/tex] Simplify
[tex]5(15+x)=8*(15)[/tex] Cross multiply
[tex]75+5x=120[/tex] Distributive Property on left and simplify on right
[tex]5x=45[/tex] Isolate the variable
[tex]x=9[/tex] Divide both sides by 5 (Division Property of Equality)