Complete Question:
Dustin is buying carpet for the living room. If the length of the room is 21 ft and the width
is 11 ft, how many square feet of carpet does he need to buy?
Answer:
231 ft²
Step-by-step explanation:
==>GIVEN:
Length of room (L) = 21 ft
Width of room (W) = 11 ft
==>REQUIRED:
Square feet of carpet to be bought = area of the rectangular room
==>SOLUTION:
The room to be covered with carpet is rectangular in shape. In order to ascertain the square feet of carpet to be bought, we need to calculate the area of the room by using the formula for area of rectangle.
Thus, area of rectangle (A) = Length (L) × Width (W)
A = 21 × 11
A = 231 ft²
Square feet of carpet to be bought = 231 ft²
Two number cubes are rolled for two separate events:
Event A is the event that the sum of numbers on both cubes is less than 10.
Event B is the event that the sum of numbers on both cubes is a multiple of 3.
Complete the conditional probability formula for event B given that event A occurs first by writing A and B in the blanks:
P ( _a0 | _a1) = P ( _a2 ∩ _ a3)
___________
P ( _a4)
Answer: [tex]\bold{P(B|A)=\dfrac{P(B\cap A)}{P(A)}=\dfrac{11}{30}}[/tex]
Step-by-step explanation:
The probability of Event B given Event A = the intersection of Event A and B divided by the probability of Event A. (see below for the symbols)
[tex]P(B|A)=\dfrac{P(B\cap A)}{P(A)}[/tex]
P(A) = (1, 6), (1, 5), (1, 4), (1, 3), (1, 2), (1, 1)
(2, 6), (2, 5), (2, 4), (2, 3), (2, 2), (2, 1)
(3, 6), (3, 5), (3, 4), (3, 3), (3, 2), (3, 1)
(4, 5), (4, 4), (4, 3), (4, 2), (4, 1)
(5, 4), (5, 3), (5, 2), (5, 1)
(6, 3), (6, 2), (6, 1)
= 30
P(B) = (1, 2), (2, 1) sum = 3
(1, 5), (2, 4), (3, 3), (4, 2), (5, 1) sum = 6
(3, 6), (4, 5), (5, 4), (5, 4), (6, 3) sum = 9
(6, 6) sum = 12
= 12
P(A ∩ B) = (1, 2), (2, 1)
(1, 5), (2, 4), (3, 3), (4, 2), (5, 1)
(3, 6), (4, 5), (5, 4), (5, 4), (6, 3)
= 11
Is (-3,4) a solution of the inequality y> - 2x – 3?
O There is not enough given information to determine this.
O (-3, 4) is a solution.
(-3, 4) would be a solution if the inequality was y > - 2x – 3.
(-3, 4) is not a solution.
Answer:
(-3, 4) is a solution
Step-by-step explanation:
The point (-3, 4) is inside the shaded area of the graph, so is a solution.
You can check in the inequality
y > -2x -3
4 > -2(-3) -3 . . . . substitute for x and y
4 > 3 . . . . . . . true; the given point is a solution
which of the following are solutions to the quadratic equation check all that apply x ^ 2 + 10x + 25 = 7
Answer:
the Answers are : B and E
Step-by-step explanation:
From the given quadratic equation [tex]x^2 + 10x + 25 = 7[/tex] Thus, the solution is x = -1 and -9.
How to find the roots of a quadratic equation?Suppose that the given quadratic equation is
[tex]ax^2 + bx + c = 0[/tex]
Then its roots are given as:
[tex]x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}[/tex]
We have been given a quadratic equation
[tex]x^2 + 10x + 25 = 7[/tex]
[tex]x^2 + 10x + 25 - 7=0\\\\x^2 + 10x + 18[/tex]
The solution of the given equation;
[tex]x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}\\\\x = \dfrac{-10 \pm \sqrt{10^2 - 4\times 18}}{2}\\\\x = \dfrac{-10 \pm \sqrt{100- 36}}{2}\\\\x = \dfrac{-10 \pm \sqrt{64}}{2}\\\\x = \dfrac{-10 \pm 8}{2}\\[/tex]
Therefore, the solution are x = -1 and -9.
Learn more about finding the solutions of a quadratic equation here:
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ASAP! GIVING BRAINLIEST! Please read the question THEN answer CORRECTLY! NO guessing. I say no guessing because people usually guess on my questions.
Answer:
B. (f - g)(x) = [tex]3^x-2x+14[/tex]
Step-by-step explanation:
→Set it up, like so:
[tex](3^x+10)-(2x-4)[/tex]
→Distribute the -1 to (2x - 4):
[tex]3^x+10-2x+4[/tex]
→Add like terms (10 and 4):
[tex]3^x-2x+14[/tex]
Using the following data on the Observations 10, 13, 4, and 20 confirm that the complete linkage distance between the cluster containing 《10, 13) and the cluster containing (4, 20) s 2.577 units as displayed in the dendrogram
Observation
13 20 0.032 0.195 -0510 0.466 0.741 0.8750.207 0.474 0.700 0.748 -0.004 -0.490 -0.892 0.735 0.219 0.655 -0.1731.013 0.943 0.083 -0.693 -0.489-0.702 -0.458 1.620 2.275 1328 1.733 -0.863 1.035 0.724 0.721 10 Income/Debt Return Cost Load Peak Sales TotalFuelCosts
If required, round your answers to three decimal places.Do not round intermediate calculations
1. Distance from Observation 10 and Observation 4:
2. Distance from Observation 10 and Observation 20:
3. Distance from Observation 13 and Observation 4:
4. Distance from Observation 13 and Observation 20:
Answer:
Step-by-step explanation:
The distance between:
10 and 4: 1.492
10 and 20: 2.055
13 and 4: 2.577
13 and 20: 2.226
The R code:
#Convert your datafile into csv and make sure your row names are 10,13,4 and 20
data=read.csv(file.choose())
data
row.names(data)=c(10,13,4,20)
data
d=dist(data,method="euclidean")
d
fit=hclust(d,method="complete")
plot(fit)
groups=cutree(fit,k=2)
rect.hclust(fit,k=2,border="red")
I need the answers for 21 and 22
Answer:
21.b
22.c
Step-by-step explanation:
idk how to explain it lol I did mental math
Alex is paid $30/hr at full rate, and $20/hr at a reduced rate. The hours of work are paid at a ratio of 2:1, full rate : reduced rate. For example, if he worked 3 hours, he would be paid 2 hours at full rate and 1 hour at reduced rate. Calculate his pay for 4 hours of work
Answer:
His pay for 4 hours of work is $106.67.
Step-by-step explanation:
2:1, full rate : reduced rate.
This means that for each 2+1 = 3 hours that he works, 2 he has full pay and 1 he has reduced pay.
4 hours
How much are full pay?
For each 3, 2 are full pay. For four?
3 hours - 2 full pay
4 hours - x full pay
[tex]3x = 8[/tex]
[tex]x = \frac{8}{3}[/tex]
So for [tex]\frac{8}{3}[/tex] hours he makes the full pay($30) and for [tex]4 - \frac{8}{3} = \frac{12}{3} - \frac{8}{3} = \frac{4}{3}[/tex] he makes reduced pay($20).
Calculate his pay for 4 hours of work
[tex]30*\frac{8}{3} + 20*\frac{4}{3} = 106.67[/tex]
His pay for 4 hours of work is $106.67.
Calculating the standard deviation (σ) for a list of n data values: 1. Calculate the average value. 2. Subtract the average value from each individual data value and enter the results in a column to the right of the data values. 3. Square each of the results obtained in step 2, and enter these in a new column to the right. 4. Sum the squares obtained in step 3. 5. Divide the result from step 4 by (n - 1) (the total number of measurements minus 1). 6. Take the square root of the result from step 5. This is the standard deviation. Expressed as an equation, the standard deviation of n measurements of data value x is: σ = ( Σ (x - xavg)2 / (n - 1) )1/2 Using the 6 steps above (or the spreadsheet function), calculate the standard deviation for the six values on page 16 and enter your answer below. Enter your result with only one sig fig, and remember to use a zero before the decimal point for values less than 1, for example 0.05 or 0.01.
Answer:
Step-by-step explanation:
The missing list of the data values for the question are as follows:
1 1.03
2 1.01
3 0.96
4 0.96
5 0.99
6 1
7 1.01
8 0.98
9 1.02
10 1.03
11 1
12 0.99
13 1
14 0.97
15 1.01
[tex]x_i[/tex] [tex](x_i - \bar x)[/tex] [tex](x_i - \bar x)^2[/tex]
1 1.03 0.03 0.0009
2 1.01 0.01 0.0001
3 0.96 -0.4 0.0016
4 0.96 -0.4 0.0016
5 0.99 -0.1 0.0001
6 1 0.0 0.0
7 1.01 0.1 0.0001
8 0.98 -0.2 0.0004
9 1.02 0.2 0.0004
10 1.03 0.3 0.0009
11 1 0.0 0.0
12 0.99 -0.1 0.0001
13 1 0.0 0.0
14 0.97 -0.03 0.0009
15 1.01 0.1 0.0001
The average value for x is calculated as:
[tex]\bar x = \dfrac{14.96}{15}[/tex]
[tex]\bar x = 0.997 \\ \\ \bar x \approx 1.00[/tex]
[tex]\sum (x-x_i)^2 = 0.0072[/tex]
[tex]\dfrac{\sum (x-x_i)^2 }{n-1}= \dfrac{0.0072}{15-1} \\ \\ = \dfrac{0.0072}{14} \\ \\ = 0.00051[/tex]
[tex]\sigma = \sqrt{\dfrac{\sum (x-x_i)^2 }{n-1}} = \sqrt{0.00051} \\ \\ \sigma =0.0226 \\ \mathbf { \\ \sigma =0.02 \ to \ one \ significant \ figure}[/tex]
A jury pool has 15 men and 21 women, from which 12 jurors will be selected. Assuming that each person is equally likely to be chosen and that the jury is selected at random, find the probability that the jury consists of:_____
(a) all men
(b) all women
(c) 8 men and 4 women
(d) 6 men and 6 women
Give all answers accurate to four decimal places.
Answer:
(a) all men = 3.6351 * 10^ -7
(b) all women = 2.3483* 10^ -4
(c) 8 men and 4 women = 0.0308
(d) 6 men and 6 women= 0.2170
Step-by-step explanation:
A jury pool has 15 men and 21 women, from which 12 jurors will be selected.
Total = 36 people
Probability of
(a) all men
= 15C12/36C12
= 455/1251677700
= 3.6351 * 10^ -7
(b) all women
= 21C12/36C12
= 293930/1251677700
= 2.3483* 10^ -4
(c) 8 men and 4 women
=( 15C8 * 21C4)/36C12
= (6435*5985)/1251677700
= 38513475/1251677700
= 0.0308
(d) 6 men and 6 women
= (15C6 * 21C6)/(36C12)
= (5005*54264)/1251677700
= 271591320/1251677700
= 0.2170
Use the following cell phone airport data speeds​ (Mbps) from a particular network. Find the percentile corresponding to the data speed 11.2 Mbps. 0.1 0.2 0.2 0.3 0.4 0.4 0.4 0.5 0.5 0.6 0.6 0.8 0.9 0.9 0.9 1.1 1.3 1.7 1.8 1.9 2.3 2.4 2.5 2.6 2.7 3.1 3.5 3.5 3.7 3.8 4.8 5.2 7.4 7.9 8.2 8.6 9.3 11.2 11.3 11.4 12.1 12.6 13.1 13.3 13.6 13.8 14.6 15.6 15.7 25.6
Answer: the percentile is 74%
Step-by-step explanation:
The given data distribution is arranged in increasing order as:
0.1 0.2 0.2 0.3 0.4 0.4 0.4 0.5 0.5 0.6 0.6 0.8 0.9 0.9 0.9 1.1 1.3 1.7 1.8 1.9 2.3 2.4 2.5 2.6 2.7 3.1 3.5 3.5 3.7 3.8 4.8 5.2 7.4 7.9 8.2 8.6 9.3 11.2 11.3 11.4 12.1 12.6 13.1 13.3 13.6 13.8 14.6 15.6 15.7 25.6
The total number of values given in the data is 50
Percentile = number of values in the distribution lesser than the given value × 100/ total number of values in the distribution
Considering the data speed of 11.2 Mbps, the number of data speed lower than 11.2 is 37
Percentile = (37 × 100)/50 = 74%
A fire hydrant with a blue cap provides water at a rate of 1,500 gallons per minute. A fire hydrant with a green cap provides water at a rate of 1,000 gallons per minute. A fire hydrant with a purple cap provides water at half the rate of a fire hydrant with a green cap. What is the equation in fraction form
Answer:
Fire hydrant with a purple cap (with respect to a fire hydrant with a green cap):
[tex]\dot Q_{purple} = \frac{1}{2}\cdot \dot Q_{green}[/tex]
Step-by-step explanation:
The volume rate of the fire hidrant with a purple cap is equal to the product of the proportion factor and the volume rate of the fire hydrant with a concrete cap.
[tex]\dot Q_{i} = k \cdot \dot Q_{j}[/tex]
There are two different solutions:
Fire hydrant with a purple cap (with respect to a fire hydrant with a green cap):
[tex]\dot Q_{purple} = \frac{1}{2}\cdot \dot Q_{green}[/tex]
Fire hydrant with a purple cap (with respect to a fire hydrant with a blue cap):
[tex]\dot Q_{purple} = \frac{1}{2} \times \frac{1000\,gpm}{1500\,gpm}\cdot \dot Q_{blue}[/tex]
[tex]\dot Q_{purple} = \frac{1}{3}\cdot \dot Q_{blue}[/tex]
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.
A statistics professor receives an average of five e-mail messages per day from students. Assume the number of messages approximates a Poisson distribution. What is the probability that on a randomly selected day she will have five messages
Answer:
The probability that on a randomly selected day the statistics professor will have five messages is 0.1755.
Step-by-step explanation:
Let the random variable X represent the number of e-mail messages per day a statistics professor receives from students.
The random variable is approximated by the Poisson Distribution with parameter λ = 5.
The probability mass function of X is as follows:
[tex]P(X=x)=\frac{e^{-5}\cdot 5^{x}}{x!};\ x=0,1,2,3...[/tex]
Compute the probability that on a randomly selected day she will have five messages as follows:
[tex]P(X=5)=\frac{e^{-5}\cdot 5^{5}}{5!}[/tex]
[tex]=\frac{0.006738\times 3125}{120}\\\\=0.17546875\\\\\approx 0.1755[/tex]
Thus, the probability that on a randomly selected day the statistics professor will have five messages is 0.1755.
At a gas station, 50% of the customers use regular gas, 30% use mid-grade gas and 20% use premium gas. Of those customers using regular gas, only 30% fill their tanks. Of those customers using mid-grade gas, 60% fill their tanks, whereas of those using premium, 50% fill their tanks. If the next customer fills the tank, what is the probability that he uses premium gas
Answer:
The probability is 0.2326 or 23.26%.
Step-by-step explanation:
The probability that a random customer fills their tank with premium gas is:
[tex]P( prem\ \&\ fill) = 0.2*0.5=0.10[/tex]
The probability that a random customer fills their tank is given by:
[tex]P(fill)=P( reg\ \&\ fill)+P( mid\ \&\ fill)+P( prem\ \&\ fill)\\P(fill) = 0.5*0.3+0.3*0.6+0.2*0.5\\P(fill) = 0.43[/tex]
Therefore, the probability that a customer used premium gas given that hey have filled their tank is:
[tex]P(prem| fill) = \frac{P( prem\ \&\ fill) }{P(fill)} \\P(prem| fill) =\frac{0.10}{0.43}=0.2326[/tex]
The probability is 0.2326 or 23.26%.
how to find a local minimum of a function?
Answer:
Find the places where the derivative is zero and the second derivative is positive.
Step-by-step explanation:
By definition, a function has a minimum where the first derivative is zero and the second derivative is positive.
That will be a "local" minimum if there are other points on the function graph that have values less than that. It will be a "global" minimum if there are no other function values less than that. A global minimum is also a local minimum.
__
On a graph, a local minimum is the bottom of the "U" where the graph changes from negative slope to positive slope.
Round $0.6683 to the nearest cent
Answer:
0.67
Step-by-step explanation:
0.668 is close to 0.67 than 0.66
The mass of the Eiffel Tower is about 9.16 ⋅ 10^6 kilograms. The mass of the Golden Gate Bridge is 8.05 ⋅ 10^8 kilograms. Approximately how many more kilograms is the mass of the Golden Gate Bridge than the mass of the Eiffel Tower? Show your work and write your answer in scientific notation.
Answer:
[tex]7.9584 \times 10^8[/tex]
Step-by-step explanation:
[tex]8.05 \times 10^8 - 9.16 \times 10^6[/tex]
[tex]805000000-9160000[/tex]
[tex]=795840000[/tex]
According to market research, a business has a 75% chance of making money in the first 3 years. According to lab testing, of a certain kind of experimental light bulb will work after 3 years. According to experts, the likelihood of a car needing major repairs in the first 3 years is 0.7. 1. Write the scenarios in order of likelihood from least to greatest after three years: the business makes money, the light bulb still works, and the car needs major repairs.
The question is incomplete! Complete question along with answer and step by step explanation is provided below.
Question:
Here are some scenarios:
According to market research, a business has a 75% chance of making money in the first 3 years.
According to lab testing, 5/6 of a certain kind of experimental light bulb will work after 3 years.
According to experts, the likelihood of a car needing major repairs in the first 3 years is 0.7.
1. Write the scenarios in order of likelihood from least to greatest after three years: the business makes money, the light bulb still works, and the car needs major repairs.
Answer:
The correct order in terms of likelihood from least to greatest would be
P(Car repair) = 0.70 -> P(Business) = 0.75 -> P(Light bulb) = 0.83
Car needs major repairs -> Business makes money -> Light bulb still works
Step-by-step explanation:
We are given probabilities of three different events.
According to market research, a business has a 75% chance of making money in the first 3 years.
P(Business) = 75% = 0.75
According to lab testing, 5/6 of a certain kind of experimental light bulb will work after 3 years.
P(Light bulb) = 5/6 = 0.83
According to experts, the likelihood of a car needing major repairs in the first 3 years is 0.7.
P(Car repair) = 0.70
We are asked to write these scenarios in order of likelihood from least to greatest after three years.
Which means that the events with least probability is less likely to occur.
The least probability is of car repair, then business and then light bulb.
So the correct order in terms of likelihood from least to greatest would be
P(Car repair) = 0.70 -> P(Business) = 0.75 -> P(Light bulb) = 0.83
Car needs major repairs -> Business makes money -> Light bulb still works
{(1,3),(2,5)(3,-4),(4-3),(5,1)} a function or not a function
Answer:
yes the above is a function.
The math department faculty at a large university wanted to know what portion of the student body believes students should be able to enroll in any math class without meeting a prerequisite. The statistics department offered to cooperate in conducting a survey, and a simple random sample of 500 students was selected from all the students enrolled in statistics classes. A survey form was sent by email to these 500 students and 236 responded. What is the population of interest for this study?
Answer:
The population of interest for this student is the students whom are enrolled in statistics classes.
Step-by-step explanation:
Sampling
This is a common statistics practice, when we want to study something from a population, we find a sample of this population.
For example:
I want to estimate the proportion of New York state residents who are Buffalo Bills fans. So i ask, lets say, 1000 randomly selected New York state residents wheter they are Buffalo Bills fans, and expand this to the entire population of New York State residents.
The population of interest are all residents of New York State.
A simple random sample of 500 students was selected from all the students enrolled in statistics classes.
This means that the population of interest for this student is the students whom are enrolled in statistics classes.
A meteorologist reports that the chance of snow is less
than 30%. The correct inequality to represent this
comparison is s < 30. The variable s represents the
likelihood of snow
Which numbers are solutions of the inequality?
Choose all that apply.
20%
35%
17%
30%
29
%
1.5%
Answer:
1, 3, 5, 6
Step-by-step explanation:
Your solution has to be less than the number they are giving you for example if you have -3 one solution could be -16
The numbers that are solutions to the inequality are as follows: 20%, 17%, 29.5%, 1.5%.
What are the solutions of the inequality?The solution of an inequality is the set of all possible values that could serve as the result of the expression. So, for the given problem, the set of values that would correspond to the likelihood of snow is 20%, 17%, 29.5%, and 1.5%.
In other words, these percentages are less than 30% and can be rightly represented by the variable s.
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The perimeter of an equivalent triangle is 15 inches. A side of the triangle is x-2. What is the length of each side of the triangle
Answer:
5
Step-by-step explanation:
We have x-2 = 5
x-2 = 5 we separate parenthesis.
x(-2) = 5(+2)
x = 7
We can check this as what the x-2 is saying is 7-2 = 5
Answer:
Since it is an equilateral triangle,
Perimeter = 3s = 3 x side
=> 15 = 3 X (x - 2)
=> 15 = 3(x - 2)
=> 15 = 3x - 6
=> 3x = 15 + 6
=> 3x = 21
=> x = 21/3
=> x = 7
When x = 7,
=> Side = 7 - 2 = 5 inches
Since, it is an equilateral triangle all sides are of 5 inches each.
A newborn baby whose Apgar score is over 6 is classified as normal and this happens in 80% of births. As a quality control check, an auditor examined the records of 100 births. He would be suspicious if the number of normal births in the sample of 100 births fell below the lower limit of "usual." What is that lower limit?
Answer:
The lower limit is 72.
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal probability distribution
When the distribution is normal, we use the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
If X is more than 2 standard deviations from the mean, it is unusual.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]
In this question, we have that:
[tex]n = 100, p = 0.8[/tex]
So
[tex]\mu = 0.8, s = \sqrt{\frac{0.8*0.2}{100}} = 0.04[/tex]
He would be suspicious if the number of normal births in the sample of 100 births fell below the lower limit of "usual." What is that lower limit?
2 standard deviations below the mean is the lower limit, so X when Z = -2.
Proportion:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]-2 = \frac{X - 0.8}{0.04}[/tex]
[tex]X - 0.8 = -2*0.04[/tex]
[tex]X = 0.72[/tex]
Out of 100:
0.72*100 = 72
The lower limit is 72.
which products have the same sign as (-2 3/7) (-6/11) check all that apply
A.) 3/8(-6/7)
B.) 1 2/9(2 16/17)
C.) -9/20(3 4/5)
D.) -1/3 (-2/3
hurry answer pls
Answer: Options B and D.
Step-by-step explanation:
We start with the equation:
(-2 3/7)*(-6/11)
now, you need to recall the signs relations:
(+)*(+) = +
(-)*(+) = -
(-)*(-) = +
Then our initial equation has a positive sign.
a) (3/8)*(-6/7) here we have (+)*(-), so this is negative, this option is not correct.
b) (1 2/9)*(2 16/17) here we have (+)*(+), so this is positive, this option is correct.
c) (-9/20)*(3 4/5) here we have (-)*(+), so this is negative, this option is not correct.
d) (-1/3)*(-2/3) here we have (-)*(-), so this is positive, then this option is correct.
Answer:
The awnser is B and D
Step-by-step explanation:
Jack has a rectangular patio with a length that is one foot less than twice its width. His neighbor Ron's patio has the same width but a length that is 5 feet more than its width. If Jack's patio is 120 square feet and Ron's patio is 104 square feet, how many square feet longer is Jack's patio than Ron's?
Answer:
difference in area = 16 ft²
if you use 8 the difference in length between Jack patio and his neighbor patio will be will be 15 - 13 = 2 ft
if you use 13 the difference i length will be 25 - 18 = 7 ft
Step-by-step explanation:
Jacks rectangular patio
width = a
length = 2a - 1
area = lw
where
l = length
w = width
area = 120 ft²
a(2a - 1)
2a² - a - 120 = 0
(a - 8) (2a + 15)
a = 8 or -15/2
Ron's rectangular patio
width = a
length = a + 5
area = lw
area = 104 ft²
a (a + 5) = 104
a² + 5a -104 = 0
(a + 8) (a - 13)
a = -8 or 13
How many square feet longer is jack patio longer than Ron's patio is the difference in their area. Therefore,
120 - 104 = 16 ft²
The value 8 or 13 can be used for a since the width a have to be the same.
if you use 8 the difference in length between Jack patio and his neighbor patio will be will be 15 - 13 = 2 ft
if you use 13 the difference i length will be 25 - 18 = 7 ft
m^2-3m+2/m^2-m. Simplify
Answer:
Step-by-step explanation:
factor out the numerator and demoninator
(m-2)(m-1)/m(m-1)
= (m-2)/m
This table gives a few (x,y) pairs of a line in the coordinate plane. What is the y-intercept of the line? (full problem attached)
Answer:
(0,34)
Step-by-step explanation:
For each rise of 14 in the x direction, this graph rises by -8 in the y direction. This means that, when x is 0, and the graph intersects the y axis, the y value will be 50-8-8=34. Therefore, the y intercept of this line is (0,34). Hope this helps!
Answer:
The answer is (0,34)
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Answer:
a. 2 groups of 2 is 4
b. 3 groups of 2 is 6
c. 4 groups of 2 is 8
d. 5 groups of 2 is 10
e. 6 groups of 2 is 12
Answer:
a - 2
b- 3
c- 4 groups of 2 is 8
d- 5 groups of 2 is 10
e- 6 groups of 2 is 12
A driver and a passenger are in a car accident. Each of them independently has probability 0.3 of being hospitalized. When a hospitalization occurs, the loss is uniformly distributed on [0, 1]. When two hospitalizations occur, the losses are independent. Calculate the expected number of people in the car who are hospitalized, given that the total loss due to hospitalizations from the accident is less than 1.
Answer:
0.534
Step-by-step explanation:
p(0 losses) = 0.7² = 0.49
p(1 loss) = 2 x 0.3 x 0.7 = 0.42
p(2 losses) = 0.09
This is a conditional probability problem. If the number of people hospitalized is 0 or 1, then the total loss will be less than 1. However, if two people are hospitalized, the probability that the total loss will be less than 1 is 0.5. we need to exclude the 50% x 0.09 chance of a double loss costing more than 1. So
P(Cost < 1)
= 0.49 + 0.42 +0.045
= 0.955
P(0 losses | Cost < 1)
= P(0 losses and Cost < 1) / P(Cost < 1)
= 0.49 / 0.955 = 0.513
P(1 loss | Cost < 1)
= 0.42 / 0.955 = 0.440
P(2 losses | Cost < 1) = 0.045 / 0.955 = 0.047
Now take the expectation:
E[X] = (0)(0.513) + (1)(0.440) + (2)(0.047)
= 0.440 + 0.094
= 0.534
What’s the correct answer for this?
Answer:
D.
Step-by-step explanation:
If we rotate the 3-D figure around y-axis, we'll obtain a cylinder with a radius of 1 unit.
