Final answer:
The probability that fewer than 32 out of 60 victims did not know their murderer can be found using the binomial probability formula, summing the probabilities where x ranges from 0 to 31 with a success rate of 42% for each trial.
Explanation:
To find the probability that fewer than 32 out of 60 murder victims did not know their murderer, given that 58% of victims did know their murderer, we can use the binomial probability formula. Considering that 42% (=100%-58%) of the victims did not know their murderer, we want the cumulative probability of x=0 to x=31 successes (victims not knowing the murderer) out of n=60 trials (total murder cases).
This can be calculated using a statistical program or a binomial probability table, as manually computing this would be time-consuming and complex. However, the specific steps would involve summing up the probabilities of all scenarios where the number of victims not knowing their murderer ranged from 0 to 31, factoring in the binomial coefficient, the probability of a single victim not knowing the murderer (42%), and its complement for each case.
The population of Bigville increased from 387,480 to 571,533 in the last 7 years. During the same time period, Smallville increased its population by 53.67%. Which town is growing at the greatest rate and by what factor? (round to nearest hundredth) A) Bigville by a factor of 1.13 B) Bigville by a factor of 6.17 C) Smallville by a factor of 1.13 D) Smallville by a factor of 6.17
Answer:
C!!
Smallville by a factor of 1.13
Bigville --
571,533 - 387,480
387,480
= 47.5%
Smallville -- 53.67
Thus,
53.67
47.5
= 1.129
Approximately how many years are needed to double a $500 investment when interest rates are 13.50 percent per year? (Round your answer to 2 decimal places)
Helen's preferences over cds (c) and sandwiches (s) are given by u(s,
c.= sc + 10(s + c), with muc = s + 10 and mus = c + 10. if the price of a cd is $9 and the price of a sandwich is $3, and helen can spend a combined total of $30 each day on these goods, find helen's optimal consumption basket.
The linear function c = 2 y + 29 models the average cost of a haircut in a certain city, where c, is the average price of a haircut y years after 1995. find the slope for the model. then describe what this means in terms of the rate of change in the average cost of a haircut over time
The rate of change implies that the city's haircut prices are consistently going up over time.
The given linear function is c=2y+29, where c represents the average cost of a haircut y years after 1995.
The slope of the linear function, 2, reflects the rate of change in the average cost of a haircut over time.
This means that for each year after 1995, the average cost of a haircut increases by $2. In other words, the slope indicates that the cost of haircuts is rising at a constant rate of $2 per year. This steady increase implies that the city's haircut prices are consistently going up over time.
The positive slope signifies that the average cost is consistently moving upward as the year progresses. Customers can expect to pay, on average, $2 more for a haircut each year compared to the previous year.
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The slope of the linear function c = 2y + 29 is 2, indicating that the average cost of a haircut increases by 2 units for every 1 increase in the number of years after 1995.
Explanation:The slope of a linear function represents the rate of change. In the given linear function c = 2y + 29, the slope is the coefficient of y, which is 2. This means that for every 1 increase in y (number of years after 1995), the average cost of a haircut will increase by 2 units.
(b) the water level drops at a rate of 0.1 cm per hour. at what rate is the radius of the water decreasing when the depth is 4 cm? round your answer to four decimal places.
The rate at which the radius of the water is decreasing when the depth is 4 cm is 0.6949 cm/hr.
Explanation:To find the rate at which the radius of the water is decreasing, we can use the chain rule from calculus. Let's denote the depth of the water as 'h' and the radius as 'r'. We are given that the water level drops at a rate of 0.1 cm per hour, so dh/dt = -0.1 cm/hr. We want to find dr/dt when h = 4 cm. Using the formula for the volume of a cone, V = (1/3)πr^2h, we can find the relationship between r and h: r = √((3V)/(πh)). Taking the derivative of this equation with respect to time, we have: dr/dt = (√((3V)/(πh)))' = -(3/2)(√((3V)/(πh^3)))(dh/dt). Plugging in the given values and solving for dr/dt when h = 4 cm, we get:
dr/dt = -(3/2)(√((3(350))/(π(4)^3)))(-0.1) = 0.6949 cm/hr
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Is y=4x+x a linear equation
A container holds 5 gallons of juice. How much is this in pints?
5 gallons is 40 pints.
Hope this helps!
Write a word problem for the absolute value
The absolute value is useful in solving problems involving distance, temperature, and error in measurement. The word problem is described below.
A word problem involving absolute value is as following:
John lives 3 blocks away from his school.
One day, he walked to school and noticed that he accidentally left his backpack at home.
He decided to go back home to get it. When John got back home, he realized that he forgot his backpack was actually in his car.
John's car is parked 5 blocks away from his house. How far did John walk in total?
To solve this problem, we need to use absolute value.
John walked 3 blocks to school, then back home, and then 5 blocks to his car.
The total distance he walked would be the absolute value of the difference between the distance from school to home and the distance from home to car:
|3 - 5| = 2
Therefore, John walked a total of 2 blocks that day.
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When an opinion poll calls landline telephone numbers at random, approximately 30% of the numbers are working residential phone numbers. the remainder are either non-residential, non-working, or computer/fax numbers. you watch the random dialing machine make calls. x is the number of calls until the first working residential number is reached. does x have a binomial distribution? give your reasons?
A submarine took 16 minutes to reach a depth of 96 meters below the surface of the water. Which integer best represents the rate of the submarines dive
(×2+1)(x3+2x)(x2+4x-16i-4xi) Solve for the roots in equation
The probability that the factory manufactures a defective light bulb is 0.02. find the probability that the plant manufactures 100 non defective light bulbs before it manufactures 10 defective ones
A model is made of a car. The car is 10 feet long and the model is 7 inches long. What is the ratio of the length of the car to the length of the model? A. 10 : 7 B. 7 : 120 C. 120 : 7 D. 7 : 10
Final answer:
To find the ratio of the car's length to the model's length, first convert the car's length to inches (120 inches), then compare it to the model's length (7 inches), which gives a ratio of 120 : 7.
Explanation:
The question asks for the ratio of the length of the car to the length of the model. First, it's essential to convert both measurements to the same unit for an accurate comparison. The car is 10 feet long, and since 1 foot equals 12 inches, the car's length in inches is 10 feet × 12 inches/foot = 120 inches. The model is 7 inches long. Therefore, the ratio of the length of the car to the length of the model is 120 inches to 7 inches, which simplifies to 120 : 7.
The ladybugs are planting a garden. They have 25-cm-by-10 cm rectangle for flowers. Each flower needs exactly 1 square centimeter for space. How many flowers can they plant?
Answer: They can plant 250 flowers.
Step-by-step explanation:
Given : The dimension of the rectangular garden = 25-cm-by-10 cm
[i.e. length by width]
Area of rectangle = length x width
⇒ Area of rectangular garden = 25 x 10 = 250 square centimeter .
Area required by each flower = 1 square centimeter
Then, the number of flowers they can plant = [tex]\dfrac{\text{Area of garden}}{\text{Area of needed by each flower}}[/tex]
[tex]=\dfrac{250}{1}=250[/tex]
Hence, they can plant 250 flowers.
Mrs. Rodger got a weekly raise of $145. If she gets paid every other week, write an integer describing how the raise will affect her paycheck.
she gets 145 every week, but paid every other week
so 145 *2 = 290
her pay check will increase by $290
The measures of a sphere with a volume of 972pi in^3 are multiplied by 1/3.
What is the volume of the sphere?
A) 324pi in^3
B) 108pi in^3
C) 54pi in^3
D 36pi in^3
The graph above can be extrapolated to determine:
Boyle's Law
PV = k
absolute zero
VT = k
nothing
We can see that
when it is extrapolated
The curve is going downward
and it is till it touches temperature axis
so, we can find point there
It intersects at temperature =-280C
Since, it is x-intercept
so, y will be 0 at that point
so, Volume will be 0 when temperature is -280C
and this is absolute zero definition of volume function
so, Absolute zero.........Answer
Employees in 2012 paid 4.2% of their gross wages towards social security (FICA tax), while employers paid another 6.2%. How much will someone earning $45,000 a year pay towards social security out of their gross wages?
Answer:
The answer is $1890.
Step-by-step explanation:
Employees in 2012 paid 4.2% of their gross wages towards social security (FICA tax)
While employers paid another 6.2%.
So, someone earning $45000, will pay [tex]0.042\times45000=1890[/tex] dollars in FICA.
The question says only individual. The earnings are exclusive to employees, so they will only pay from earnings. The employer will not pay from employee's earnings.
The answer is $1890.
The number of earnings towards social security should be $1,890.
Given that,
The employers in 2012 paid 4.2%.The employer should paid 6.2%.And, the earning should be $45,000.Based on the above information, the calculation is as follows:
[tex]= 4.2\% \times \$45,000[/tex]
= $1,890
Therefore we can conclude that the number of earnings towards social security should be $1,890.
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Two standardized tests, a and b, use very different scales of scores. the formula upper a equals 40 times upper b plus 50a=40×b+50 approximates the relationship between scores on the two tests. use the summary statistics for a sample of students who took test b to determine the summary statistics for equivalent scores on test
a. lowest score equals= 2121 mean equals= 2929 standard deviation equals= 22 q3 equals= 2828 median equals= 2626 iqr equals= 66 find the summary statistics for equivalent scores on test
a. lowest scoreequals= nothing meanequals= nothing standard deviationequals= nothing q3equals= nothing medianequals= nothing iqrequals= nothing
Final answer:
Using the transformation formula a = 40×b + 50, we calculated equivalent scores on Test A based on the given summary statistics of Test B, demonstrating the effects of linear transformation on statistical measures.
Explanation:
Using the formula a = 40×b + 50, we can calculate the equivalent scores on test A from the given summary statistics for test B. This formula allows us to transform the scores from one scale to another, maintaining the distribution's shape but adjusting the scale and location.
Lowest score on Test A = 40×(21) + 50 = 890Mean score on Test A = 40×(29) + 50 = 1,210Standard deviation remains unchanged as we are scaling and shifting the data. So, it is 40×(22) = 880.Q3 (third quartile) on Test A = 40×(28) + 50 = 1,170Median on Test A = 40×(26) + 50 = 1,090IQR (Interquartile range) remains constant as it's a measure of spread, not affected by linear transformations. So, it would be 40×(6) = 240.By applying linear transformation to the test scores, we can effectively compare results from tests using different scales, making it easier for educational institutions and researchers to evaluate data cohesively.
What does x equal in 3(x+3)-2<25
A mixture of 17 %disinfectant solution is to be made from 10% and 20% disinfectant solution. How much of each solution should be used if 20 gallons of the 17% solution are needed?
You have 5 pieces of wood. What is the total length of the wood? 73cm, 1.6m, 2.87m, 325cm and 4.04m
If p = .9, what is the frequency of the heterozygote? .81+(2)(.9)(.1) + (.01) .10 .81 + .18 .18
What is the solution of the system of equations shown in the graph ?
a. (0, 2) c. (0, 4)
b. (2, 0) d. (0, -1)
The solution of graphed equations is the point of intersection of the equations.
The ordered pair that represent the solution is [tex]\mathbf{(b)\ (2, 0)}[/tex]
From the graph, we have the following highlights.
The x-coordinate of the point of intersection is at x = 2The y-coordinate of the point of intersection is at y =0So, the coordinates are 2 and 0
Hence, the ordered pair that represents the solution is [tex]\mathbf{(b)\ (2, 0)}[/tex]
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The boy : Girl ratio is 4:5. If there are 225 students, how many girls are in the school? answer and proportion answer and proportion breakdown please
solve w = 9x + 5y for y
To solve the equation w = 9x + 5y for y, subtract 9x from both sides to get w - 9x = 5y. Then, divide every term by 5 to obtain y = (w - 9x) / 5
Explanation:To solve the equation w = 9x + 5y for y, you should first isolate y on one side of the equation. This involves a series of steps.
Start by subtracting 9x from both sides of the equation. This will give you w - 9x = 5y.Next, divide every term in the equation by 5 to solve for y. This would give you (w - 9x) / 5 = y or y = (w - 9x) / 5.Now, the equation has been solved for y, meaning you can now substitute any values for w and x into this equation to find the corresponding value for y.
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A bridge club had 22 members with a mean age of 68. Then two new members joined. One was 62 years old, and the other was 80 years old. How did the mean age change after they joined?
List five staple convenience goods that you or your household buys on a regular basis. (you do not need to use complete sentences. 2.5 points)
The five staple convenience goods are:
Food items,
Petrol,
Detergents,
Drinking water, and
Fruits.
Staple convenience goods are those items that are purchased by consumers on a regular basis because they are constantly used by them.
These items are readily available nearby a domestic environment because they are always on a high demand by consumers.
These goods listed above are called staple convenience goods because they share some common features which include:
These goods can be bought in small quantity especially when needed.These goods doesn't require a purchase plan before they are bought.They are bought frequently and regularly.Learn more here:
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$74.95 jacket; 5% tax
the selling price of a refrigerator, is $471.45. if the markup is 5% OF THE DEALER cost, what is the dealers cost of the refrigerator