Some parts of California are particularly earthquake- prone. Suppose that in one metropolitan area, 25% of all homeowners are insured against earthquake damage. Four homeowners are to be selected at random; let X denote the number among the four who have earthquake insurance. a. Find the probability distribution of X. [Hint: Let S denote a homeowner who has insurance and F one who does not. Then one possible outcome is SFSS, with proba bility (.25)(.75)(.25)(.25) and associated X value 3. There are 15 other outcomes.] b. Draw the corresponding probability histogram. c. What is the most likely value for X
Answers
Answer:
a. Binomial random variable (n=4, p=0.25)
b. Attached.
c. X=1
Step-by-step explanation:
This can be modeled as a binomial random variable, with parameters n=4 (size of the sample) and p=0.25 (proportion of homeowners that are insured against earthquake damage).
a. The probability that X=k homeowners, from the sample of 4, have eartquake insurance is:
[tex]P(x=k) = \dbinom{n}{k} p^{k}(1-p)^{n-k}\\\\\\P(x=k) = \dbinom{4}{k} 0.25^{0}\cdot0.75^{4}[/tex]
The sample space for X is {0,1,2,3,4}
The associated probabilties are:
[tex]P(x=0) = \dbinom{4}{0} p^{0}(1-p)^{4}=1*1*0.3164=0.3164\\\\\\P(x=1) = \dbinom{4}{1} p^{1}(1-p)^{3}=4*0.25*0.4219=0.4219\\\\\\P(x=2) = \dbinom{4}{2} p^{2}(1-p)^{2}=6*0.0625*0.5625=0.2109\\\\\\P(x=3) = \dbinom{4}{3} p^{3}(1-p)^{1}=4*0.0156*0.75=0.0469\\\\\\P(x=4) = \dbinom{4}{4} p^{4}(1-p)^{0}=1*0.0039*1=0.0039\\\\\\[/tex]
b. The histogram is attached.
c. The most likely value for X is the expected value for X (E(X)).
Is calculated as:
[tex]E(X)=np=4\cdot0.25=1[/tex]
Related Questions
Johana works in the crime lab at the New York City Police Department. A woman’s shoe was found at a crime scene. Johana measures it and then uses the following function equation to predict the estimated height of the suspect: y =1.19x+56 where x represents a woman’s shoe size and y represents the estimated likely height of the woman in inches. a. Using a calculator, determine an ordered pair that is a solution to this function. b. Interpret your solution in the context of this problem, using one or more complete sentences. Use the information given in the problem when describing the values of your input and output. 58
Answers
Answer:
(7, 64.33)
Step-by-step explanation:
For a woman suspect whose shoe size was found at the crime scene, the equation which can be used to predict the estimated height is given as:
[tex]y=1.19x+56,$ where:\\x = woman's shoe size\\ y= the estimated likely height of the woman in inches.[/tex]
(a)Let x=7
Then: y =1.19(7)+56=64.33
An ordered pair that is a solution to the function is (7, 64.33)
(b) The estimated height of a woman who is of shoe size 7 is 64,33 inches.
Eighty four percent of adults want to live to age 100. You randomly select five adults and ask them whether they want to live to age 100. The random variable represents the number of adults who want to live to age 100.
1) Construct a binomial distribution.
2) Graph the binomial distribution using a histogram and describe its shape. Graph the binomial distribution.
3) What is the shape of the histogram?
A. Symmetric
B. Skewed left
C. Skewed right
4) What values of the random variablex would you consider unusual?
The value(s)_____would be unusual because the associated probability (probabilities) is(are)______.
Answers
Answer:
1) Binomial distribution with n=5 and p=0.84.
2) Attached. Skewed.
3) C. Skewed right
4) The values 0 and 1 would be unusual because the associated probabilities are lower than 0.3%.
Step-by-step explanation:
1) A binomial distribution for this case can be constructed with the parameters n=5 and p=0.84.
The probability of k adults from the sample respond Yes is:
[tex]P(x=k) = \dbinom{n}{k} p^{k}(1-p)^{n-k}=\dbinom{5}{k} 0.84^{k}\cdot 0.16^{5-k}[/tex]
[tex]P(x=0) = \dbinom{5}{0} p^{0}(1-p)^{5}=1*1*0.0001=0.0001\\\\\\P(x=1) = \dbinom{5}{1} p^{1}(1-p)^{4}=5*0.84*0.0007=0.0028\\\\\\P(x=2) = \dbinom{5}{2} p^{2}(1-p)^{3}=10*0.7056*0.0041=0.0289\\\\\\P(x=3) = \dbinom{5}{3} p^{3}(1-p)^{2}=10*0.5927*0.0256=0.1517\\\\\\P(x=4) = \dbinom{5}{4} p^{4}(1-p)^{1}=5*0.4979*0.16=0.3983\\\\\\P(x=5) = \dbinom{5}{5} p^{5}(1-p)^{0}=1*0.4182*1=0.4182\\\\\\[/tex]
2) The graph is attached.
The shape is skewed to the right. This is due to the value of p being close to 1.
The sample space is [0,1,2,3,4,5] and the biggest values have the highest probabilities.
3) The shape is skewed right.
4) The values 0 and 1 would be unusual because the associated probabilities are lower than 0.3%.
The value k=2 can also be considered unusual as it has an associated probability of 2.8%.
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Analysis reveals that a company had a net increase in cash of $21,760 for the
current year. Net cash provided by operating activities was $19,600; net cash
used in investing activities was $10,800 and net cash provided by financing
activities was $12,960. If the year-end cash balance is $26,400, the beginning
cash balance was:
Answers
Answer:
Beginning Cash balance was $4,640.
Step-by-step explanation:
Net cash flow from operating activities = $19,600
Net cash flow used in investing activities = ($10,800)
Net cash provided by financing activities = $12,960
Net increase in cash $21,760
Beginning cash balance = Closing balance ($26,400) less net increase in cash ($21,760) = $4,640
The increase in cash represents the cash that was generated from operating, investing, and financing activities. These three activities are the classifications of an entity's activities. Operating activities are those activities that are normal to the business, i.e. activities the business undertakes under its mission. The investing activities arise from the purchase and sale of investments. These are not normal activities of most entities, except investment companies. Financing activities are activities engaged by an entity to raise finance, including the repayment of the borrowed funds plus interest.
b) On one rectangular coordinate system, show approximate radian values for one circle, as
well as the degree values for every 1/8 of one circle. (2 pts.)
Answers
Answer:
(See explanation below for further details)
Step-by-step explanation:
Any point in rectangular form can be described in terms of radius and angle of the circle. That is:
[tex]P = (r\cdot \cos \theta, r\cdot \sin \theta)[/tex]
Since circunference is divided into 8 equal parts, the point can be modelled as:
[tex]P = (r\cdot \cos \frac{2\pi\cdot n}{8}, r \cdot \sin \frac{2\pi\cdot n}{8} )[/tex]
The approximate radian and degree values for one circle are:
Radians
[tex]0 (0), \frac{\pi}{4} (0.785), \frac{\pi}{2} (1.571), \frac{3\pi}{4} (2.355), \pi (3.142), \frac{5\pi}{4} (3.925), \frac{3\pi}{2} (4.71), \frac{7\pi}{4} (5.495), 2\pi (6.280)[/tex]
Degrees
[tex]0^{\circ}, 45^{\circ}, 90^{\circ}, 135^{\circ}, 180^{\circ}, 225^{\circ}, 270^{\circ}, 315^{\circ}, 360^{\circ}[/tex]
HELPPPPP ASAP I NEED IT I BEG OF U I DONT UNDERSTAND THIS PLSSSSSSSS
Ross walks every morning. He can cover 6 miles in 2 hours.
His speed is___
miles per hour. He can cover_____
more miles in 4 hours than he can in 3 hours.
Answers
Answer:
speed = distance ÷ time
6÷2 = 3
his speed is 3 miles per hour
he can cover 3 more miles....
what is the next term in the arithmetic sequence? 9,17,25,33,...
Answers
Answer:
41
Explanation:
To solve this problem we must first understand what the pattern is in the arithmetic sequence. Once we understand the pattern, we can then apply it to the final known term to find the next term.
Take a look at the arithmetic sequence given:
9, 17, 25, 33,...
Let's start by figuring out how they got the second term in the sequence. To do that, subtract the second term by the first term. This will reveal the pattern.
9 - first term
17 - second term
17 - 9 = 8
So, this means they added eight to get the next term. Therefore, the pattern should be 'add eight' to get the next term. Just to be sure the pattern we found is correct, apply it to the given arithmetic sequence.
9, 17, 25, 33,...
9 + 8 = 17
17 + 8 = 25
25 + 8 = 33
So, since 'adding eight' every time gives us the next term, the pattern is correct.
Finally, let's continue the pattern to find the next term.
9, 17, 25, 33,...
33 + 8 = 41
9, 17, 25, 33, 41,...
Therefore, the next term in the arithmetic sequence is 41.
A pizzeria offers 10 different toppings. They have pepperoni, green peppers, onion, bacon, sausage, pineapple, ham, spinach, chicken and extra cheese. a. State if this problem is a permutation or combination. Briefly explain your reasoning.
Answers
Answer:
combination
Step-by-step explanation:
We have that permutations are groupings in which the order of the objects matters. Combinations are groupings where content matters but order does not.
In this case we have a list of ingredients for the pizza, therefore the order does not matter as long as the ingredients are indicated, which means that this is an example of a combination.
To estimate what percent of employees are at least 1 minute late for their work in the morning, a company put registers at the office entrance that could identify each employee and collect data about the time when they arrived at work. The company found that 18% of the employees are late. What is the sample and what is the population
Answers
Answer:
Population: all company employees.
Sample: arrival times of the employees during the data collection.
Step-by-step explanation:
In this case, the population is the group about which the company wants to estimate a parameter (proportion of employees who are at least 1 minute late for work). This group is all employees of the company.
The sample is comprised of the arrival times of the individuals who went to work during the data collection by the entry time recording machine. The proportion of the sample is calculated on these arrival times, with which the proportion of the population will be inferred.
Rosalyn has three different-shaped containers that contain marbles. She has 3 round containers, each holding 16 marbles.
She has 4 square containers, each holding 25 marbles. She has 2 rectangular containers, each holding 33 marbles.
How many marbles are in the containers altogether?
Answers
Answer:
42,996
Step-by-step explanation:
3*16+4*25+2*33=48+100+66=214
Too Tall Tower has office space below the 57th floor and condominiums above. Too Tall Tower is an example of a
Answers
Nathaniel wants to build 50 birds using Lego blocks. How many birdhouses can he build at most with the remaining Lego blocks? Graph your solution.
Answers
Answer:
18
Step-by-step explanation:
Even if we both break down tonight
And you say you hate me
And we go to bed angry
I know everything will be alright
I'll be here waiting
I promise I'm changing
I just need
A little time to show you I'm worth it
I know that I can be a difficult person
I'm a stress case drive you up the wall when I'm workin'
Actually I'm prolly worse when I'm not you don't deserve it
Make you nervous 'cause you know I'ma break soon
Every time I do I say something that hurts you
Actin' like I'm gone, but we both in the same room
I don't like to be wrong which I know you relate to
And I know I make you feel like you're at the end of your road
That's when I look at you and tell you I'd be better alone
That's just the pride talkin' isn't it cause both of us know
A perfect square trinomial can be represented by a square model with equivalent length and width. Which polynomial can be represented by a perfect square model?
x2 – 6x + 9
x2 – 2x + 4
x2 + 5x + 10
x2 + 4x + 16
Answers
Answer:
A
Step-by-step explanation:
i got it right on the exam
Please answer this question !! Thank you !! Will give brainliest !!
Answers
IQ scores are measured with a test designed so that the mean is 116 and the standard deviation is 16. Consider the group of IQ scores that are unusual. What are the z scores that separate the unusual IQ scores from those that are usual? What are the IQ scores that separate the unusual IQ scores from those that are usual? (Consider a value to be unusual if its z score is less than minus2 or greater than 2.)
Answers
Answer:
So the z-scores that separate the unusual IQ scores from those that are usual are Z = -2 and Z = 2.
The IQ scores that separate the unusual IQ scores from those that are usual are 84 and 148.
Step-by-step explanation:
Problems of normally distributed samples are solved using 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.
In this question, we have that:
[tex]\mu = 116, \sigma = 16[/tex]
What are the z scores that separate the unusual IQ scores from those that are usual?
If Z<-2 or Z > 2, the IQ score is unusual.
So the z-scores that separate the unusual IQ scores from those that are usual are Z = -2 and Z = 2.
What are the IQ scores that separate the unusual IQ scores from those that are usual?
Those IQ scores are X when Z = -2 and X when Z = 2. So
Z = -2
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]-2 = \frac{X - 116}{16}[/tex]
[tex]X - 116 = -2*16[/tex]
[tex]X = 84[/tex]
Z = 2
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]2 = \frac{X - 116}{16}[/tex]
[tex]X - 116 = 2*16[/tex]
[tex]X = 148[/tex]
The IQ scores that separate the unusual IQ scores from those that are usual are 84 and 148.
Answer:
[tex]\mu -2*\sigma = 116-2*16= 84[/tex]
[tex]\mu +2*\sigma = 116+2*16= 148[/tex]
Step-by-step explanation:
We know that the distirbution for the IQ have the following parameters:
[tex]\mu=116, \sigma=16[/tex]
The z score is given by this formula
[tex] z = \frac{X -\mu}{\sigma}[/tex]
And replacing the limits we got:
[tex] X = \mu \pm z \sigma[/tex]
For this case we know that a value to be unusual if its z score is less than minus2 or greater than 2, so then we can find the limits with this formulas:
[tex]\mu -2*\sigma = 116-2*16= 84[/tex]
[tex]\mu +2*\sigma = 116+2*16= 148[/tex]
A student participates in a Coke versus Pepsi taste test. She correctly identifies which soda is which four times out of six tries. She claims that this proves that she can reliably tell the difference between the two soft drinks. You have studied statistics and you want to determine the probability of anyone getting at least four right out of six tries just by chance alone. Which of the following would provide an accurate estimate of that probability?
a. Have the student repeat this experiment many times and calculate the percentage time she correctly distinguishes between the brands.
b. Simulate this on the computer with a 50% chance of guessing the correct soft drink on each try, and calculate the percent of times there are four or more correct guesses out of six trials.
c. Repeat this experiment with a very large sample of people and calculate the percentage of people who make four correct guesses out of six tries.
Answers
Answer:
C.
Repeat this experiment with a very large sample of people and calculate the percentage of people who make four correct guesses out of six tries
Step-by-step explanation:
Why I choose the answer c is because for this kind of experiment to determine probability..it needs to be tested on variety of people as different people have different taste issue.
Trying it on one person alone will accumulate much error that will be very hard and uneasy to detect.
where can we put parentheses in 19 - 3 times 5 to make it equivalent to 80
Answers
Answer:
(19-3)*5 = 80
Step-by-step explanation:
(19-3)*5 = 80
Parentheses first
16*5 = 80
80
Answer: (19 - 3) * 5 = 80
Check to see if this is right.
(19 - 3) * 5 = 80
16 * 5 = 80
80 = 80
Best of Luck!
The human body has a normal temperature of 98.6°F. Doctors will get worried if a sick patient has a temperature that varies from the normal by more than 3°F. Create an absolute value inequality and solve it to determine what body temperatures would be considered unhealthy.
Answers
Answer:
[tex] |T- 98.6| \geq 3[/tex]
And in order to solve this we have two possibilities:
Solution 1
[tex] T -98.6 \leq -3[/tex]
And solving for T we got:
[tex] T \leq 98.6- 3[/tex]
[tex] T\leq 95.6[/tex]
Solution 2
And the other options would be:
[tex] T -98.6 \geq 3[/tex]
[tex] T \geq 101.6[/tex]
Step-by-step explanation:
For this case we can define the variable os interest T as the real temperature and we know that if we are 3 F more than the value of 98.6 we will be unhealthy so we can set up the following equation:
[tex] |T- 98.6| \geq 3[/tex]
And in order to solve this we have two possibilities:
Solution 1
[tex] T -98.6 \leq -3[/tex]
And solving for T we got:
[tex] T \leq 98.6- 3[/tex]
[tex] T\leq 95.6[/tex]
Solution 2
And the other options would be:
[tex] T -98.6 \geq 3[/tex]
[tex] T \geq 101.6[/tex]
What is 0.59 in words
Answers
Answer:
fifty nine hundredths
what dose x equal 4x + 4 = -7 +2x +19
Answers
Answer:
[tex]x=4[/tex]
Step-by-step explanation:
[tex]4x + 4 = -7 +2x +19[/tex]
[tex]4x + 4 = 2x +12[/tex]
[tex]4x-2x=12-4[/tex]
[tex]2x=8[/tex]
[tex]x=8 \div 2[/tex]
[tex]x=4[/tex]
Step 1: Simplify both sides of the equation.
4x+4=−7+2x+19
4x+4=(2x)+(−7+19)(Combine Like Terms)
4x+4=2x+12
4x+4=2x+12
Step 2: Subtract 2x from both sides.
4x+4−2x=2x+12−2x
2x+4=12
Step 3: Subtract 4 from both sides.
2x+4−4=12−4
2x=8
Step 4: Divide both sides by 2.
2x/2 = 8/2
Description:
The first step is to Simplify both sides of the equation, when you do it correct and follow the steps above you equation will end up 4x+4=2x+12. For steps 2 Subtract 2x from both sides, when you do it correct your equation will end up like 2x+4=12. For step 3 you Subtract 4 from both sides, when you do it correct equation will end up like 2x=8. Last step is to Divide both sides by 2, when you do it correct your answer will come as x=4 .
Answer: x=4
Please mark brainliest
Hope this helps.
an acute angle can have all of the following measures except
Answers
Answer:
An acute angle is an angle that has a measure that is less than 90 degrees. Any measure that is less than 90 degrees could be an acute angle. For example, 8°, 15°, °26°, and 89° are all acute angles. Anything that is 90 degrees is a right angle and greater than 90 degrees is an obtuse angle. An acute angle can have all of the following measures except 90 degrees or greater than 90 degrees.
Answer:
0 is not an acute angle
Step-by-step explanation:
if the measurement of an angle is between 0 and 90 degrees then we called it an acute angle. it means acute angle is greater than 0 and less than 90 degrees. among the the other options it is between 0 and 90 therefore 0 is not it
hope this helps
Paper and Pencil Construction: Construct a Line Perpendicular to a Given Line through a Point on the Line
Answers
Step-by-step explanation:
wait a person was about to report it sorry ;/
had to take it off
The independent-samples t testResearch Scenario: A forensic psychologist has developed a new program that teaches empathy and positive social skills to youth offenders who are incarcerated for a violent offense. She wants to know whether this new treatment is more effective in increasing empathy than the standard treatment that these youth offenders usually receive. She sets up a treatment group that consists of 8 youth offenders incarcerated for violent offenses who will receive the new treatment. Her control group consists of 8 similar youth offenders who receive the standard treatment only. At the end of treatment, she administers the Basic Empathy Scale (BES; Jolliffe and Farrington, 2006), a 20-item questionnaire where higher scores indicate higher levels of empathy, and records the results in the table below.Using this table, enter the data into a new SPSS data file and run an independent-samples t test to test the claim that violent youth offenders who receive the new treatment will have higher BES scores than violent youth offenders who receive standard treatment. Follow the directions below the table to complete the homework.Language-Based Spatially-based 93 83 77 89 89 72 87 95 78 76 62 63 67 99 90 84 95 931. Paste SPSS output. 2. Write an APA-style Results section based on your analysis. Include your boxplot as an APA-style figure as demonstrated in the APA writing presentation. (Results = 8 pts: Graph = 5 pts)
Answers
Answer:
Step-by-step explanation:
Hello!
The researcher developed a treatment to teach social skills to youth offenders. To test if the treatment is effective in increasing empathy compared to the standard treatment she randomly selected a group of 9 offenders and applied the new treatment and to another group of 9 randomly selected youth offenders, she applied the standard treatment. (Note: the data corresponds to two samples of 9 units each, so I've used those sizes to conduct the test)
At the end of the treatment, she administers BES to measure their empathy levels. Her claim is that the offenders that received the new treatment will have higher BES scores than those who received the standard treatment.
1) Using the records obtained for both groups, she intends to conduct an independent t-test to analyze her claim.
X₁: BES results of a youth offender treated with the new treatment.
X₂: BES results of a youth offender treated with the standard treatment.
H₀: μ₁ = μ₂
H₁: μ₁ ≠ μ₂
α:0.05
test statistic
[tex]t_{H_0}= -0.32[/tex]
p-value: 0.7517
The p-value is greater than the significance level so the decision is to not reject the null hypothesis. This means that at a 5% significance level you can conclude that there is no difference between the mean BES scores of the youth offenders treated with the new treatment and the mean BES score of the youth offenders treated with the standard treatment. The new treatment doesn't increase the levels of social empathy of the youth offenders.
I hope this helps
(Box plot in attachment)
find the sum of the equations: 1/(x-2)+3/(x+3)=4/(x^2+x-6)
Answers
Answer:
x= 7/4
Step-by-step explanation:
Find the LCM for x-2,x+3,x^2+x-6 which is (x-2) (x+3)
then multiply
Raymond is installing a new kitchen counter top . The counter top is a rectangular piece of quartz that is 5.75 feet long and 2.47 feet wide .Round the length and width to the nearest whole number . Then estimate the perimeter of the countertop
Answers
Answer:
5.75 ft ≈ 6 ft
2.47 ft ≈ 2 ft
perimeter of the rectangular counter top = 16 ft
Step-by-step explanation:
The counter top he is installing is a rectangular piece of quartz that is 5.75 ft long and 2.47 ft wide. The length and the width can be rounded off to the nearest whole number as follows.
length = 5.75 ft to the nearest whole number will be 6 ft
width = 2.47 ft to the nearest whole number will be 2 ft
The logic in rounding off the number to the nearest whole number is that the value on the left hand side of the decimal is rounded off to an integer. If the number at the right hand side of the number is greater or equal to 5 we borrow 1 and add to the left hand side number of the decimal number.
Therefore,
Perimeter of the rectangle = 2l + 2w
perimeter of the rectangle = 2 × 6 + 2 × 2
perimeter of the rectangle = 12 + 4
perimeter of the rectangle = 16 ft
A 2013 study by pediatrician investigates whether it in better to give children the diphtheria, tetanus and pertussis (DTaP) vaccine in the thigh or the arm. The pediatricians collected the data from two different random samples. The first random sample was collected from children who were given the vaccine in the thigh. The second random sample was collected from children who were given the vaccine in the arm. Pediatricians recorded whether the children had a severe reaction or not. Reference: Jackson. LA., Peterson. D., Nelson. J.C., et al. (13 00 authors). 2013. Vaccination site and risk of local reaction in children one through six years of age. Pediatrics 131:283-289 Pediatricians conducted a chi square test of independence. The chi square test statistic fix this data is 2.0609 with a P value of O 1511. What can the pediatrician conclude? A) There is a statistically significant association between vaccine location and severe reaction. B) Pediatrician, have strong evidence that the severe reaction, to vaccine depend on location of the vaccine. C) The pediatricians cannot make a conclusion The conditions, for use of the chi-square test are not met. D) There is not enough evidence to conclude that there is. an association between vaccine location and severe reaction.
Answers
Answer:
A
Step-by-step explanation:
Since chi-squared calculated value is greater than p-value, there is a relationship between vaccine location and severe reaction.
Answer:
Step-by-step explanation:
This survey is testing for an association between the vaccine location and severe reactions using the chi-square test of independence.
Null hypothesis: Vaccine location and severe reactions are independent
Alternative: Vaccine location and severe reactions are not independent
With a chi square test statistic of 2.0609 with a P value of 0.1511. Using the p- value in comparison to either α = 0.05 or 0.01, the pediatricians can fail to reject the null as the p-value is greater than 0.05 or 0.01 and can conclude that there is a statistically significant association between vaccine location and severe reaction.
This approach was appropriate because the sampling method was simple random sampling, the variables that were under study were categorical, and the expected frequency count was at least 5 in all values to be able to reach value of 283 and 289.
Sara is a drummer in her school is marching band she wants to make a geometrically similar model of a snare drum for her stuffed animals. To find the dimensions she should use to make a cylindrical model with a scale of 1 : 4, Sara measures the radius and height of a snare drum and multiplies each dimension by 1/2. Which statement is true?
A. A cylinder with Sara’s dimensions will be geometrically similar, and the scale factor will be 1:4
B. A cylinder with Sara’s dimensions will be geometrically similar, but the scale factor will be 1:2
C. A cylinder with Sara’s dimensions will be geometrically similar, but the scale factor will be 1:8
D. A cylinder with Sara’s dimensions will not be geometrically similar
Answers
Answer:
Option B.
Step-by-step explanation:
Let the radius of the snare drum = r
and radius of the model = R
Ratio of the dimensions of the snare drum and the model = 1 : 4
So, [tex]\frac{r}{R}=\frac{1}{4}[/tex]
Now as per question, dimensions of the snare drum is multiplied by a scale factor of [tex]\frac{1}{2}[/tex]
Radius of the snare drum = [tex]\frac{r}{2}[/tex]
Ratio of the radius of the snare drum and cylindrical model ,
[tex]\frac{\frac{r}{2}}{R} =\frac{1}{4}[/tex]
[tex]\frac{r}{2R}=\frac{1}{4}[/tex]
[tex]\frac{r}{R}=\frac{1}{2}[/tex]
Therefore, the cylinder with Sara's dimensions will be geometrically similar but the scale factor will be 1 : 2
Option B is the answer.
100 points for brainliest
Answers
Answer:
565.71 yd²
Step-by-step explanation:
Surface area = [tex]2 \pi r (r+h)[/tex]
Area = 2 × 22/7 × 6 (6 + 9)
Area = 22 × 12/7 × 15
Area = 565.71 yd²
Answer:
565.71 yd²
Step-by-step explanation:
Surface area =
Area = 2 × 22/7 × 6 (6 + 9)
Area = 22 × 12/7 × 15
Area = 565.71 yd²
1. The function h is the sum of the functions f(x)=3x+5 and g(x)=2x^2 - 6x - 2. Which represents h? A.h(x) = 5x^2 - x - 2 B. h(x) = 2x^2 - 3x + 3 C. h(x) = 2x^2 - 9x + 7
D. h(x) = -3x + 3
Answers
Answer:
B. h(x) = 2x^2 - 3x + 3
Step-by-step explanation:
Given
f(x)=3x+5
g(x)=2x^2 - 6x - 2
h(x) is sum of the functions f(x) and g(x)
Thus,
h(x) = f(x) + g(x)
substituting value of f(x) and g(x) as given above we have
h(x) = 3x+5 + 2x^2 - 6x - 2
as ( 3x - 6x = -3x and 5- 2 = 3) , we have
h(x) = 2x^2 -3x + 3
Thus, correct answer is option B. h(x) = 2x^2 - 3x + 3.
Match each transformation of f(x) with its description. shifts f(x) 4 units down arrowRight compresses f(x) by a factor of toward the y-axis arrowRight stretches f(x) by a factor of 4 away from the x-axis arrowRight shifts f(x) 4 units right arrowRight
Answers
The different transformations have been matched to their respective operations below.
How to Interpret Transformations?Parent function is given as: f(x) = 2x - 6
Thus, the transformations are:
When f(x) shifts 4 units down, we have;
f(x) → f(x) - 4
⇒ g(x)= 2x - 6 - 4 = 2x - 10
When it stretches f(x) by a factor of 4 away from the x-axis;
f(x) → 4*f(x)
⇒ g(x) = 4(2x - 6) = 8x - 24
When it shifts f(x) 4 units right;
f(x) → f(x - 4)
⇒ g(x) = 2(x - 4) - 6 = 2x - 14
When it compresses f(x) by a factor of 4 toward the y-axis;
f(x) → f(4x)
⇒ g(x) = 2*4x - 6 = 8x - 6
Read more about Transformations at; https://brainly.com/question/4289712
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Two scientists are measuring the temperature of liquids in two beakers. Liquid A has a temperature of -105.4° C and Liquid B has a temperature of -10.83 ° C.
Which liquid is warmer and why?
Answers
Answer: Liquid B is warmer.
Step-by-step explanation:
The data that we have is:
Temperature A = -105.4° C
Temperature B = -10.83° C
We want to know which liquid is warmer, this is equivalent to see which temperature is bigger, Ta or Tb.
Now, you can see that temperature A is larger in module, but this is a negative number.
When we work with negative numbers, the bigger ones are the ones closer to zero. This means that for example, -1 is larger than - 150.
From this, we can conclude that Liquid B is warmer.
Another way to see it is with a change of units.
If we have A degrees Celcius, and we want to to transform it into Kelvins, we must add 273.15°.
Then we have:
Ta = (-105.4° + 273.15°) K = 167.75 K
Tb = (-10.83 ´273.15°) = 262.35 K
where you can see that liquid B has a larger temperature.
Answer:
Liq A= -105.4ºC < LiqB= -10.83ºC
Step-by-step explanation:
Hello!
The easiest and quickest way to compare two negative values and determine which one is greater is by sorting them in a number line. (Check attachment)
You can also compare the absolute value of the temperature measurements. |10.83| < |105.4|. As the negative value decrease, the absolute value increases.
So the temperature of Liquid B > Temperature of liquid A.
I hope this helps!