Answer:
(2,1), (1,2) is your base step
if (a,b) is in the set (a+1,b+1) will be in the set
if (a,b) is in the set (a+2,b) will be in the set
if (a,b) is in the set (a,b+2) will be in the set.
Step-by-step explanation:
Think about how to solve this problem in general. How can you assure that the sum a+b is odd ?
Think about this, what happens when you sum two even numbers ? The result is even or odd ?
2+6 = 8 (even )
10+12 = 22 (even)
And what happens when you sum two odd numbers ? The result will be even or odd ? Look
3+7 = 10 (even)
5+11 = 16 (even)
Therefore to assure that a+b is odd, one of them has to be odd and one of them has to be even, that is why
(2,1), (1,2) is your base step
if (a,b) is in the set (a+1,b+1) will be in the set
if (a,b) is in the set (a+2,b) will be in the set
if (a,b) is in the set (a,b+2) will be in the set.
The set of ordered pairs that are positive integers and have an odd sum can be defined recursively by starting with the set {(1,2)}, and then adding 2 to either a or b for every pair in the set to generate additional pairs that satisfy the conditions.
Explanation:The set of ordered pairs of positive integers S given by S = {(a, b) | a ∈ Z+ , b ∈ Z+ , and a + b is odd} can be defined recursively as follows: Start with S = {(1,2)}, which is the smallest possible set that satisfies the conditions. For every (a,b) in S, (a+2, b) and (a, b+2) are also in S, since adding 2 to either a or b results in a sum that is still odd (since an even number plus an odd number equals an odd number).
As a result, the set S of all ordered pairs that result from these operations will satisfy the conditions given, namely being positive integers and having an odd sum. This demonstrates a recursive method for defining the set of ordered pairs.
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Throughout the US presidential election of 2012, polls gave regular updates on the sample proportion supporting each candidate and the margin of error for the estimates. This attempt to predict the outcome of an election is a common use of polls. In each case below, the proportion of voters who intend to vote for each candidate is given as well as a margin of error for the estimates. Indicate whether we can be relatively confident that candidate A would win if the election were held at the time of the poll. (Assume the candidate who gets more than of the vote wins.)
Answer:
1.) We cannot say for certain which candidate will win. But A has a statistical edge.
2.) We can say certainly that candidate A will win the election; albeit with a not so big margin.
3.) Candidate A will win this election based on the results of the final poll's before the election.
4.) We cannot say for certain which candidate will win. But A has a statistical edge.
The reasons are explained below.
Step-by-step explanation:
Confidence interval expresses a range of values in the distribution where the true proportion or mean can be found with some level of confidence.
Confidence Interval = (Sample Mean or Proportion) ± (Margin of error)
1. Candidate A: 54% & Candidate B:46% with Margin of error: + 5%
The confidence interval for candidate A
(54%) ± (5%) = (49%, 59%)
The confidence interval for candidate B
(46%) ± (5%) = (41%, 51%)
Since values greater than 50% occur in both intervals, we cannot say for certain that either of the two candidates will outrightly win the election. It just slightly favours candidate A who has A bigger range of confidence interval over 50% for the true sample proportion to exist in.
2. Candidate A: 52% & Candidate B:48% with Margin of error: + 1%
The confidence interval for candidate A
(52%) ± (1%) = (51%, 53%)
The confidence interval for candidate B
(48%) ± (1%) = (47%, 49%)
Here, it is outrightly evident that candidate A will win the elections based on the result of the final polls. The overall range of the confidence interval that contains the true sample proportion of voters that support candidate A is totally contained in a region that is above 50%. So, candidate A wins this one, easily; albeit with a close margin though.
3. Candidate A: 53% & Candidate B:47% with Margin of error: + 2%
The confidence interval for candidate A
(53%) ± (2%) = (51%, 55%)
The confidence interval for candidate B
(47%) ± (2%) = (45%, 49%)
Here too, it is outrightly evident that candidate A will win the elections based on the result of the final polls. The overall range of the confidence interval that contains the true sample proportion of voters that support candidate A is totally contained in a region that is above 50%. Hence, statistics predicts that candidate A wins this one.
4. Candidate A: 58% & Candidate B:42% with Margin of error: + 10%
The confidence interval for candidate A
(58%) ± (10%) = (48%, 68%)
The confidence interval for candidate B
(42%) ± (10%) = (32%, 52%)
Since values greater than 50% occur in both intervals, we cannot say for certain that either of the two candidates will outrightly win the election. It just slightly favours candidate A who has A bigger range of confidence interval over 50% for the true sample proportion to exist in.
Hope this Helps!!!
What is the value of (Negative 14 Superscript 0 Baseline) Superscript negative 2?
Answer:
1
Step-by-step explanation:
We are given that an expression
[tex]{(-14)^0)^{-2}[/tex]
We have to find the value of given expression.
We know that
[tex]a^0=1[/tex]
Using the property
[tex](-14)^0=1[/tex]
We know that
[tex]a^{-b}=\frac{1}{a^b}[/tex]
Using the property
[tex](1)^{-2}=\frac{1}{1^2}[/tex]
[tex](1)^{-2}=1[/tex]
[tex]((-14)^0)^{-2}=1[/tex]
The package of a particular brand of rubber band says that the bands can hold a weight of 7 lbs. Suppose that we suspect this might be an overstatement of the breaking weight. So we decide to take a random sample of 36 of these rubber bands and record the weight required to break each of them. The mean breaking weight of our sample of 36 rubber bands is 6.6 lbs. Assume that the standard deviation of the breaking weight for the entire population of these rubber bands is 2 lbs. True or false
Answer:
The statement is True.
Step-by-step explanation:
In this case we need to determine whether the rubber bands in a package of a particular brand of rubber band can hold a weight of 7 lbs or less.
A one-sample test can be used to perform the analysis.
The hypothesis can be defined as follows:
H₀: The mean weight the rubber bands can hold is 7 lbs, i.e. μ = 7.
Hₐ: The mean weight the rubber bands can hold is less than 7 lbs, i.e. μ < 7.
The information provided is:
[tex]n=36\\\bar x=6.6\ \text{lbs}\\\sigma=2\ \text{lbs}[/tex]
As the population standard deviation is provided, we will use a z-test for single mean.
Compute the test statistic value as follows:
[tex]z=\frac{\bar x-\mu}{\sigma/\sqrt{n}}=\frac{6.6-7}{2/\sqrt{36}}=-1.20[/tex]
The test statistic value is -1.20.
Decision rule:
If the p-value of the test is less than the significance level then the null hypothesis will be rejected.
Compute the p-value for the two-tailed test as follows:
[tex]p-value=P(Z<-1.20)=0.1151[/tex]
*Use a z-table for the probability.
The p-value of the test is 0.1151.
The p-value of the test is very large for all the commonly used significance level. The null hypothesis will not be rejected.
Thus, it can be concluded that the mean weight the rubber bands can hold is 7 lbs.
Hence, the statement is True.
A study by Consumer Reports showed that 64% of supermarket shoppers believe supermarket brands to be as good as national name brands. To investigate whether this result applies to its own product, consider the hypothesis testing with H subscript 0 colon space p space equals space 0.64 space space space v s. space H subscript a colon space p space not equal to 0.64If a sample of 100 shoppers showed 52 stating that the supermarket brand was as good as the national brand, what is the p-value
Answer:
[tex]z=\frac{0.52 -0.64}{\sqrt{\frac{0.64(1-0.64)}{100}}}=-2.5[/tex]
The p value for this case is given by:
[tex]p_v =2*P(z<-2.5)=0.0124[/tex]
Step-by-step explanation:
Data given and notatio
n=100 represent the random sample selected
X=52 represent the shoppers stating that the supermarket brand was as good as the national brand
[tex]\hat p=\frac{52}{100}=0.52[/tex] estimated proportion of stating that the supermarket brand was as good as the national brand
[tex]p_o=0.64[/tex] is the value that we want to test
z would represent the statistic
[tex]p_v[/tex] represent the p value
System of hypothesis
We need to conduct a hypothesis in order to test the claim that the true proportion of shoppers stating that the supermarket brand was as good as the national brand is 0.64 or not, then the system of hypothesis are.:
Null hypothesis:[tex]p=0.64[/tex]
Alternative hypothesis:[tex]p \neq 0.64[/tex]
The statistic is given by:
[tex]z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}[/tex] (1)
Calculate the statistic
The statistic is given by:
[tex]z=\frac{0.52 -0.64}{\sqrt{\frac{0.64(1-0.64)}{100}}}=-2.5[/tex]
Statistical decision
The p value for this case is given by:
[tex]p_v =2*P(z<-2.5)=0.0124[/tex]
An adult African elephant weighs 8.25 tons. How much do 27 elephants weigh in tons? Answer without units.
Answer:
222.75 tons
Step-by-step explanation:
1 elephant = 8.25 tons
x 27 x 27
27 elephants = 222.75 tons
I hope this helps.
Final answer:
To find the weight of 27 elephants, multiply the weight of one elephant by 27. The total weight of 27 elephants, each weighing 8.25 tons, is 222.75 tons.
Explanation:
To calculate the total weight of 27 elephants each weighing 8.25 tons, we simply multiply the weight of one elephant by the number of elephants:
8.25 tons/elephant × 27 elephants = 222.75 tons
It's clear we need to multiply when converting from a single elephant's weight to the combined weight of multiple elephants. We use the fact that 1 ton = 2,000 pounds for conversion between units if needed, but here we keep the weight in tons as the question requested.
4.37 is what% of 460
Answer:
0.95%
Step-by-step explanation:
Simply divide 100 with 460 then multiply 4.37
100/460 = 0.2173913043
Multiply by 4.37 and you get 0.95
write a quadratic function f whose zeros are 6 and 1
Answer:
x^2-7x+6
Step-by-step explanation:
(x-6)(x-1)
x^2-1x-6x+6
x^2-7x+6
The quadratic function whose zeros are 6 and 1 is: f(x) = x² - 7x + 6.
How do we find the quadratic function with zero's at x = 6 and x = 1?To write a quadratic function f(x) with zeros at x=6 and x=1, we can start by representing it in factored form:
f(x) = a(x−6)(x−1)
Where a is a constant. Depending on the desired leading coefficient, you can choose any value for a. For simplicity, let's choose a=1.
Therefore, the quadratic function with zeros at 6 and 1 is:
f(x) = (x−6)(x−1)
f(x) = x² − 7x + 6
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Which of the following is a required deduction? O A. Medicare B. Health insurance C. Disability insurance D. Medicaid
Answer:
Medicare!
Step-by-step explanation:
Una escalera de 6 pies esta apoyada a
una pared. La distancia entre la pared y la base
de la escalera es 4 pies. A qué altura se
encuentra la parte superior de la escalera
del piso?
The U.S. Bureau of Labor Statistics reports that 11.3% of U.S. workers belong to unions (BLS website, January 2014). Suppose a sample of 400 U.S. workers is collected in 2014 to determine whether union efforts to organize have increased union membership.
Formulate the hypothesis that can be used to determine whether union membership increased in 2014.
Answer:
Null Hypothesis, [tex]H_0[/tex] : p [tex]\leq[/tex] 11.3%
Alternate Hypothesis, [tex]H_A[/tex] : p > 11.3%
Step-by-step explanation:
We are given that U.S. Bureau of Labor Statistics reports that 11.3% of U.S. workers belong to unions.
Suppose a sample of 400 U.S. workers is collected in 2014 to determine whether union efforts to organize have increased union membership.
Let p = % of U.S. workers belonging to union membership
So, Null Hypothesis, [tex]H_0[/tex] : p [tex]\leq[/tex] 11.3%
Alternate Hypothesis, [tex]H_A[/tex] : p > 11.3%
Here, null hypothesis states that the union membership has decreased or remained same in 2014.
On the other hand, alternate hypothesis states that the union membership has increased in 2014.
Also, The test statistics that will be used here is One-sample z proportion statistics;
T.S. = [tex]\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] ~ N(0,1)
Hence, the above hypothesis is appropriate that can be used to determine whether union membership increased in 2014.
A freight train rumbles by as bob watches. Each freight container on the train is shaped like a rectangular prism 17 meters long,3 meters wide, and 3 meters tall. What is the volume of a freight container on that train
Answer:
The answer is 153
Step-by-step explanation:
You multiply 17 by 3 by 3.
The volume of a rectangular prism-shaped freight container is calculated by multiplying its length, width, and height. For a container that is 17 meters long, 3 meters wide, and 3 meters high, the volume is 153 cubic meters.
Explanation:The question is asking for the volume of the rectangular prism-shaped freight container. In mathematics, the volume of a rectangular prism is found by multiplying its length, width, and height. For the freight container with dimensions of 17 meters long, 3 meters wide, and 3 meters high, we can find the volume by multiplying all these values together.
So, the volume V = length x width x height = 17m x 3m x 3m = 153 cubic meters. Therefore, each freight container on the train has a volume of 153 cubic meters.
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Kesha threw her baton up in the air from the marching band platform during practice. The equation h(t) = −16t² + 54t + 40 gives the height of the baton, in feet, t seconds after it is thrown from the platform. What is the height of the platform? At what speed was the baton thrown? If she doesn't catch it, when will it hit the ground?
Answer:
a) 40 feet
b) 54 ft/min
c) 4 mins
Step-by-step explanation:
Solution:-
- Kesha models the height ( h ) of the baton from the ground level but thrown from a platform of height hi.
- The function h ( t ) is modeled to follow a quadratic - parabolic path mathematically expressed as:
h ( t ) = −16t² + 54t + 40
Which gives the height of the baton from ground at time t mins.
- The initial point is of the height of the platform which is at a height of ( hi ) from the ground level.
- So the initial condition is expressed by time = 0 mins, the height of the baton h ( t ) would be:
h ( 0 ) = hi = -16*(0)^2 + 54*0 + 40
h ( 0 ) = hi = 0 + 0 + 40 = 40 feet
Answer: The height of the platform hi is 40 feet.
- The speed ( v ) during the parabolic path of the baton also varies with time t.
- The function of speed ( v ) with respect to time ( t ) can be determined by taking the derivative of displacement of baton from ground with respect to time t mins.
v ( t ) = dh / dt
v ( t )= d ( −16t² + 54t + 40 ) / dt
v ( t )= -2*(16)*t + 54
v ( t )= -32t + 54
- The velocity with which Kesha threw the baton is represented by tim t = 0 mins.
Hence,
v ( 0 ) = vi = -32*( 0 ) + 54
v ( 0 ) = vi = 54 ft / min
Answer: Kesha threw te baton with an initial speed of vo = 54 ft/min
- The baton reaches is maximum height h_max and comes down when all the kinetic energy is converted to potential energy. The baton starts to come down and cross the platform height hi = 40 feet and hits the ground.
- The height of the ball at ground is zero. Hence,
h ( t ) = 0
0 = −16t² + 54t + 40
0 = -8t^2 + 27t + 20
- Use the quadratic formula to solve the quadratic equation:
[tex]t = \frac{27+/-\sqrt{27^2 - 4*8*(-20)} }{2*8}\\\\t = \frac{27+/-\sqrt{1369} }{16}\\\\t = \frac{27+/-37 }{16}\\\\t = \frac{27 + 37}{16} \\\\t = 4[/tex]
Answer: The time taken for the baton to hit the ground is t = 4 mins
Dana has 12 action figures that she wants to give to 3 friends she wants 3 each friend to have the same number if action figures
Answer:
4 action figures per friend
Step-by-step explanation:
To split the 12 action figures between 3 friends, divide 12 by 3.
12/3 = 4
Therefore, each friend gets 4 action figures.
Answer:
each friend gets 12 divided by 3 action figures. Each friend gets 12/3 action figures. Each friend gets 4 of the 12 action figures.
Step-by-step explanation:
i put this and i got it right.
Try it
Explore the properties of angles formed by
two intersecting chords.
mZ DE
1. The intersecting chords form vertical
angles. If m DEB = 105°,
then m AEC =
Answer:105°
Step-by-step explanation:
The intersecting chords form a pair of vertical angles.
Given is a circle, with chords AB and CD intersecting at E and m∠DEB = 105°, we need to find, m∠AEC
By vertical angle theorem:
Vertically opposite angles are congruent.
⇒ m∠AEC = m∠DEB
⇒ m∠AEC = 105°
The measure of angle AEC is 105°.
Therefore, the intersecting chords form a pair of vertical angles.
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A cupcake shop produces 5 types of cupcakes, one of which is chocolate. Assume there is a large amount available of each type of cupcake.
1/ How many different selections of 8 cupcakes are there?
2/ How many different selections of 8 cupcakes have at least 3 chocolate cupcakes?
3/ How many different selections of 8 cupcakes have at most 2 chocolate cupcakes?
Answer: 1) 390625, 2) 1365, 3) 411105.
Step-by-step explanation:
Since we have given that
Number of types of cupcakes = 5
Number of chocolate type = 1
1/ How many different selections of 8 cupcakes are there?
Number of cupcakes we need to select = 8
Since we have 5 options for each 8 cupcakes.
So, the number of ways to select 8 cupcakes would be :
[tex]5^8=390625[/tex]
2/ How many different selections of 8 cupcakes have at least 3 chocolate cupcakes?
Number of different selection would be :
=[tex]4^5+4^4+4^3+4^2+4+1=1365[/tex]
3/ How many different selections of 8 cupcakes have at most 2 chocolate cupcakes?
Number of ways to select no chocolate + Number of ways to select 1 chocolate + Number of ways to select 2 chocolate
[tex]5^8+4^7+4^6=411105[/tex]
Hence, 1) 390625, 2) 1365, 3) 411105.
What is the approximate value of the expression below?
-3,033 ÷ (-56)
Answer:
54.1607142857
Step-by-step explanation:
just simplify it
The approximate value of -3,033 divided by -56 is -54 when rounded to two significant figures.
To approximate the value of -3,033 ÷ (-56), you can perform the division by changing both numbers into their absolute values and divide normally as the negative signs will cancel each other out. This results in the division of 3,033 by 56. Using a calculator, you would get 54.1607142857. However, since we need an approximate value with two significant figures, the result would be rounded to -54.
Amir stands on a balcony and throws a ball to his dog who is at ground level. The ball's height, in meters above the ground, after t seconds that Amir has thrown the ball is given by:
H (t) = -(t-2)^2+9
Answer:
Time t = 2 seconds
It will reach the maximum height after 2 seconds
Completed question;
Amir stands on a balcony and throws a ball to his dog who is at ground level. The ball's height, in meters above the ground, after t seconds that Amir has thrown the ball is given by:
H (t) = -(t-2)^2+9
many seconds after being thrown will the ball reach its maximum height?
Step-by-step explanation:
The equation of the height!
h(t) = -(t-2)^2 + 9 = -(t^2 -4t +4) + 9
h(t) = -t^2 +4t -4+9
h(t) = -t^2 + 4t +5
The maximum height is at dh/dt = 0
dh/dt = -2t +4 = 0
2t = 4
t = 4/2 = 2
Time t = 2 seconds
It will reach the maximum height after 2 seconds
The ball hits the ground at [tex]\( t = 5 \)[/tex] seconds.
Let's analyze the given height function of the ball:
[tex]\[ H(t) = -(t-2)^2 + 9 \][/tex]
This function describes the height of the ball [tex]\( H \)[/tex] in meters at any time [tex]\( t \)[/tex] in seconds.
The function is in the vertex form of a quadratic equation, which is generally written as:
[tex]\[ H(t) = a(t - h)^2 + k \][/tex]
Here, [tex]\( a = -1 \), \( h = 2 \), and \( k = 9 \).[/tex]
Time When the Ball Hits the Ground
- The ball hits the ground when [tex]\( H(t) = 0 \):[/tex]
[tex]\[ 0 = -(t-2)^2 + 9 \] \\\ (t-2)^2 = 9 \][/tex]
Taking the square root of both sides:
[tex]\[ t-2 = \pm 3 \\\ t = 2 + 3 \quad \text{or} \quad t = 2 - 3 \\\ t = 5 \quad \text{or} \quad t = -1 \][/tex]
Since negative time doesn't make sense in this context, we discard [tex]\( t = -1 \):[/tex]
[tex]\[ t = 5 \, \text{seconds} \][/tex]
Therefore, the ball hits the ground at [tex]\( t = 5 \)[/tex] seconds.
The complete question is:
Amir stands on a balcony and throws a ball to his dog, who is at ground level. The ball's height (in meters above the ground), x seconds after Amir threw it, is modeled by: h(x)=-(x-2)^2+16 How many seconds after being thrown will the ball hit the ground?
A credit card company wants to test the hypothesis that its account holders spend an average of $100 per month at gasoline stations. They take a sample of 1000 accounts and find an average spend of $115 with a standard deviation of $41. Conduct this hypothesis test with a .01 level of significance. What is the test statistic?
Answer:
test statistics = 11.57
Step-by-step explanation:
test statics = [tex]\frac{average spend from the sample - average spend from theory}{Standard deviation / \sqrt{no of samples} }[/tex]
= [tex]\frac{115-100}{41/\sqrt{1000} }[/tex] = 11.57
1. Whitney Gourmet Cat Food has determined the weight of their cat food can is normally distributed with a mean of 3 ounces and a standard deviation of 0.05 ounces. To meet legal and customer satisfaction goals each can must weigh between 2.95 and 3.1 ounces. a. If a single can is chosen, what is the probability it will weigh less between 2.95 and 3.1 ounces
Answer:
The probability it will weigh between 2.95 and 3.1 ounces is 0.8186.
Step-by-step explanation:
We are given that Whitney Gourmet Cat Food has determined the weight of their cat food can is normally distributed with a mean of 3 ounces and a standard deviation of 0.05 ounces.
Let X = weight of their cat food can
So, X ~ Normal([tex]\mu=3,\sigma^{2} =0.05^{2}[/tex])
The z score probability distribution for normal distribution is given by;
Z = [tex]\frac{X-\mu}{\sigma}[/tex] ~ N(0,1)
where, [tex]\mu[/tex] = population mean = 3 ounces
[tex]\sigma[/tex] = standard deviation = 0.05 ounces
Now, the probability it will weigh between 2.95 and 3.1 ounces is given by = P(2.95 ounces < X < 3.1 ounces)
P(2.95 ounces < X < 3.1 ounces) = P(X < 3.1 ounces) - P(X [tex]\leq[/tex] 2.95 ounces)
P(X < 3.1 ounces) = P( [tex]\frac{X-\mu}{\sigma}[/tex] < [tex]\frac{3.1-3}{0.05}[/tex] ) = P(Z < 2) = 0.97725
P(X [tex]\leq[/tex] 2.95 ounces) = P( [tex]\frac{X-\mu}{\sigma}[/tex] [tex]\leq[/tex] [tex]\frac{2.95-3}{0.05}[/tex] ) = P(Z [tex]\leq[/tex] -1) = 1 - P(Z < 1)
= 1 - 0.84134 = 0.15866
The above probabilities is calculated by looking at the value of x = 2 and x = 1 in the z table which has an area of 0.97725 and 0.84134 respectively.
Therefore, P(2.95 ounces < X < 3.1 ounces) = 0.97725 - 0.15866 = 0.8186
Hence, the probability it will weigh between 2.95 and 3.1 ounces is 0.8186.
Kevin installed a certain brand of automatic garage door opener that utilizes a transmitter control with four independent switches, each one set on or off. The receiver (wired to the door) must be set with the same pattern as the transmitter. If six neighbors with the same type of opener set their switches independently, what is the probability of at least one pair of neighbors using the same settings?
Kevin installed a certain brand of automatic garage door opener that utilizes a transmitter control with four independent switches, each one set on or off. The receiver (wired to the door) must be set with the same pattern as the transmitter. If six neighbors with the same type of opener set their switches independently.The probability of at least one pair of neighbors using the same settings is 0.65633
Step-by-step explanation:
Step 1
In the question it is given that
Automatic garage door opener utilizes a transmitter control with four independent switches
So .the number of Combinations possible with the Transmitters =
2*2*2*2= 16
Step 2
Probability of at least one pair of neighbors using the same settings = 1- Probability of All Neighbors using different settings.
= 1- 16*15*14*13*12*11/(16^6)
Step 3
Probability of at least one pair of neighbors using the same settings=
= 1- 0.343666
Step 4
So the probability of at least one pair of neighbors using the same settings
is 0.65633
Is this an example of a horizontal asymptote?
Answer:
Step-by-step explanation:
Hi there,
The graph indicated is showing a horizontal asymptote. In fact, it is showing both a horizontal and a vertical asymptote.
To tell which type it is, notice where the graph "shoots off" and almost forms an imaginary straight line in one direction. Using this logic, the horizontal asymptote will be exactly horizontal, parallel to x-axis, and vertical asymptote will be exactly vertical, parallel to y-axis.
With this graph, we notice the horizontal asymptote is at y=0, where the x-axis is. The vertical asymptote is bit more difficult to determine graphically, but can definitely say it is past x=-10. We could determine it if we had the function, but that is not necessary for this question.
Study well, and persevere. If you liked this solution, leave a Thanks or give a rating!
thanks,
Final answer:
A horizontal asymptote is a horizontal line that a curve approaches but never touches as the x-values (or y-values) go to positive or negative infinity. In the case of the function y = 1/x, the graph has a horizontal asymptote at y = 0.
Explanation:
A horizontal asymptote is a horizontal line that a curve approaches but never touches as the x-values (or y-values) go to positive or negative infinity. To determine if a function has a horizontal asymptote, we need to analyze the behavior of the function as x approaches positive or negative infinity.
In the case of the function y = 1/x, as x approaches positive or negative infinity, the value of y approaches 0. Therefore, the graph of the function has a horizontal asymptote at y = 0.
Other functions may have different horizontal asymptotes, depending on their behavior as x approaches positive or negative infinity.
10 boys share 7 cereal bars equally what fraction of the cereal bars does each boy get? show the work.
Answer:
1 43/100
Step-by-step explanation:
10 boys divide 7 cereal bars equally or
10 / 7 = 1.428571428571429
Or 1.43 rounded Or 1 43/100
Find all of the eigenvalues λ of the matrix A. (Hint: Use the method of Example 4.5 of finding the solutions to the equation 0 = det(A − λI). Enter your answers as a comma-separated list.) A = 3 5 8 0
Answer:
[tex]\lambda=8,\ \lambda=-5[/tex]
Step-by-step explanation:
Eigenvalues of a Matrix
Given a matrix A, the eigenvalues of A, called [tex]\lambda[/tex] are scalars who comply with the relation:
[tex]det(A-\lambda I)=0[/tex]
Where I is the identity matrix
[tex]I=\left[\begin{array}{cc}1&0\\0&1\end{array}\right][/tex]
The matrix is given as
[tex]A=\left[\begin{array}{cc}3&5\\8&0\end{array}\right][/tex]
Set up the equation to solve
[tex]det\left(\left[\begin{array}{cc}3&5\\8&0\end{array}\right]-\left[\begin{array}{cc}\lambda&0\\0&\lambda \end{array}\right]\right)=0[/tex]
Expanding the determinant
[tex]det\left(\left[\begin{array}{cc}3-\lambda&5\\8&-\lambda\end{array}\right]\right)=0[/tex]
[tex](3-\lambda)(-\lambda)-40=0[/tex]
Operating Rearranging
[tex]\lambda^2-3\lambda-40=0[/tex]
Factoring
[tex](\lambda-8)(\lambda+5)=0[/tex]
Solving, we have the eigenvalues
[tex]\boxed{\lambda=8,\ \lambda=-5}[/tex]
If the volume of a cube is 64 in3, how long is each side?
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Answer:[tex]\boxed{ \bf Each~side~is~4~in~long.}[/tex]
Explanation:We know that the formula for volume of a cube is:
V = a³
64 = a³
To find the side length, all we have to do is find the cube root of both sides.
[tex]\sqrt{64} = \sqrt{a^3}[/tex]
4 = a
A scientist claims that 7%7% of viruses are airborne. If the scientist is accurate, what is the probability that the proportion of airborne viruses in a sample of 418418 viruses would be greater than 6%6%? Round your answer to four decimal places.
The probability that the proportion of airborne viruses in the sample would be greater than 6% is approximately 0.5596.
Explanation:To find the probability that the proportion of airborne viruses in a sample of 418 viruses would be greater than 6%, we can use the normal distribution. First, let's find the mean and standard deviation of the proportion of airborne viruses. The mean is 7% (0.07) and the standard deviation can be calculated using the formula: sqrt((p(1-p))/n), where p is the proportion and n is the sample size.
Using the given information, the standard deviation is sqrt((0.07(1-0.07))/418) ≈ 0.0064.
Next, we convert the 6% threshold to a z-score using the formula (x - mean) / standard deviation. So, the z-score is (0.06 - 0.07) / 0.0064 ≈ -0.156.
To find the probability that the proportion is greater than 6%, we look up the z-score (-0.156) in the standard normal distribution table and subtract the corresponding probability from 1. The probability is approximately 0.5596.
A Ferris wheel is 40 meters in diameter and boarded from a platform that is 2 meters above the ground. The six o'clock position on the Ferris wheel is level with the loading platform. The wheel completes 1 full revolution in 10 minutes. How many minutes of the ride are spent higher than 34 meters above the ground?
Answer:
t = 2.9517 min
Step-by-step explanation:
Given
D = 40 m ⇒ R = D/2 = 40 m/2 = 20 m
ybottom = 2 m
ytop = ybottom + D = 40 m + 2 m = 42 m
yref = 34 m
t = 10 min
The height above the ground (y) is a sinusoidal function.
The minimum height is ybottom = 2 m
The maximum height is ytop = 42 m;
The midline is (ybottom + ytop)/2 = (2 m + 42 m)/2 = 22 m
If we model the wheel as follows
x² + y² = R²
where
y = yref - (R + ybottom) = 34 m - (20 m + 2 m) = 12 m
R = 20 m
we have
x² + (12 m)² = (20)²
⇒ x = 16 m
then
tan (θ/2) = x/y
⇒ tan (θ/2) = 16 m/12 m
⇒ θ = 106.26°
Knowing the angle of the circular sector, we apply the relation
t = (106.26°)*(10 min/360°)
⇒ t = 2.9517 min
Since the period of revolution is 10 minutes, the ride is above 34 meters for 2.9517 minutes each revolution.
To determine how many minutes of the ride are spent higher than 34 meters, trigonometry can be used to find the proportion of the ride above this height. This results in a total time of 3.136 minutes spent higher than 34 meters.
Explanation:This problem involves trigonometric calculations to solve real-world scenarios. A Ferris wheel is a circle, and when you boarded at the six o'clock position you are 2 meters above the ground. The diameter of this Ferris wheel is 40 meters, so the radius is 20 meters. The highest point you can get to on the Ferris wheel is the diameter plus the height of the platform, or 42 meters. We want to know how much time is spent higher than 34 meters.
When you are 34 meters in the air, you are 16 meters above the centre of the wheel (because the center is 20 + 2 = 22 meters off the ground). The angle θ that satisfies this condition is the arcsin of 16/20, which is 56.44 degrees (or 0.986 radians). Since the Ferris wheel turns around completely, we should consider the same angle on the other side of the wheel, meaning you spend 2*56.44 = 112.88 degrees or (112.88/360) = 31.36% of the time above 34 meters. Since one full revolution takes 10 minutes, this corresponds to 31.36% * 10 = 3.136 minutes above 34 meters.
Learn more about Ferris wheel problem here:https://brainly.com/question/32857193
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b. Interpret the Rsquared value. Does the multiple regression equation help us predict the total golf score much better than we could without knowing that equation? A. No, because Rsquared is close to 1. B. Yes, because Rsquared is not close to 1. C. No, because Rsquared is not close to 1. D. Yes, because Rsquared is close to 1.
Answer:
Depending upon the golf score predictors we can conclude the answer from given Conditional statements
If Someone want Total golf score better then, following .condition
Yes, Because R squared is close to 1 . ....(If Regression values are prefect to fit with model then only)
(But the data is not sufficient to say 100%, it depends on score given)
Step-by-step explanation:
Given :
Explanatory Question on r-squared in regression.
To Find :
Does regression equation help us to know total golf score much better.
Solution;
As in Question there is no golf score given so we cant see "yes" or "no".
But we can be conditional here ,
1) If golf score to be accurate then , multiple regression predict points should fit the model prefect ,hence the R squared value "must be close to 1" .
2) If gold score is not accurate then multiple regression suggest that model does not explain any variables, no linear relationship.
then r squared value "must not be close to 1".
Depending upon the golf score predictors we can conclude the answer from given Conditional statements.
that Yes, Because R squared is close to 1 .
A number line showing 2/3 divided by 1/12
Answer:
how do you thik,,, n vm
Step-by-step explanation:
absolute magnitude of a star that has a period of 50 days
Answer: 6.07 I believe
Step-by-step explanation:
Answer:
-6.07
Step-by-step explanation:
What is the absolute magnitude of a star that has a period of 50 days?
Create 3 fraction whose product is -5/24
Step-by-step explanation:
1.)
[tex] - \frac{5}{3} \times \frac{1}{8} = - \frac{5}{24} \\ \\ [/tex]
2.)
[tex] - \frac{5}{2} \times \frac{1}{12} = - \frac{5}{24} \\ [/tex]
3.)
[tex] - \frac{1}{6} \times \frac{5}{4} = - \frac{5}{24} \\ [/tex]