Answer:
3.78% probability that exactly five cars will arrive over a five-minute interval during rush hour
Step-by-step explanation:
In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:
[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]
In which
x is the number of sucesses
e = 2.71828 is the Euler number
[tex]\mu[/tex] is the mean in the given time interval.
20 cars per 10 minutes
So for 5 minutes, [tex]\mu = 10[/tex]
What is the probability that exactly five cars will arrive over a five-minute interval during rush hour?
This is P(X = 5).
[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]
[tex]P(X = 5) = \frac{e^{-10}*(10)^{5}}{(5)!} = 0.0378[/tex]
3.78% probability that exactly five cars will arrive over a five-minute interval during rush hour
The probability that exactly five cars will arrive over a five-minute interval during rush hour is approximately 0.0378 or 3.78%.
Firstly, the arrival rate is given as 20 cars per 10 minutes. Thus, the arrival rate per minute, λ, is 20 cars / 10 minutes = 2 cars per minute. To find the arrival rate for a 5-minute interval, we multiply this rate by 5 minutes: λ = 2 cars/minute * 5 minutes = 10 cars.
The Poisson probability formula is:
P(X = k) = (λ^k * e^(-λ)) / k!
where λ is the average number of cars in the interval, k is the number of cars, and e is the base of the natural logarithm (approximately equal to 2.71828).
In this problem, we need to find the probability of exactly 5 cars arriving in a 5-minute interval. Thus, λ = 10 and k = 5:
P(X = 5) = (10^5 * e^(-10)) / 5!
P(X = 5) = (100000 * e^(-10)) / 120
P(X = 5) ≈ (100000 / 148.4132) / 120
P(X = 5) ≈ 0.0378
Therefore, the probability that exactly five cars will arrive over a five-minute interval during rush hour is approximately 0.0378 or 3.78%.
A number line showing 2/3 divided by 1/12
Answer:
how do you thik,,, n vm
Step-by-step explanation:
The sodium content of a popular sports drink is listed as 205 mg in a 32-oz bottle. Analysis of 20 bottles indicates a sample mean of 219.2 mg with a sample standard deviation of 18.0 mg. (a) State the hypotheses for a two-tailed test of the claimed sodium content. H0: μ ≥ 205 vs. H1: μ < 205 H0: μ ≤ 205 vs. H1: μ > 205 H0: μ = 205 vs. H1: μ ≠ 205
Answer:
[tex]t=\frac{219.2-205}{\frac{18}{\sqrt{20}}}=3.528[/tex]
[tex]p_v =2*P(t_{19}>3.528)=0.0022[/tex]
If we compare the p value and a significance level for example [tex]\alpha=0.05[/tex] we see that [tex]p_v <\alpha[/tex] so we can conclude that we have enough evidence to reject the null hypothesis, and we can conclude that the lifetime is signficantly different from 205 hours.
Step-by-step explanation:
Data given and notation
[tex]\bar X=219.2[/tex] represent the sample mean
[tex]s=18[/tex] represent the sample standard deviation
[tex]n=20[/tex] sample size
[tex]\mu_o =205[/tex] represent the value that we want to test
[tex]\alpha[/tex] represent the significance level for the hypothesis test.
t would represent the statistic (variable of interest)
[tex]p_v[/tex] represent the p value for the test (variable of interest)
State the null and alternative hypotheses.
We need to apply a two tailed test.
What are H0 and Ha for this study?
Null hypothesis: [tex]\mu = 205[/tex]
Alternative hypothesis :[tex]\mu \neq 205[/tex]
Compute the test statistic
The statistic for this case is given by:
[tex]t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}[/tex] (1)
t-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".
Calculate the statistic
We can replace in formula (1) the info given like this:
[tex]t=\frac{219.2-205}{\frac{18}{\sqrt{20}}}=3.528[/tex]
Give the appropriate conclusion for the test
The degreed of freedom are:
[tex] df = n-1= 19[/tex]
Since is a two sided test the p value would be:
[tex]p_v =2*P(t_{19}>3.528)=0.0022[/tex]
Conclusion
If we compare the p value and a significance level for example [tex]\alpha=0.05[/tex] we see that [tex]p_v <\alpha[/tex] so we can conclude that we have enough evidence to reject the null hypothesis, and we can conclude that the lifetime is signficantly different from 205 hours.
Answer:
H0: mu equals 205 vs. H1: mu not equals 205.
Step-by-step explanation:
A null hypothesis (H0) is a statement from a population parameter which is either rejected or accepted (fail to reject) upon testing. It expresses equality.
An alternate hypothesis (H1) is also a statement from the population parameter which negates the null hypothesis and is accepted if the null hypothesis is true. It expresses inequality.
A two-tailed test is one in which the alternate hypothesis is expressed using any of the inequality signs below:
not equal to, less than or equal to, greater than or equal to.
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]
A manufacturer claims that the thickness of the spearmint gum it produces is 7.5 one-hundredths of an inch. A quality control specialist regularly checks this claim. From his experience, the specialist knows the distribution is right skewed and that the standard deviation is 0.4 one-hundredths of an inch. On one production run, he took a random sample of n = 100 pieces of gum and measured their thickness. Which hypothesis test would be most appropriate for this task?
The most appropriate hypothesis test for this task would be a one-sample t-test.
Explanation:For this task, the most appropriate hypothesis test to use would be a one-sample t-test. A one-sample t-test is used to determine whether the mean of a sample is significantly different from a population mean.
In this case, the quality control specialist wants to test whether the mean thickness of the gum produced by the manufacturer is significantly different from the claimed value of 7.5 one-hundredths of an inch. The specialist takes a random sample of n = 100 pieces of gum and measures their thickness.
The one-sample t-test is appropriate because the population distribution is assumed to be right skewed and the standard deviation is known. The t-test allows for the use of a smaller sample size and accommodates the assumption of a non-normal distribution.
Learn more about Hypothesis testing here:
https://brainly.com/question/34171008
#SPJ12
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.
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 .
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?
A teacher is experimenting with computer-based instruction. In which situation could the teacher use a hypothesis test for a population mean?
A) She gives each student a pretest. Then she teaches a lesson using a computer program. Afterwards, she gives each student a posttest. The teacher wants to see if the difference in scores will show an improvement.
B) She randomly divides the class into two groups. One groups receives computer-based instruction. The other group receives traditional instruction without computers. After instruction, each student has to solve a single problem. The teachers wants to compare the proportion of each group who can solve the problem.
C) The teacher uses a combination of traditional methods and computer-based instruction. She asks students which they liked better. She wants to determine if the majority prefer the computer-based instruction.
A teacher can use a hypothesis test for a population mean in situation A, where pretest scores are compared to posttest scores to determine if there is a significant improvement.
Explanation:A hypothesis test for a population mean can be used in situation A. The teacher can use the pretest scores as the population mean and then compare it to the posttest scores to see if there is a statistically significant improvement. The hypothesis test will determine if the difference in scores is due to chance or if it is a result of the computer-based instruction.
Learn more about Hypothesis test for a population mean here:https://brainly.com/question/31962294
#SPJ12
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 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.
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
A process that fills packages is stopped whenever a package is detected whose weight falls outside the specification. Assume that each package has probability 0.01 of falling outside the specification and that the weights of the packages are independent. Find the mean number of packages that will be filled before the process is stopped.
The mean number of packages that will be filled before the process is stopped is 100
Step-by-step explanation:
Step 1
Given that each package has probability 0.01 of falling outside the specification (Probability of Failure)
The probability of Success is (100-probability of failure)=(100-0.01)=0.99
It is important to note that the weight of the packages are independent
Using the data given in the question we get the following:
P(fail) =Probability of Failure
P(success)=Probability of Success
P(fail) = 0.01 and P(success) = 0.99
Step 2
The mean of the Geometric distribution is:
P = 0.01;
μx = 1/p = 1/0.01 = 100
Step 3
Thus, we can say that the mean number of packages that will be filled before the process is stopped is 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]
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
Find more exercises on Quadratic function;
https://brainly.com/question/27958964
#SPJ3
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.
Learn more about Volume Calculation here:https://brainly.com/question/33318354
#SPJ12
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
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.
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]
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.
Learn more about vertical angles click;
https://brainly.com/question/24460838
#SPJ7
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.
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
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?
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.
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
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.
If the volume of a cube is 64 in3, how long is each side?
asap 14 pts
more coming soon!
Hello!
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
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:
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.
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]