Answer:
The option b) quadratic function is correctA nonlinear function with at least one term raised to the power of two is known as a quadratic functionStep-by-step explanation:
A nonlinear function with at least one term raised to the power of two is known as a quadratic function
FOR :
A non-linear system of equations is a set of equations where one or more terms have a variable of power two or higher .
In Algebra, linear functions are polynomials with highest exponent equal to 1 or of the form y = c where c is constant. Non-linear functions are all other rest functions with exponent atleast 2.
Hence A nonlinear function with at least one term raised to the power of two is known as a quadratic function
Therefore the option b) quadratic function is correctwhat is the radius and diameter of the following circle
Answer:
Radius 6.5cm
Diameter 13cm
Step-by-step explanation:
Diameter ia a straight line passing from side to side through the center a circle or sphere.
Radius formula is simply derived by halving the diameter of the circle
13/2=6.5
Click to review the online content. Then answer the question(s) below, using complete sentences. Scroll down to view additional questions. Online Content: Site 1 Online Content: Site 2 Describe how you would use the rules of exponents to simplify (7x2yz)3. You may indicate an exponent in your answer with ^. For example, 3x2 y2as 3x^2y^2. (Site 1)
Answer:
First, apply the power of a product rule by which you raise each factor to the power 3, and then multiply all the factors, to obtain:
[tex](7x^2yz)^3=7^3(x^2)^3y^3z^3[/tex]
Next, apply the power of a power rule, in virtue of which you raise the factor x² to the power 3 and obtain:
[tex]7^3(x^2)^3y^3z^3=7^3x^6y^3z^3[/tex]
Finally, compute the numerical values, doing 7³ = 7×7×7 = 343.
Therefore, the final result is:
[tex]343x^6y^3z^3[/tex]
Explanation:
The expression you have to simplify is:
[tex](7x^2yz)^3[/tex]
You have to apply two rules:
1. Power of a product2. Power of a power1. Power of a product
This rule states that the power of a product is equal to the product of each factor raised to the same exponent of the whole prduct:
For instance:
[tex](abc)^z=a^z\cdot b^z\cdot c^z[/tex]
Using this with the expression [tex](7x^2yz)^3[/tex] it is:
[tex](7x^2yz)^3=7^3\cdot (x^2)^3\cdot y^3\cdot z^3[/tex]
In complete sentences that is: raise every factor, 7, x², x, and z to the exponent 3 and, then, multiply them.
2. Power of a power:
This rule states that to raise a power to a power, you must multiply the exponents.
For instance:
[tex](a^n)^m=a^{m\times n}[/tex]
You must apply that rule to the factor [tex](x^2)^3[/tex]
That is:
[tex](x^2)^3=x^{(3\times 2)}=x^6[/tex]
3. Final result and description using complete sentences:
The first step is to apply the power of a product rule by rasing each factor to the power 3, and then multiply all the factors, to obtain:
[tex](7x^2yz)^3=7^3(x^2)^3y^3z^3[/tex]
The second step is to apply the power of a power rule, in virtue of which you raise the factor x² to the power 3, in this way:
[tex]7^3(x^2)^3y^3z^3=7^3x^6y^3z^3[/tex]
The last step is to calculate the numerical values, doing 7³ = 7×7×7 = 343.
The final result is: [tex]343x^6y^3z^3[/tex]
Average starting salaries for students using a placement service at a university have been steadily increasing. A study of the last four graduating classes indicates the following average salaries:
$60,000, $72,000, $84,500, and $96,000 (last graduating class).
(a) Predict the starting salary for the next graduating class using a simple exponential smoothing model with α = 0.25. Assume that the initial forecast was $55,000.
Given Information:
Smoothing constant = α = 0.25
Initial forecast salary = F₀ = $55,000
Actual salaries = A = $60,000, $72,000, $84,500, and $96,000
Required Information:
Forecast salaries = F = ?
Answer:
[tex]F_{1} = \$56,250\\F_{2} =\$ 60,187.5\\F_{3} = \$66,265.6\\F_{4} = \$73,699.2\\[/tex]
Step-by-step explanation:
The exponential smoothing model is given by
[tex]F_{n} = \alpha \cdot A_{n - 1} + (1 - \alpha ) F_{n - 1}[/tex]
Where
[tex]F_{n}[/tex] is the forecast salary for nth graduate class
α is the smoothing constant
[tex]A_{n-1}[/tex] is the actual salary of n - 1 graduate class
[tex]F_{n-1}[/tex] is the forecast salary of n - 1 graduate class
For n = 1
[tex]F_{1} = 0.25 \cdot A_0} + (1-0.25) \cdot F_{0}\\F_{1} = 0.25 \cdot 60,000} + (0.75) \cdot 55,000\\F_{1} = 56,250[/tex]
For n = 2
[tex]F_{2} = 0.25 \cdot A_1} + (1-0.25) \cdot F_{1}\\F_{2} = 0.25 \cdot 72,000} + (0.75) \cdot 56,250\\F_{2} = 60,187.5[/tex]
For n = 3
[tex]F_{3} = 0.25 \cdot A_2} + (1-0.25) \cdot F_{2}\\F_{3} = 0.25 \cdot 84,500} + (0.75) \cdot 60,187.5\\F_{3} = 66,265.625[/tex]
For n = 4
[tex]F_{4} = 0.25 \cdot A_3} + (1-0.25) \cdot F_{3}\\F_{4} = 0.25 \cdot 96,000} + (0.75) \cdot 66,265.625\\F_{4} = 73,699.218[/tex]
Therefore, the foretasted starting salaries are
[tex]F_{1} = \$56,250\\F_{2} =\$ 60,187.5\\F_{3} = \$66,265.6\\F_{4} = \$73,699.2\\[/tex]
Using an exponential smoothing model with α = 0.25, we sequentially calculate the forecasted starting salary for each year, then use that to estimate the starting salary for the next graduating class.
Explanation:To predict the starting salary for the next graduating class using a simple exponential smoothing model with α = 0.25 and an initial forecast of $55,000, we follow these steps:
Calculate the exponentially smoothed forecast for each year after the initial year. The formula is: Next Forecast = α(Current Actual) + (1-α)(Previous Forecast).For the class with a starting salary of $60,000: Forecast = 0.25($60,000) + 0.75($55,000) = $56,250.Continue the process using each actual salary to get the forecast for the next year, eventually reaching the forecast for the class after the $96,000 graduating class.By applying this model, we will obtain the predicted starting salary for the next class after performing these calculations for each given salary data point in sequence.
Select the correct image.
Based on the albedo values given, identify the object that will reflect more than half of the solar radiation it receives.
Answer: The ice image, bottom left.
Step-by-step explanation:
The albedo values give information about the proportion of radiation that a given object surfaces, for example, if an object has an albedo value of 0.2, this means that the object reflects 0.2*100% = 20% of the radiation.
You usually can see that darker objects have a smaller albedo value, while clearer objects have a bigger albedo value, meaning that as clearer is the color, usually it reflects a bigger proportion of the radiation.
Here we have that the bigger albedo value is in the ice ( 0.55), so the correct image is the ice image, at the bottom left.
On the way to the Samuelsons’, Mr. Anderson filled his car with gas. He put in 9.7 gallons and paid $3.45 per gallon. Estimate the total charge. What was the actual charge for gas?
Answer:
Estimate = $34.50
Actual charge $33.47
Step-by-step explanation:
To estimate, we round the numbers
9.7 gallons rounds to 10 gallons
10 gallons * 3.45 per gallon =34.50
This is an overestimation
The actual charge
9.7* 3.45 =33.465
We round to the nearest cent
33.47
Answer:
Estimate: $34.5
Actual: $33.465
Step-by-step explanation:
9.7 is approximately 10
Estimate
10 × 3.45 = 34.5
Actual:
9.7 × 3.45 = 33.465
Let the Poisson random variable U (see p. 227) be the number of calls for technical assistance received by a computer company during the firm’s nine normal work- day hours. Suppose the average number of calls per hour is 7.0 and that each call costs the company $50. Let V be a Poisson random variable representing the number of calls for technical assistance received during a day’s remaining 3.10 Order Statistics 193 fifteen hours. Suppose the average number of calls per hour is 4.0 for that time period and that each such call costs the company $60. Find the expected cost and the vari- ance of the cost associated with the calls received during a twenty-four-hour day.
Answer:
Expected cost = $6,750
Variance of the cost = $373,500
Step-by-step explanation:
During normal 9 work hours: average number of calls = 7.0
Cost of each call = $50
During 15 off hours:
average number of calls = 4.0
Cost of each call = $60
Let's take U as the number of calls during the normal 9 hours.
I.e, [tex] U = U_1+U_2+U_3+U_4....+ U_9[/tex]
Therefore,
[tex] E(U) = E(U_1)+E(U_2)+E(U_3)+E(U_4)....+E(U_9)[/tex]
= 7+7+7+7+7+7+7+7+7
= 63
In Poisson random variable, Variance= mean, thus:
[tex] Var(U) =Var(U_1)+Var(U_2).....+Var(U_9) [/tex]
= 7+7+7+7+7+7+7+7+7
=63
Let's take V as the number of calls during the day's remaining 15 hours.
E(V) = Var(V)
= 15(4)
=60
The expected cost and the variance of cost associated with the calls received during a 24 hour day:
The expected cost =
$50U + $60V
= $50(63) + $60(60)
= $3150 + $3600
= $6750
The variance of the cost :
= Var(50U + 60V)
= 50²Var(U) + 60²Var(V)
= 2500*63 + 3600*60
= $373,500
Therefore, the expected cost is $6,750 and the variance of the cost is $373,500
The normal curve with a mean of 0 and standard deviation of 1 is called ________________
Answer:
A normal distribution with a mean of 0 and a standard deviation of 1 is called a standard normal distribution.
For a sample of 27 New England cities, a sociologist studies the crime rate in each city (crimes per 100,000 residents) as a function of its poverty rate (in %) and its median income (in $1,000s). He finds that SSE = 4,102,577 and SST = 7,622,089.
a. Calculate the standard error of the estimate.
Answer:
The standard error of the estimate is 413.4498
Step-by-step explanation:
According to the given data of ,in order to calculate the standard error of the estimate we would have to use the following formula:
Standard Error =sqrt(SSE/(n-p-1))
Standard Error =sqrt(4102577/(27-2-1))
Standard Error = 413.4498
The standard error of the estimate is 413.4498
On a coordinate plane, a rectangle has points (4, 1), (4, negative 3), (negative 2, negative 3), (negative 2, 1).
Marina is drawing a plan for a new garden. The rectangle plotted in the coordinate plane represents the garden, measured in feet. How much soil will she need to cover the garden?
10 ft2
12 ft2
20 ft2
24 ft2
Answer:
24 feet
Step-by-step explanation:
sorry I'm so late
Tiffany has a 30% chance of winning a game. She uses random numbers to simulate a series of 7 games. In her simulation, the numbers 0–2 represent a win, and the numbers 3–9 represent a loss. Select all the trials whose results show 3 wins in 7 games played. A. 8531905 B. 4963184 C. 7269108 D. 0689271 E. 7042351 F. 9094562
Answer:
C. 7269108
D. 0689271
E. 7042351
Step-by-step explanation:
If the number is 0,1 or 2, it is a win.
Otherwise, it is a loss.
Each number is a match.
A. 8531905
Two wins(0,1), 5 losses(8,5,3,9,5)
B. 4963184
One win(1), 6 losses(4,9,6,3,8,4)
C. 7269108
Three wins(2,1,0) and four losses (7,6,9,8)
D. 0689271
Three wins (0,2,1) and four losses (6,8,9,7)
E. 7042351
Three wins (0,2,1), four losses (7,4,3,5)
F. 9094562
Two wins (0,2) and five losses (9,9,4,5,6)
Answer:
C.
D.
E.
Step-by-step explanation:
Design an expression that can be used to find the surface area of tower n cubes tall
Answer: The surface is (4*n + 2)*L^2
Step-by-step explanation:
The surface of a cube is equal to 6 times the area of one of the sides.
So if the sides of the cube have a length L, we have that the area of one face is L^2, and the surface of the cube is 6*L^2
Now, if we put n of those cubes in a tower, we will have a shape were the bottom and the top still have an area of L^2, then the total area of the bottom and the top is 2*L^2
But each one of the sides has two sides of length L, and two sides of length n*L (n times the length of one of the sides), then the area of each side is equal to n*L*L = n*L^2
and we have 4 sides, then the total area of the sides is 4*n*L^2
Then the total surface of the tower is:
A = 4*n*L^2 + 2*L^2 = (4*n + 2)*L^2
The average maximum monthly temperature in Campinas, Brazil is 29.9 degrees Celsius. The standard deviation in maximum monthly temperature is 2.31 degrees. Assume that maximum monthly temperatures in Campinas are normally distributed. What percentage of months would have a maximum temperature of 34 degrees or higher?
We need to calculate a z-score to determine the probability of getting a month with a temperature of 34 degrees or higher, and then subtract that probability from 1 to get the final result.
Explanation:To solve this problem, we're dealing with a normal distribution. The average maximum monthly temperature in Campinas, Brazil is given as the mean (29.9 degrees). The standard deviation has been given as 2.31 degrees.
We're asked to find the percentage of months that would have a maximum temperature of 34 degrees or higher. This can be interpreted as finding the probability of a temperature being more than 34 degrees. We first need to find the number of standard deviations away from the mean 34 degrees is, which is known as Z-score.
The formula for Z-score is (X - mean) / standard deviation. So, our calculation would be (34 - 29.9) / 2.31. The resultant Z-score would have to be looked up in a standard normal distribution table, which will give us the probability up to that point. As we want the probability of the temperature being higher, we'll subtract the value we get from 1 (as total probability is 1), which would give us the percentage of months with a maximum temperature of 34 degrees or higher.
Learn more about Normal Distribution here:https://brainly.com/question/30390016
#SPJ3
I NEED HELPP‼️l
Which number is farthest from 2 on the number line?
O 12.1
O √24
O 12.5
O 129
Answer:
129
Step-by-step explanation:
GPA and study time. A survey was conducted on 218 undergraduates from Duke University who took an introductory statistics course in Spring 2012. Among many other questions, this survey asked them about their GPA and the number of hours they spent studying per week. The scatterplot below displays the relationship between these two variables. a) The explanatory variable is and the response variable is ? b) The relationship between the variables is and . c) Is this experiment or an observational study? A. Experiment B. Observational study d) Can we conclude that studying longer hours leads to higher GPAs? A. No. We cannot conclude that studying longer hours leads to higher GPA since this study is observational. B. Yes, we can conclude that studying longer hours leads to higher GPA since this study is an experiment. C. Yes, we can conclude that studying longer hours leads to higher GPA since this study this is an observational study. D. No. We cannot conclude that studying longer hours leads to higher GPA since this study is an experiment. E. We cannot draw any conclusion because the scatterplot has no distinct form.
Answer: a) The explanatory variable is hours of study per week and the response variable is GPA.
b) The relantioship between the variables seems to be positive.
c) B. Observational Study.
d) A. NO. We cannot conclude that studying loger hours leads to higher GPA since this study is observational.
Step-by-step explanation: a) Explanatory Variable is a type of independent variable, which means it is a variable that doesn't depend on the other variables. However, in explanatory variable, there is a subtle relation between variables. For that reason, Hours of Study per week is an explanatory variable. Response Variable is the dependent variable, it is the result when you change the other variable. For that reason, GPA is the response variable.
b) Observing the graphic, which is in the attachment, it can be observed that students who study more hours per week, tend to have higher GPA. For example, people who studied 60 hours per week have a GPA closer to 4.
c) Observational Studies are those experiment where the researches only observe their object of interest without changing or interfering in the outcome. Experimental Studies are the ones where the researchers introduce an interference and study their effect on the randomized groups.
Since this experiment is based on observation only, the study is an Observational Study.
d) Because it's an observational study, we can't correlate or associate the variables, since the researchers only obtain their results through observation of the behaviour of the students, without changing it.
Please help numbers 2-20 evens only
Answer: x=9,y=-1/3
Step-by-step explanation: This is for Q. 16
Rearrange terms to line up properly.
x-3y=10
x+3y=8
eliminate y terms
x=10
x=8 now add all like terms, remember it's a given that there's a one in
front of a variable.
2x=18 solve for x
x=9 now plug in the nine into one of the original eq.s and solve for y
9+3y=8
3y=-1
y=-1/3 always check solutions in both eq.s to vertify. they both work
Answer:
Q6: x= 10, y = -11
Q8: x= -3; y= 8
Q10: k= 7; j= -1
Step-by-step explanation:
Question6.
2x + y = 9..............1
-2x - 3y = 13...............2
Let's eliminate x by adding equation 1 and 2.
-2y = 22
y = 22/-2
y = -11
Substitute y = -11 in equation 1.
2x + y = 9
2x + (-11) = 9
2x - 11 = 9
2x = 9 + 11
2x = 20
x = 20/2
x = 10
x =10; y= -11
Question 8.
x + 2y = 13.............(I)
x + 6y = 45......…....(2)
By elimination method, let's take off x by subtracting equation 1 from 2.
6y - 2y = 45 - 13
4y = 32
y = 8.
Substitute y = 8 in equation 1.
x + 2y = 13
x + 2(8) = 13
x + 16 = 13
x = 13 - 16
x = -3
y= 8; x = -3
Question 10:
2j + 3k = 19 ..............1
2j + 7k = 47...............2
Let's eliminate j by subtracting equation 1 from equation 2.
4k = 28
k = 28/4
k= 7
Substitute k = 7 in equation 1.
2j + 3k = 19
2j + 3(7) = 19
2j + 21 = 19
2j = 19 - 21
2j = -2
j= -1
k= 7; j = -1
Repeated student samples. Of all freshman at a large college, 16% made the dean’s list in the current year. As part of a class project, students randomly sample 40 students and check if those students made the list. They repeat this 1,000 times and build a distribution of sample proportions.
(a) What is this distribution called?
(b) Would you expect the shape of this distribution to be symmetric, right skewed, or left skewed? Explain your reasoning.
(c) Calculate the variability of this distribution.
(d) What is the formal name of the value you computed in (c)?
(e) Suppose the students decide to sample again, this time collecting 90 students per sample, and they again collect 1,000 samples. They build a new distribution of sample proportions. How will the variability of this new distribution compare to the variability of the distribution when each sample contained 40 observations?
Answer:
a) p-hat (sampling distribution of sample proportions)
b) Symmetric
c) σ=0.058
d) Standard error
e) If we increase the sample size from 40 to 90 students, the standard error becomes two thirds of the previous standard error (se=0.667).
Step-by-step explanation:
a) This distribution is called the sampling distribution of sample proportions (p-hat).
b) The shape of this distribution is expected to somewhat normal, symmetrical and centered around 16%.
This happens because the expected sample proportion is 0.16. Some samples will have a proportion over 0.16 and others below, but the most of them will be around the population mean. In other words, the sample proportions is a non-biased estimator of the population proportion.
c) The variability of this distribution, represented by the standard error, is:
[tex]\sigma=\sqrt{p(1-p)/n}=\sqrt{0.16*0.84/40}=0.058[/tex]
d) The formal name is Standard error.
e) If we divided the variability of the distribution with sample size n=90 to the variability of the distribution with sample size n=40, we have:
[tex]\frac{\sigma_{90}}{\sigma_{40}}=\frac{\sqrt{p(1-p)/n_{90}} }{\sqrt{p(1-p)/n_{40}}}}= \sqrt{\frac{1/n_{90}}{1/n_{40}}}=\sqrt{\frac{1/90}{1/40}}=\sqrt{0.444}= 0.667[/tex]
If we increase the sample size from 40 to 90 students, the standard error becomes two thirds of the previous standard error (se=0.667).
Using the Central Limit Theorem, we get that:
a) Sampling distribution of sample proportions of size 40.
b) Symmetric.
c) 0.0580.
d) Standard error.
e) It would decrease.
The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean and standard deviation , the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean and standard erro .
For a skewed variable, we need n of 30 and greater.
For a proportion p in a sample of size n, we have that: and standard deviation .
In this problem:
Proportion of 16%, thus [tex]p = 0.16[/tex].Sample of 40 students, thus [tex]n = 40[/tex]Item a:
We are working proportions, and sample of 40, thus:
Sampling distribution of sample proportions of size 40.
Item b:
Sample size of 40, thus, by the Central Limit Theorem, approximately normal, which is symmetric.Item c:
This is the standard error, thus:
[tex]s = \sqrt{\frac{p(1-p)}{n}} = \sqrt{\frac{0.16(0.84)}{40}} = 0.0580[/tex]
It is of 0.0580.
Item d:
The formal name is standard error.Item e:
The formula is:
[tex]s = \frac{\sigma}{\sqrt{n}}[/tex]
Since n is in the denominator, we can see that the standard error and the sample size are inversely proportional, and thus, increasing the sample size to 90, the variability would decrease.A similar problem is given at https://brainly.com/question/14099217
who runs the fastest ? (ONLY ANSWER IF YOU KNOW IT BECAUSE CORRECT ONE GETS BRAINLIEST)
stephanie runs 14 feet per second
brooke runs 589 feet in 44 seconds
will runs 1 mile in 454 seconds
rob runs 548 feet in 1 minute
Answer:
Stephanie runs the fastest per second: 14 feet per second
Step-by-step explanation:
To find the fastest speed, you need to see which person runs the most per second:
Stephanie runs 14 feet per second
Brooke runs 589 feet in 44 seconds.
Find the amount of feet per second by dividing:
[tex]\frac{589}{44} =13.4[/tex]
Brooke runs about 13.4 feet per second
Will runs 1 mile in 454 seconds.
Convert the miles to feet:
There are 5,280 feet in a mile. If Will runs 5,280 feet in 454 seconds, divide to find how much he runs per second:
[tex]\frac{5280}{454}= 11.6[/tex]
Will runs about 11.6 feet per second.
Rob runs 548 feet in a minute.
Convert the minute into seconds. There are 60 seconds in a minute. Divide the feet by the seconds to find how fast he runs per second:
[tex]\frac{548}{60}= 9.1[/tex]
Rob runs about 9.1 feet per second.
Stephanie runs 14 feet per second, the fastest time:
| 14 |, 13.4, 11.6, 9.1
Finito.
Simplifying each side of the equation results in x2 − 3x − 4 = x2 − 5x + 6.
Find the solution:
x + 2
3x
−
1
x − 2
=
x − 3
3x
x =
Answer:
x = 5
Step-by-step explanation:
x² -3x -4 = x² - 5x + 6.
-x² - x²
-3x -4 = -5x + 6
+3x + 3x
-4 = -2x +6
-6 -6
-10 = -2x
÷-2 ÷-2
5 = x
Hope this Helps
Answer:
x = 5
Step-by-step explanation:
hope this helps!
what is the ratio of 3 circles to 4 triangles
The ratio of 3 circles to 4 triangles is 3:4, meaning there are 3 circles for every 4 triangles.
To find the ratio of 3 circles to 4 triangles, we compare the number of circles to the number of triangles.
Given:
Circles = 3
Triangles = 4
The ratio of circles to triangles is expressed as 3:4. This means for every 3 circles, there are 4 triangles.
If we want to express it as a fraction, we can write it as 3/4. This implies that for every set of 3 circles, there are 4 triangles.
To simplify the ratio, we can divide both numbers by their greatest common divisor, which is 1 in this case. Therefore, the simplified ratio is still 3:4.
In conclusion, the ratio of 3 circles to 4 triangles is 3:4, meaning there are 3 circles for every 4 triangles.
The complete question is here:
What is the ratio of 3 circles to 4 triangles?
f(x) = (x + 5)(x + 6)
Answer:(-5,0) , (-6,0)
Y= (0,30)
Step-by-step explanation:
Select the correct answer.
Which type of discontinuity exists at x = 2 for f(x)=x^2-4/x-2?
A.
removable discontinuity
B.
jump discontinuity
C.
infinite discontinuity
D.
none of the above
Answer:
Answer A.
Step-by-step explanation:
Recall that [tex]f(x) = \frac{x^2-4}{x-2}[/tex]
we will calculate the lateral limits of f when x approches x=2. Note that
[tex] \lim_{x\to 2^{+}} \frac{x^2-4}{x-2} = \lim_{x\to 2^{+}} \frac{(x-2)(x+2)}{x-2} = 2+2 = 4[/tex]
[tex] \lim_{x\to 2^{-}} \frac{x^2-4}{x-2} = \lim_{x\to 2^{-}} \frac{(x-2)(x+2)}{x-2} = 2+2 = 4[/tex]
We can clasify the discontinuity as follows:
- Removable discontinuity if both lateral limits are equal and finite.
- Jump discontinuity if both lateral limits are finite but different.
- Essential discontinuity if one of the limits is not finite and the other one is finite.
Based on this classification, since both lateral limits are equal, the discontinuity is a removable discontinuity
Find the lateral area of the cylinder. Give answer in terms of pi. 6ft is the radius and 11ft is the height.
Answer:
[tex]132\pi[/tex]
Step-by-step explanation:
The lateral area is the area of a rectangle. Think of a soup can with the label removed and laid out flat on a table. The height of the rectangle is the same as the height of the can (cylinder). Where does the base of the rectangle come from? It's the circumference of the can "unrolled."
Area of a rectangle = base x height
Circumference of a circle [tex]C=2\pi r[/tex]
Lateral Area [tex]=2\pi r \times h[/tex] [tex]=2 \pi (6)(11) =132\pi[/tex]
What is the perimeter of the triangle if s=3 feet? Round your answer to the nearest hundredth
Answer:
9 feet = Perimeter of the triangle.
Step-by-step explanation:
Here, this question is incomplete and lacks essential data. So, still we will try to figure it out. What we can learn from this question.
So, first of all it talks about perimeter. So, let's understand first, what is perimeter and how it can be calculated for a triangle.
What is Perimeter?
So, Perimeter is actually the distance or path covered by a particular 2 dimensional shape. For example, square, triangle, rectangle.
Furthermore,
In this question, we have been given s = 3 feet. We can say that it is a length of one side of a triangle and triangle must be equilateral triangle having all sides equal to one another.
Equilateral Triangle have all sides equal to one another.
Here, we s1 = 3 so, other sides would be s2 = 3 and s3 = 3
Finally, here is the formula for the calculation of Perimeter of a triangle.
P = a + b + c
where, a, b, c represents sides of the triangle.
P = 3 + 3 + 3
P = 9
Hence, the perimeter of the triangle in this question is 9 feet.
what is the value of h in the equation 8h = 60
Answer:
h= 7.5
Step-by-step explanation:
8h=60
One solution was found :
h = 15/2 = 7.500
Rearrange:
Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :
8*h-(60)=0
Step by step solution :
Step 1 :
Pulling out like terms :
1.1 Pull out like factors :
8h - 60 = 4 • (2h - 15)
Equation at the end of step 1 :
Step 2 :
Equations which are never true :
2.1 Solve : 4 = 0
This equation has no solution.
A a non-zero constant never equals zero.
Solving a Single Variable Equation :
2.2 Solve : 2h-15 = 0
Add 15 to both sides of the equation :
2h = 15
Divide both sides of the equation by 2:
h = 15/2 = 7.500
One solution was found :
h = 15/2 = 7.500
Processing ends successfully
Answer: h = 7.5
Step-by-step explanation: To solve for h in this equation, we want to to get h by itself on the left side of the equation.
Since h is being multiplied by 8, to get h by itself, we need to divide by 8 on the left side of the equation.
If we divide by 8 on the left side,
we must also divide by 8 on the right side.
On the left, the 8's cancel out so we are simply left with h.
On the right we have 60/8 which is 7.5.
So we have h = 7.5.
A certain rare form of cancer occurs in 37 children in a million, so its probability is 0.000037. In the city of Normalville there are 74,090 children. A Poisson distribution will be used to approximate the probability that the number of cases of the disease in Normalville children is more than 2. Find the mean of the appropriate Poisson distribution (the mean number of cases in groups of 74,090 children).
Answer:
Mean = 2.7
In a group of 74090 we would expect about 3 (rounding to nearest whole number) children with the rare form of cancer.
Step-by-step explanation:
We are given that the rate of cancer in children is 37 children in 1 million. So the probability of cancer in a child is P(C) = 0.000037
Poisson distribution is used to approximate the number of cases of diseases and we have to find what will be the mean number of cases for 74,090.
In simple words we have to find the expected number of children with cancer in a group of 74,090 children.
The mean value of expected value can be obtained by multiplying the probability with the sample size. So, in this case multiplying probability of child having a cancer with total group size will give us the expected or mean number of children in the group with cancer.
Mean = E(x) = P(C) * Group size
Mean = 0.000037 x 74090
Mean = 2.7
This means in a group of 74090 we would expect about 3 (rounding to nearest whole number) children with the rare form of cancer.
Final answer:
The mean of the Poisson distribution for the number of cancer cases among 74,090 children in Normalville is approximately 2.7413 cases.
Explanation:
To find the mean of the appropriate Poisson distribution for the number of cases in groups of 74,090 children in Normalville, we multiply the probability of the disease by the number of children. Thus, the mean (μ) is:
μ = probability of one child having the disease × total number of children
μ = 0.000037 × 74,090 = approximately 2.7413
The mean of the Poisson distribution, in this case, indicates the average number of children who would have this rare form of cancer in groups of 74,090 children in Normalville.
An environmentalist would like to compare air pollution levels in cities A and B. From each city 10 measurements are taken. For city A, the average of all measurements (where measurements are percentage of pollutants in the air) is 5 percent with sample standard deviation 1.5 percent. For city B the average of all 10 measurements is 5.4 percent with sample standard deviation 2 percent. Assume that for each city air pollution level at a random time and location follows a normal distribution, and nd a 90% confidence interval for difference between the true average air pollution levels of city A and city B.
Answerhshxbx
Ste-by-step explanation:
Hwsjbb
today's local newspaper lists 20 stocks of local interest. of those stocks ten increased five decreased and five remained unchanged yesterday. if wwe decide to buy two of stocks what is the likelyhood that both increased yesterday?
Answer:
P(x=2) = 0.2368
Step-by-step explanation:
given data
stocks of local interest N = 20
stocks increased K = 10
stocks decreased = 5
remained unchanged = 5
solution
we take here no of stock that are increased randomly n = 2
so here Hypergeometric random variable can take integer value
{max(0, n+k - N ), min(n,K) } = {0,2}
so here
P(x=2)
so
P(x=k) = [tex]\frac{(^K_k)\times (^{N-K}_{n-k}) }{(^N_n)}[/tex] .......................1
P(x=2 ) = [tex]\frac{(^{10}_2)\times (^{20-10}_{2-2}) }{(^{20}_2)}[/tex]
solve it we get
P(x=2 ) = 0.236842
now we use excel function as
HYPGEOM.DIST (k,n,N.cumulative) .....................2
so it will be
HYPGEOM.DIST (2,2,10,,false)
we get
HYPGEOM.DIST (2,2,10,,false) = 0.236842
so
P(x=2) = 0.2368
S = the team's score
g = the number of goals a team has scored
Which of the variables is independent and which is dependent?
Answer:
s would be the dependent variable, and g the independent.
Step-by-step explanation:
Whatever the score is, it would depend on how many goals the team has scored.
Final answer:
The independent variable is typically the one that is manipulated, like the number of goals scored (g), and the dependent variable is the one that responds, like the team's score (S). A scatter plot can reveal patterns, and the correlation coefficient indicates the strength of the relationship. The least-squares line represents a best-fit line through the data.
Explanation:
The independent variable is typically the one that is controlled or manipulated, whereas the dependent variable is the one that responds to changes in the independent variable. In the context of a team's score (S) and the number of goals scored (g), the independent variable is usually the number of goals scored (g) because it can be controlled or affected through the team's actions. The dependent variable is the team's score (S), because it depends on the number of goals scored.
In a broader context, such as analyzing the relationship between the ranking of a state and the area of the state, the independent variable could be the ranking (since it is not influenced by the area), and the dependent variable would be the area of the state (since it could be influenced by a variety of factors, including ranking).
When creating a scatter plot, it is common to place the independent variable on the x-axis and the dependent variable on the y-axis. This scatter plot could reveal correlations or trends between the two variables. The correlation coefficient is a statistical measure that describes the strength and direction of a relationship between two variables. A correlation coefficient close to 1 or -1 indicates a strong relationship, while a number close to 0 indicates a weak relationship. The least-squares line is a regression line that minimizes the sum of the squared differences between the observed values and the values predicted by the line.
9 more than the quotient of 52 divided by 4
The solution of ''9 more than the quotient of 52 divided by 4'' is 22.
Now,
Given statement is, ''9 more than the quotient of 52 divided by 4''
What is Quotient?
A quotient is the answer a division problem. The divisor is the number of parts you divide the dividend by.
Now,
The quotient of 52 divided by 4 is,
52 ÷ 4 = 13
And, 9 more than the quotient of 52 divided by 4 is,
( 52 ÷ 4 )+ 9 = 13 + 9 = 22
Hence, The solution of ''9 more than the quotient of 52 divided by 4'' is 22.
Learn more about the Quotient visit:
https://brainly.in/question/848408
#SPJ2
To solve the expression, divide 52 by 4 to get 13, then add 9 to the quotient, resulting in the final answer of 22.
Explanation:The question asks to find '9 more than the quotient of 52 divided by 4'.
First, we need to calculate the quotient of 52 divided by 4, which is done by performing the division.
So, 52 ÷ 4 equals 13. Next, we add 9 to this quotient to get the final result.
Adding 9 to 13 gives us 22.
Therefore, 9 more than the quotient of 52 divided by 4 is 22.
HELP ASAP PLEASE!!!
What is the range for the set of data?
a. 4
b. 6
c. 3.5
d. 0
Answer:
Step-by-step explanation:
Answer:
b
Step-by-step explanation:
because i said so