Answer:
the drop in the level of water in the container is 2.03 cm
Step-by-step explanation:
The volume of a cylinder can be written as;
[tex]V = \pi r^2h=\frac{\pi d^2h}{4} \\where;\\r = radius \\h = height \\d = diameter[/tex]
the change in height when the volume changes can be derived by differentiating the equation.
[tex]dV =\frac{\pi d^2}{4} dh\\dh = dV\frac{4}{\pi d^2}[/tex]
substituting the given values;
[tex]\left \{ {{dV=5 litres= 5000cm^3} \atop {d=56 cm}} \right.[/tex]
[tex]dh = 5000\frac{4}{\pi * 56^2}\\dh = 2.03cm[/tex]
the drop in the level of water in the container is 2.03 cm
Which of the following is best described as sets of three whole numbers (a, b, and c) that satisfy the equation ?
A.
The Pythagorean theorem
B.
Prime numbers
C.
Pythagorean triples
D.
Perfect squares
Answer:
Option C
Step-by-step explanation:
The whole numbers a,b and c such that [tex]a^2+b^2 = c^2[/tex] are Pythagorean triples satisfying the Pythagorean theorem.
Answer:
C
Step-by-step explanation:
a, b, and c are side lengths of the triangle.
The three side lengths that make up a right triangle are most commonly known as Pythagorean triples.
Find the next two !!!
It's adding 3 and subtracting 2 every time.
This means the next two terms would be +3 and -2 since the last one was -2.
The next term = 4+3=7
The next next term = 7-2=5
Answer:
Answer : 7 , 5Please see the attached picture.
Hope it helps...
Best regards!!
Solve the quadratic equation x2 + 2x – 20 = 0 by completing the square.
Answer:
x^2 + 2x - 20 = 0
x^2 + 2x - 20 + 20 = 0 + 20 ( add 20 to both sides)
x^2 + 2x = 20
x^2 + 2x + 1^2 = 20 + 1^2 ( add 1^2 to both sides)
( x + 1 )^2 = 21
x = [tex]\sqrt{21}-1[/tex]
x = [tex]-\sqrt{21}-1[/tex]
Answer:
A) x = –1 ± square root 21
is the answer:)
Multiply (x2 + 3x + 4)(3x2 - 2x + 1).
Answer:
The answer is
3x⁴ + 7x³ + 7x² - 5x + 4Step-by-step explanation:
(x² + 3x + 4)(3x² - 2x + 1)
Expand the terms
We have
3x⁴ - 2x³ + x² + 9x³ - 6x² + 3x + 12x² - 8x + 4
Group like terms
That's
3x⁴ - 2x³ + 9x³ + x² - 6x² + 12x² + 3x - 8x + 4
Simplify
We have the final answer as
3x⁴ + 7x³ + 7x² - 5x + 4Hope this helps you
The function g(x) is a transformation of f(x). If g(x) has a y-intercept of -2, which of the following functions could represent g(x)
Answer:
b. [tex]g(x)=f(x)-5[/tex]
Step-by-step explanation:
You have that the function f(x) has its y-intercept for y=3.
Furthermore, you have that g(x) is a transformation of f(x) with y-intercept for y=-2.
In this case you have that f(x) has been translated vertically downward.
The general way to translate a function vertically in the coordinate system is:
[tex]g(x)=f(x)+a[/tex] (1)
being a positive or negative.
if g(x) has its y-intercept for y=-2, and the y-intercept of f(x) is for y=3, then the value of a in the equation (1) must be a = -5, which is the difference between both y-intercepts, in fact:
a = -2 -3 = -5
Then, the answer is:
b. [tex]g(x)=f(x)-5[/tex]
Answer: g(x) = f(x) - 5
Step-by-step explanation:
just took this
Salaries of 43 college graduates who took a statistics course in college have a mean,66,000 , of . Assuming a standard deviation, 18908 , of $, construct a %99 confidence interval for estimating the population mean .
Answer:
$[58543.42; 73456.58]
Step-by-step explanation:
Hello!
For the variable
X: salary of a college graduate that took a statistics course
Out of n= 43 students, the calculated mean is [tex]\frac{}{X}[/tex]= $66000
The population standard deviation is δ= $18908
There is no information about the variable distribution, but since the sample size is big enough (n≥30), you can apply the CLT and approximate the distribution of the sample mean to normal [tex]\frac{}{X}[/tex]≈N(μ;σ²/n)
Then you can apply the approximation of the standard normal distribution to calculate the 99% CI
[tex]\frac{}{X}[/tex] ± [tex]Z_{1-\alpha /2}[/tex] * [tex]\frac{Singma}{\sqrt{n} }[/tex]
[tex]Z_{1-\alpha /2}= Z_{0.995}= 2.586[/tex]
[tex]\frac{Singma}{\sqrt{n} }= \frac{18908}{\sqrt{43} }= 2883.44[/tex]
[66000±2.586*2883.44]
$[58543.42; 73456.58]
With a 99% confidence level you'd expect that the interval $[58543.42; 73456.58] will include the average salary of college graduates that took a course of statistics.
I hope this helps!
What is the excluded value?
Answer:
Excluded value = -7
Solution = [tex] x = \frac{5}{9} [/tex]
Step-by-step Explanation:
The excluded value is the value that will make the denominator 0.
Thus,
[tex] x + 7 = 0 [/tex]
Subtract 7 from both sides
[tex] x + 7- 7 = 0 - 7 [/tex]
[tex] x = -7 [/tex]
The excluded value is -7
Solution=>
[tex] \frac{2x}{x + 7} + \frac{3x + 1}{x + 7} = \frac{1}{2} [/tex]
[tex] \frac{2x + (3x + 1)}{x + 7} = \frac{1}{2} [/tex]
[tex] \frac{5x + 1}{x + 7} = \frac{1}{2} [/tex]
Cross multiply
[tex] 2(5x + 1) = 1(x + 7) [/tex]
[tex] 10x + 2 = x + 7 [/tex]
[tex] 10x - x = -2 + 7 [/tex]
[tex] 9x = 5 [/tex]
[tex] x = \frac{5}{9} [/tex]
need answers (ASAP!!!) with equations, please!!
Answer:
a=6, b=5.5
Step-by-step explanation:
By looking at the sides of the triangles it can easily be seen that some of the sides match up. Side b is similar to the side of 11 and same with side a and the side of 3. Since one side is 16 and the other side on the smaller triangle is 8, the bigger triangle is twice as large than the smaller one. So 3 x 2 = 6 and 11 / 2 = 5.5
A poll of 61 students found that 22% were in favor of raising tution to pave new parking lots. The standard deviation of this poll is 6%. What would be the standard deviation if the sample size were increased from 61 to 290?
Answer:
The standard Deviation would increase
Step-by-step explanation:
Is this advantages?
A soup company puts 12 ounces of soup in each can. The company has determined that 97% of cans have the correct amount. Which of the following describes a binomial experiment that would determine the probability that a case of 36 cans has all cans that are properly filled?
a. n=36, p=0.97, x=1
b. n=12, p=0.36, x=97
c. n=12, p=0.97, x=0
d. n=36, p=0.97, x=36
Answer:
Option d: n = 36, p = 0.97, x = 36.
Step-by-step explanation:
We are given that a soup company puts 12 ounces of soup in each can. The company has determined that 97% of can have the correct amount.
We have to describe a binomial experiment that would determine the probability that a case of 36 cans has all cans that are properly filled.
Let X = Number of cans that are properly filled
The above situation can be represented through binomial distribution;
[tex]P(X = x) = \binom{n}{x} \times p^{x} \times (1-p)^{n-x} ; x = 0,1,2,........[/tex]
where, n = number of trials (samples) taken = 36 cans
x = number of success = all cans are properly filled = 36
p = probabilitiy of success which in our question is probability that
can have the correct amount, i.e. p = 97%
So, X ~ Binom (n = 36, p = 0.97)
Hence, from the options given the correct option which describes a binomial experiment that would determine the probability that a case of 36 cans has all cans that are properly filled is n = 36, p = 0.97, x = 36.
What is the converse and the truth value of the converse of the following conditional? If an angle is a right angle, then it’s measure is 90
Answer:
"If an angle has measure 90°, then it is a right angle" , True
Step-by-step explanation:
We have the following:
"If an angle is a right angle, then it’s measure is 90"
The idea is to write the opposite of the previous conditional statement.
We know that if the statement is "If p, then q", then its inverse will be "If q, then p".
So the opposite of our given statement will be :
"If an angle has measure 90°, then it is a right angle"
And this statement is true since every angle that measures 90 ° is considered a right angle.
If A divided by B = 10 remainder of 6 what is b
Answer:
B = (A - 6) / 10
Step-by-step explanation:
This problem has 2 variables and 1 equation so it is not trivial to solve with confidence the value of B; however, we can solve for B in terms of A. With that being said, let's start.
If A divided by B = 10:
A/B = 10
10 remainder of 6
Could also be written as 10 & 6/B since B is the divisor. Rewrite this, you can get the equation:
A/B = (10B + 6) / B
A = 10B + 6
A - 6 = 10B
B = (A - 6) / 10
Thus, you have solve B in terms of A.
Cheers.
The more error we allow, the less precise our estimate.Therefore, as the confidence level increases, the precision of our estimate increases stays roughly the same ___________.
Answer:
Increase
Step-by-step explanation:
Precision describes the closeness of estimates from different samples, it refers to the width of the confidence interval and can aso be described as the margin of error. While the confidence level describes the accuracy.
Going for a higher confidence level will bring about a wider confidence interval, and thus lead to a less precise estimate.
Hey, the question is with the image. Pls help
Answer:
8
Step-by-step explanation:
The graph for the equation y = 2 x + 4 is shown below. On a coordinate plane, a line goes through (negative 2, 0) and (0, 4). If another equation is graphed so that the system has one solution, which equation could that be?
Answer: x = 1
Step-by-step explanation:
x = 1 provides one solution for any linear equation, as it is a straight vertical line.
Hope it helps <3
Answer:
x=2
Step-by-step explanation:
Our equation is y=2x+4
the line goes through (2,0) and (0,4)
(2,0) is the x-axis intercept wich is given by y=0(0,4) is the y-intercept wich by y= 2*0+4This equation has one solution for y=0
there are millions of similar equations that has one solution like:
x = 2
Use Stokes' Theorem to evaluate S curl F · dS. F(x, y, z) = zeyi + x cos(y)j + xz sin(y)k, S is the hemisphere x2 + y2 + z2 = 16, y ≥ 0, oriented in the direction of the positive y-axis.
Stokes' theorem equates the surface integral of the curl of F to the line integral of F along the boundary of the hemisphere. The boundary itself is a circle C (the intersection of the hemisphere with the plane y = 0) with equation
[tex]x^2+z^2=16[/tex]
Parameterize this circle by
[tex]\mathbf r(t)=4\cos t\,\mathbf i+4\sin t\,\mathbf k[/tex]
with [tex]0\le t\le2\pi[/tex].
The surface is oriented such that its normal vector points in the positive y direction, which corresponds to the curve having counterclockwise orientation. The parameterization we're using here already takes this into account.
Now compute the line integral of F along C :
[tex]\displaystyle\iint_S\mathrm{curl}\mathbf F(x,y,z)\cdot\mathrm d\mathbf S=\int_C\mathbf F(x,y,z)\cdot\mathrm d\mathbf r[/tex]
[tex]=\displaystyle\int_0^{2\pi}\mathbf F(4\cos t,0,4\sin t)\cdot\frac{\mathrm d\mathbf r}{\mathrm dt}\,\mathrm dt[/tex]
[tex]=\displaystyle\int_0^{2\pi}(4\sin t\,\mathbf i+4\cos t\,\mathbf j)\cdot(-4\sin t\,\mathbf i+4\cos t\,\mathbf k)\,\mathrm dt[/tex]
[tex]=\displaystyle\int_0^{2\pi}-16\sin^2t\,\mathrm dt[/tex]
[tex]=-8\displaystyle\int_0^{2\pi}(1-\cos(2t))\,\mathrm dt=\boxed{-16\pi}[/tex]
Line integral of F along C is,
[tex]\rm \int \int_S curl F(x,y,z) dS = -16\pi[/tex]
Step-by-step explanation:
Given :
Hemisphere - [tex]x^2 +y^2+z^2=16[/tex]
Calculation :
Accordind to Stoke's theorem the surface integral of the curl of F to the line integral of F along the boundary of the hemisphere. The boundary itself is a circle C (the intersection of the hemisphere with the plane y = 0) with equation
[tex]x^2+z^2=16[/tex]
then parameterize the circle,
[tex]\rm r(t) = 4 cos(t) \;\hat{i} + 4 sin(t)\;(\hat{k})[/tex]
with , [tex]0\leq t\leq 2\pi[/tex]
Line integral of F along C is,
[tex]\rm \int \int_S curl F(x,y,z) dS = \int_{C}^{} F(x,y,z) \;dr[/tex]
[tex]= \int_{0}^{2\pi} F(4cos(t),0,4sin(t)) \;\dfrac{dr}{dt}.dt[/tex]
[tex]= \int_{0}^{2\pi}(4sin(t)i+4cos(t) j).(-4sin(t)i+4cos(t)k) \;dt[/tex]
[tex]= \int_{0}^{2\pi} -16sin^2tdt[/tex]
[tex]=-8 \int_{0}^{2\pi} (1-cos(2t))dt[/tex]
[tex]= -16\pi[/tex]
For more information, refer the link given below
https://brainly.com/question/8130922?referrer=searchResults
Blue ribbon taxis offers shuttle service to the nearest airport. You loop up online reviews for blue ribbon taxis and find that there are 17 reviews, six of which report that the taxi never showed up.
Is this a biased sampling method for obtaining customer opinion on the taxi service?
If so, what is the likely direction of bias?
explain your reasoning carefully.
Answer:
In order for a sample to be considered biased, some members of the total population must have either a larger or lower chance of being included in the sample. In this case, your sample contained 17 reviews. It is biased because it was completely voluntary and customers who have a bad experience with a product or service generally tend to express more their dissatisfaction than satisfied customers show their satisfaction.
In marketing, there is a saying that unsatisfied clients talk bad about our product or service 4 times more than satisfied clients. I'm not sure if this saying is exact or not, but all marketing research point in the same direction.
This means that clients that did not get a good service or got no service at all, are more likely to post a review about the company than clients who got a good service. This is what makes the sample biased.
Suppose we use a person's dad's height to predict how short or tall the person will be. Suppose we decided to build a regression model to investigate if there is a relationship between these two variables. What should we use as the variables in the analysis
Answer:
The variables that can be used in the analysis are:
Dependent variable: person's height (Height)
Independent variable: person's dad's height (DadsHt)
Step-by-step explanation:
A linear regression model is used to predict the value of the dependent variable based upon the value of the independent variable.
The general form of a linear regression model is:
[tex]y=a+bx[/tex]
Here,
y = dependent variable
x = independent variable
a = intercept
b = slope
Dependent variables are those variables that are under study, i.e. they are being observed for any changes when the other variables in the model are changed.
The dependent variables are also known as response variables.
Independent variables are the variables that are being altered to see a proportionate change in the dependent variable. In a regression model there can be one or more than one independent variables.
The independent variables are also known as the predictor variables.
In this vase we need to form a regression model such that, a person's dad's height can be used to predict how short or tall the person will be.
That is, the dependent variable is the person's height and the independent variable is the person's dad's height.
The variables that can be used in the analysis are:
Dependent variable: person's height (Height)
Independent variable: person's dad's height (DadsHt)
the sum of place value of 5 in 15954
Answer:
5050
Step-by-step explanation:
Place value of a digit is the value of digit based on its position the given number.
to determine the place value of a digit
we multiply the digit by number of 10's which is equal to number of digits in its right.
example
for a number 1234687
the place value of 3 is
we take 3 and
multiply it by number of 10' in its right
number of 10's in the right is 4
thus place value of 3 = 3*10*10*10*10 = 30000
________________________________________________
15954
place value of 5 at thousandth position = 5*10*10*10 = 5000
place value of 5 at tens position = 5*10 = 50
Thus, sum of place value of 5 in 15954 = 5000+50 = 5050
Solve the equation below for x.
-1
2(3x - 4) = 11
A truck averages 23 mpg. Gas costs $2.28 per gallon. How much would it cost to pay for the gas if this truck made a trip of 2,093 miles?
Answer:$207.48
Step-by-step explanation:You need to find how much gallons he would need so you divide 2,093 by 23 and you get 91. After that you multiply it by $2.28, The price per gallon and you get 207.48.
Find the mean, median, and mode of the data, if possible. f any of these measures cannot be found or a measure does not represent the center of the data, explain why.
A sample of seven admission test scores for a professional school are listed below
11.3 10.6 11.7 9.7 11.7 9.5 11.7
What is the mean score? Select the correct choice below and fill in any answer box to complete your choice
A. The mean score is Round to one decimal place as needed.)
B. There is no mean score. Does the mean represent the center of the data?
A. The mean represents the center
B. The mean does not represent the center because it is the smallest data value.
C. The mean does not represent the center because it is not a data value.
D. The mean does not represent the center because it is the largest data value.
What is the median score? Select the correct choice below and fill in any answer box to complete your choice.
A. The median score is 0
B. There is no median score.
Does the median represent the center of the data? (Round to one decimal place as needed.)
A. The median represents the center.
B. The median does not represent the center because it is not a data value. °
C. The median does not represent the center because it is the largest data value.
D. The median does not represent the center because it is the smallest data value.
What is the mode of the scores? Select the correct choice below and fill in any answer box to complete your choice
A. The mode(s) of the scores is (are)
B. There is no mode. Does (Do) the mode(s) represent the center of the data?
(Use a comma to separate answers as needed.)
A. The mode(s) represent(s) the center
B. The mode(s) can't represent the center because it (they) is (are) not a data value.
C. The mode(s) does (do) not represent the center because it (one) is the largest data value.
D. The mode(s) does (do) not represent the center because it (one) is the smallest data value.
Answer:
Step-by-step explanation:
Given a sample of seven admission test scores for a professional school listed 11.3, 10.6, 11.7, 9.7, 11.7, 9.5 and 11.7, the mean of the numbers is the sum total of the values divided by the total number of admission test score. The mean is as calculated below.
Mean = {11.3 + 10.6 + 11.7 + 9.7 + 11.7 + 9.5 + 11.7}/7
Mean = 76.2/7
Mean = 10.9
The mean score is 10.9 to 1 decimal place.
Note that the mean does not represent the centre of the data. It represents the average value of the datas. The mean does not represent the center because it is not a data value. The mean will give a value that is different from the values given in the data.
b) The median score is the score in the centre after re-arrangement. The arrangement can either be ascending or descending order. On re-arranging in ascending order;
9.5, 9.7, 10.6, (11.3), 11.7, 11.7, 11.7
After rearranging, it can be seen that the number at the centre of the data is 11.3, hence the median score is 11.3.
The median represents the center
c) The mode is the scores that occurs most. According to the data given, the score that occur most is 11.7. The score occurs the highest number of times (3 times) compare to other scores in the data. Hence, the modal score is 11.7.
The mode(s) does (do) not represent the center because it (one) is the largest data value.
The circular clock face in the clock tower on campus has a radius of about 4 meters. What is the area of the clock to the nearest square meter? Use 3.14 as an approximation for pi
Answer:
50 meters
Step-by-step explanation:
The area of a circle is [tex]\pi r^2[/tex], so assuming that [tex]\pi[/tex] is 3.14, we can make the equation [tex]3.14 \cdot r^2[/tex].
Assuming the radius is r, which is 4, we can substitute the values into the equation.
[tex]3.14 \cdot 4^2\\3.14\cdot16\\50.24[/tex]
This question is asking for the area to the nearest square meter so rounding 50.24 to the nearest square meter results in 50.
Hope this helped!
You were recently hired by a company and will recieve a starting salary of $45,000 per year. You will receive a $2,500 raise each year you are with the company. What will your salary be in your 6th year with the company?
Answer:
$60,000
Step-by-step explanation:
$2500*6=15000
45000+15000=60000
The letters "A", "B", "C", "D", "E", and "F" are written on six slips of paper, and the slips are placed into a hat. If the slips are drawn randomly without replacement, what is the probability that "E" is drawn first and "B" is drawn second?
Answer:
1/30
Step-by-step explanation:
The probability of getting ”E” is 1/6.
There is only 1 “E” out of 6 letters.
There is no replacement.
There are now 5 letters without “E”.
”A”, “B”, “C”, “D”, “F”
The probability of getting ”B” is 1/5.
There is only 1 “B” out of 5 letters.
⇒ 1/6 × 1/5
⇒ 1/30
The polynomial −16t^2+550 gives the height of a ball t seconds after it is dropped from a 550-foot-tall building. Find the height after t=2 seconds.
Answer:
486 feet
Step-by-step explanation:
h = -16t² + 550
h = -16(2)² + 550
h = 486
g There are 60 mountain climbers in a club. 10 of these have climbed Mt. Everest. 15 have climbed Mt. Rainier. 8 have climbed both. How many have not climbed either mountain?
Answer:
43 mountain climbers have not climbed either mountain.
Step-by-step explanation:
Total number of mountain climbers, i.e. n(U) = 60
Number of mountain climbers who have climbed Mt. Everest, n(E) = 10
Number of mountain climbers who have climbed Mt. Rainier, n(R) = 15
Number of mountain climbers who have climbed both, n(E [tex]\cap[/tex] R) = 15
Using the formula to find number of climbers who have climbed either of the mountains:
[tex]n(A \cup B) = n(A)+n(B)-n(A\cup B )[/tex]
[tex]\therefore n(E \cup R) = n(E)+n(R)-n(E\cup R )\\\Rightarrow n(E \cup R) = 10+15-8 = 17[/tex]
To find, who have not climbed either mountain:
[tex]n(E\cup B)'=n(U) - n(E\cap B)\\\Rightarrow n(E\cup B)'=60 - 17 = \bold{43}[/tex]
So, the answer is:
43 mountain climbers have not climbed either mountain.
HELP- find the volume of the prism
Answer:
The answer is
1728″Step-by-step explanation:
From the above question the prism in the picture is a cube since all it's sides are equal
So the formula for finding the volume of a cube is
V = l³
where l is the length of one side
From the question l = 12″
Volume of the prism = 12³
= 1728″
Hope this helps you
The 2010 General Social Survey reported a sample where about 48% of US residents thought marijuana should be made legal. If we wanted to limit the margin of error of a 95% confidence interval to 4%, about how many Americans would we need to survey
Answer:
The sample size is [tex]n = 600[/tex]
Step-by-step explanation:
From the question we are told that
The sample proportion is [tex]\r p = 0.48[/tex]
The margin of error is [tex]MOE = 0.04[/tex]
Given that the confidence level is 95% the level of significance is mathematically represented as
[tex]\alpha = 100 - 95[/tex]
[tex]\alpha = 5 \%[/tex]
[tex]\alpha = 0.05[/tex]
Next we obtain the critical value of [tex]\frac{\alpha }{2}[/tex] from the normal distribution table , the values is
[tex]Z_{\frac{\alpha }{2} } = 1.96[/tex]
The reason we are obtaining critical value of [tex]\frac{\alpha }{2}[/tex] instead of [tex]\alpha[/tex] is because
[tex]\alpha[/tex] represents the area under the normal curve where the confidence level interval ( [tex]1-\alpha[/tex]) did not cover which include both the left and right tail while
[tex]\frac{\alpha }{2}[/tex] is just the area of one tail which what we required to calculate the margin of error
Generally the margin of error is mathematically represented as
[tex]MOE = Z_{\frac{\alpha }{2} } * \sqrt{ \frac{\r p(1- \r p )}{n} }[/tex]
substituting values
[tex]0.04= 1.96* \sqrt{ \frac{0.48(1- 0.48 )}{n} }[/tex]
[tex]0.02041 = \sqrt{ \frac{0.48(52 )}{n} }[/tex]
[tex]0.02041 = \sqrt{ \frac{ 0.2496}{n} }[/tex]
[tex]0.02041^2 = \frac{ 0.2496}{n}[/tex]
[tex]0.0004166 = \frac{ 0.2496}{n}[/tex]
=> [tex]n = 600[/tex]
What is the inverse of the function below?
f(x) = x-5
A. f^-1(x) = x + 5
B. f^-1(X) = x-5
C. f^-1(x) = -x + 5
D. f^-1(x) = -x-5
Answer:
f^-1(x) = x + 5
Step-by-step explanation:
f(x) = x-5
y = x-5
Exchange x and y
x = y-5
Solve for y
x+5 = y-5+5
x+5 =y
The inverse is x+5