Question:
A solid lies between planes perpendicular to the x-axis at x=0 and x=12. The cross-sections perpendicular to the axis on the interval 0≤x≤12 are squares with diagonals that run from the parabola y=-2√x to the parabola y=2√x. Find the volume of the solid.
Answer:
576
Step-by-step explanation:
Given:
Length of diagonal square:
[tex] D = 2\sqrt{x} - (-2\sqrt{x}) [/tex]
[tex] D = 4\sqrt{x} [/tex]
Here, the diagonal is the hypotenus of a right angle triangle, with leg S, where the square has a side of length S.
Using Pythagoras theorem:
[tex] S^2 + S^2 = D^2 [/tex]
[tex] S^2 + S^2 = (4\sqrt{x})^2 [/tex]
[tex] 2S^2 = 16x [/tex]
Divide both sides by 2
[tex] S^2 = 8x [/tex]
Thus,
Area, A = S² = 8x
Take differential volume, dx =
dV = Axdx
dV = 8xdx
Where limit of solid= 0≤x≤12
Volume of solid, V:
V =∫₀¹² dV
V = 8 ∫₀¹² xdx
V = [4x²]₀¹²
V = 4 (12)²
V = 12 * 144
= 576
Volume of solid = 576
Rectangle WXYZ was dilated to create W'X'Y'Z'. Point G is the center of dilation. Rectangle W X Y Z was dilated to create smaller rectangle W prime X prime Y prime Z prime. The length of G Z prime is 1.5. The length of Z prime Z is 7.5. Side W X is 3 units and side X Y is 6 units. What is W'X'? 0.5 units 1.2 units 1.5 units 1.8 units
Answer:
0.5 units
Step-by-step explanation:
The dilation factor is ...
(GZ')/(GZ) = (GZ')/(GZ' +Z'Z) = 1.5/(1.5 +7.5) = 1/6
Side WX is 3 units, so side W'X' is (1/6)(3 units) = 1/2 units
W'X' is 0.5 units.
Answer:
It is .5 on edge
Step-by-step explanation:
I took the test
Provide three logically possible directions of causality, indicating for each direction whether it is a reasonable explanation for the correlation based on the variables involved. Explain why?
Answer:
Step-by-step explanation:
Does a point have a one dimension length
Answer:
No.
Step-by-step explanation:
A point has no length, height or depth. It only has position.
A line has one dimensional length.
If a random sample of 53 students was asked for the number of semester hours they are taking this semester. The sample standard deviation was found to be s = 4.7 semester hours. How many more students should be included in the sample to be 99% sure that the sample mean x is within 1 semester hour of the population mean for all students at this college?
Answer:
94 more students should be included in the sample.
Step-by-step explanation:
We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:
[tex]\alpha = \frac{1-0.99}{2} = 0.005[/tex]
Now, we have to find z in the Ztable as such z has a pvalue of [tex]1-\alpha[/tex].
So it is z with a pvalue of [tex]1-0.005 = 0.995[/tex], so [tex]z = 2.575[/tex]
Now, find the margin of error M as such
[tex]M = z*\frac{\sigma}{\sqrt{n}}[/tex]
In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.
How many students we need to sample to be 99% sure that the sample mean x is within 1 semester hour of the population mean?
We need to survey n students.
n is found when M = 1.
We have that [tex]\sigma = 4.7[/tex]
So
[tex]M = z*\frac{\sigma}{\sqrt{n}}[/tex]
[tex]1 = 2.575*\frac{4.7}{\sqrt{n}}[/tex]
[tex]\sqrt{n} = 2.575*4.7[/tex]
[tex](\sqrt{n})^{2} = (2.575*4.7)^{2}[/tex]
[tex]n = 146.47[/tex]
Rounding up
147 students need to be surveyed.
How many more students should be included...?
53 have already been surveyed
147 - 53 = 94
94 more students should be included in the sample.
There are 15 marbles in a bag; 10 are blue, 4 are red and 1 is green. Marbles are drawn and NOT replaced 8 times, with the number of red marbles being recorded. What is the probability of getting exactly 3 red marbles? (Write as a percentage, correct to two decimals. eg: 12.34%)
Answer: There is a 0.88% chance of pulling three red marbles in a row.
Step-by-step explanation:
First pull = 4/15 (26.67%)
second pull = 3/14 (21.43%)
Third pull = 2/13 (15.38%)
You need to multiply these three fractions to get the probability of pulling three reds in a row, doing that will get you 4/455 or 0.88%
List the important features for the graph of a quadratic function.
Answer:
VertexMinimum PointMaximum PointRootsAxis of SymmetryStep-by-step explanation:
The bottom (or top) of the U is called the vertex, or the turning point. The vertex of a parabola opening upward is also called the minimum point. The vertex of a parabola opening downward is also called the maximum point.
The x-intercepts are called the roots, or the zeros. To find the x-intercepts, set ax^2 + bx + c = 0.
The parabola is symmetric (a mirror image) about a vertical line drawn through its vertex (turning point). This line is called the axis of symmetry.
If possible, please mark brainliest
The quadratic function can be expressed in the form of vertex form and the parabola is symmetric about the line which is passing through focus.
What is a quadratic equation?The quadratic equation is given as ax² + bx + c = 0. Then the degree of the equation will be 2.
The important features for the graph of a quadratic function will be
The parabola is symmetric about the line which is passing through focus.
The quadratic function can be expressed in the form of vertex form.
Let the point (h, k) be the vertex of the parabola and a be the leading coefficient.
Then the equation of the parabola will be given as,
y = a(x - h)² + k
More about the quadratic equation link is given below.
https://brainly.com/question/2263981
#SPJ2
Math Activity #1
The number of the day is 1,853,604,297.
Write this number in word form:
What’s the correct answer for this question?
Answer:
B.
Step-by-step explanation:
The cottage inside the pen is a shape of a cylinder.
Answer:
Cylinder
As u can see the shape it's like a cylinder
Can someone help me with this I’m sorry I really just don’t know
Answer:
15
Step-by-step explanation:
Because the two triangles are similar:
[tex]\dfrac{LN}{30}=\dfrac{6}{30-18} \\\\\\\dfrac{LN}{30}=\dfrac{6}{12} \\\\\\LN=30\cdot \dfrac{1}{2}=15[/tex]
Hope this helps!
Let the velocity of a particle be given by v(t) = 2t+a.(a) Find the number a such that the average value of v(t) on the interval [0,1] is -2.(b) Using v(t) from part (a), find the distance traveled by the particle during the time period from [0,4].
Answer:
The velocity is v(t) = 2*t + a
a) we want to find the average velocity betwen t = 0 and t = 1.
We can do this as:
Average = (v(1) + v(0))/2 = (2*1 + a + 2*0 + a)/2 = 1 + a
b) now we want to find the total distance traveled in the time lapse from t = 0 to t = 4.
For this we can see the integral:
[tex]d = \int\limits^4_0 {2*t + a} \, dt = 4^2 + a*4 - 0^2 - a*0 = 4^2 + a*4 = 16 + a^2[/tex]
Please answer this correctly
Answer:
1 flowers
Step-by-step explanation:
The graph shows that only one flower received more than [tex]4\frac{1}{2}[/tex] cups of water and that is the plant that received 5 cups of water.
1 flower
Step-by-step explanation:
the question asks for flowers above the 4 1/2 mark and only 1 flower is there.
Two fair coins are flipped at the same time What is the probability that both display tails?
1/8
1/4
1/3
1/2
Answer:
Step-by-step explanation:
Your answer would be 1/2.
Because they are 2 coins and each have a probability of landing on tails.
The probability that both display tails are 1/2.
We have given that,
Two fair coins are flipped at the same time
We have to determine the, what is the probability that both display tails.
What is the probability?
Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true. The probability of an event is a number between 0 and 1, where, roughly speaking, 0 indicates the impossibility of the event and 1 indicates certainty.
Because they are 2 coins and each has a probability of landing on tails.
To learn more about the probability visit:
https://brainly.com/question/25870256
#SPJ2
Age (years) Population Under 15 2600 15 - 64 16000 Over 64 4000 Calculate the child dependency ratio from the chart above. Round to 3 decimals places.
Answer:
16.25%
=0.163 (correct to 3 decimal places)
Step-by-step explanation:
The child dependency ratio of a population is defined as the number of children (Under 15 years) divided by the working-age population (15–64 years old).
[tex]\mathrm{ Child}\;\mathrm{ dependency}\;\mathrm{ ratio}=\dfrac{{\mathrm{ Population}\,\left( \text{Under 15} \right)}}{{\mathrm{ Population}\,\left( {15-64} \right)}}\times 100[/tex]
From the given table:
Population Under 15 years = 2600
Population of the working class (between 15-64) = 16000
Therefore:
[tex]\mathrm{ Child}\;\mathrm{ dependency}\;\mathrm{ ratio}=\dfrac{2600}{16000}\times 100\\\\=16.25\%[/tex]
=0.163 (correct to 3 decimal places)
A tree is 12 feet tall and casts a shadow 9 feet long. A building nearby casts a shadow that measures 24 feet. How tall is the building?
(Hint: Draw a picture and Set up a proportion)
The building height is 32 feet.
Let us consider that building height is x feet.
From attached diagram shown below,
Two triangles are formed.
Apply law of similarity of triangles.
Corresponding sides are in equal proportion.
[tex]\frac{x}{24}=\frac{12}{9} \\\\9x=12*24\\\\x=\frac{12*24}{9}=32 feet[/tex]
Learn more:
https://brainly.com/question/14285697
The total claim amount for a health insurance policy follows a distribution with density function 1 ( /1000) ( ) 1000 x fx e− = , x > 0. The premium for the policy is set at the expected total claim amount plus 100. If 100 policies are sold, calculate the approximate probability that the insurance company will have claims exceeding the premiums collected.
Answer:
the approximate probability that the insurance company will have claims exceeding the premiums collected is [tex]\mathbf{P(X>1100n) = 0.158655}[/tex]
Step-by-step explanation:
The probability of the density function of the total claim amount for the health insurance policy is given as :
[tex]f_x(x) = \dfrac{1}{1000}e^{\frac{-x}{1000}}, \ x> 0[/tex]
Thus, the expected total claim amount [tex]\mu[/tex] = 1000
The variance of the total claim amount [tex]\sigma ^2 = 1000^2[/tex]
However; the premium for the policy is set at the expected total claim amount plus 100. i.e (1000+100) = 1100
To determine the approximate probability that the insurance company will have claims exceeding the premiums collected if 100 policies are sold; we have :
P(X > 1100 n )
where n = numbers of premium sold
[tex]P (X> 1100n) = P (\dfrac{X - n \mu}{\sqrt{n \sigma ^2 }}> \dfrac{1100n - n \mu }{\sqrt{n \sigma^2}})[/tex]
[tex]P(X>1100n) = P(Z> \dfrac{\sqrt{n}(1100-1000}{1000})[/tex]
[tex]P(X>1100n) = P(Z> \dfrac{10*100}{1000})[/tex]
[tex]P(X>1100n) = P(Z> 1) \\ \\ P(X>1100n) = 1-P ( Z \leq 1) \\ \\ P(X>1100n) =1- 0.841345[/tex]
[tex]\mathbf{P(X>1100n) = 0.158655}[/tex]
Therefore: the approximate probability that the insurance company will have claims exceeding the premiums collected is [tex]\mathbf{P(X>1100n) = 0.158655}[/tex]
a cereal box is an example of a
Answer: recantagle
Step-by-step explanation:
What is the value of k?
k=
8
m
o
4
k
N
M
Answer: It’s 2
Step-by-step explanation:
look at picture
You are rolling two dice. When the two numbers (1-6) come up, you multiply the numbers
together. What is the probability of getting a product that is NOT divisible by 2?*
Answer:
1/4 probability of getting a product that isn't divisible by 2.
Step-by-step explanation:
These are all the possible outcomes
1 x 1 = 1 2 x 1 = 2 3 x 1 = 3 4 x 1 = 4 5 x 1 = 5 6 x 1 = 6
1 x 2 = 2 2 x 2 = 4 3 x 2 = 6 4 x 2 = 8 5 x 2 = 10 6 x 2 = 12
1 x 3 = 3 2 x 3 = 6 3 x 3 = 9 4 x 3 = 12 5 x 3 = 15 6 x 3 = 18
1 x 4 = 4 2 x 4 = 8 3 x 4 = 12 4 x 4 = 16 5 x 4 = 20 6 x 4 = 24
1 x 5 = 5 2 x 5 = 10 3 x 5 = 15 4 x 5 = 20 5 x 5 = 25 6 x 5 = 30
1 x 6 = 6 2 x 6 = 12 3 x 6 = 18 4 x 6 = 24 5 x 6 = 30 6 x 6 = 36
All of the outcomes that aren't divisible by 2 are in bold
There are 9 out of 36 possible outcomes that aren't divisible by 2
9/36 = 1/4
A hospital claims that the proportion, , of full-term babies born in their hospital that weigh more than pounds is . In a random sample of babies born in this hospital, weighed over pounds. Is there enough evidence to reject the hospital's claim at the
Complete question is:
A hospital claims that the proportion, p, of full-term babies born in their hospital that weigh more than 7 pounds is 36%. In a random sample of 170 babies born in this hospital, 56 weighed over 7 pounds. Is there enough evidence to reject the hospital's claim at the level of significance?
Answer:
Yes, there is enough evidence to reject the claim.
Step-by-step explanation:
We are given;
n = 170
x = 56
So, will use one sample proportion test to solve this.
p^ = x/n
p^ = 56/170
p^ = 0.3294
Since the proportion, p, of full-term babies born in their hospital that weigh more than 7 pounds is 36%.
Thus;
Null Hypothesis H0: p ≠ 0.36
Alternative Hypothesis Ha: p = 0.36
Formula for test statistic = (p^ - p)/√(p(1 - p)/n)
This gives;
Test statistic = (0.3294 - 0.36)/√(0.36(1 - 0.36)/170)
Test statistic = -0.8311
From z-table and online z-calculator, the p - value is 0.203.
level of significance is; α = 0.05
Now, Since the p value < α, we reject the null hypothesis .
Thus, the claim is true
In a lottery, you pay $1 and pick a number from 000 to 999. If your number comes up, you win $350, which is a profit of $349. If you lose, you lose $1. Your probability of winning is 0.001. What is the expected value of your profit
Answer:
The expected value of profit is -$0.65.
Step-by-step explanation:
The rules of the lottery are as follows:
You pay $1 and pick a number from 000 to 999.If your number comes up, you win $350, which is a profit of $349.If you lose, you lose $1.The probability of winning is, P (W) = 0.001.
Then the probability of losing will be,
P (L) = 1 - P (W)
= 1 - 0.001
= 0.999
Let the random variable X represent the amount of profit.
The probability distribution table of the lottery result is as follows:
Result X P (X)
Win +349 0.001
Lose -1 0.999
The formula to compute the expected value of X is:
[tex]E(X)=\sum X\cdot P(X)[/tex]
Compute the expected value of profit as follows:
[tex]E(X)=\sum X\cdot P(X)[/tex]
[tex]=(349\times 0.001)+(-1\times 0.999)\\\\=0.349-0.999\\\\=-0.65[/tex]
Thus, the expected value of profit is -$0.65.
A retail company estimates that if it spends x thousands of dollars on advertising during the year, it will realize a profit of P ( x ) dollars, where P ( x ) = − 0.5 x 2 + 120 x + 2000 , where 0 ≤ x ≤ 187 . a . What is the company's marginal profit at the $ 100000 and $ 140000 advertising levels? P ' ( 100 ) = P ' ( 140 ) = b . What advertising expenditure would you recommend to this company? $
Answer:
Step-by-step explanation:
If the profit realized by the company is modelled by the equation
P (x) = −0.5x² + 120x + 2000, marginal profit occurs at dP/dx = 0
dP/dx = -x+120
P'(x) = -x+120
Company's marginal profit at the $100,000 advertising level will be expressed as;
P '(100) = -100+120
P'(100) = 20
Marginal profit at the $100,000 advertising level is $20,000
Company's marginal profit at the $140,000 advertising level will be expressed as;
P '(140) = -140+120
P'(140) = -20
Marginal profit at the $140,000 advertising level is $-20,000
Based on the marginal profit at both advertising level, I will recommend the advertising expenditure when profit between $0 and $119 is made. At any marginal profit from $120 and above, it is not advisable for the company to advertise because they will fall into a negative marginal profit which is invariably a loss.
5/2 = 11/x
What is x
Answer:
X=22/5
Step-by-step explanation:
By cross multiplication
5/2 =11/x
5x = 2(11)
5x =22
X=22/5
Hope this helps..
Drivers who are members of the teamsters Union earn an average of $17.15 per hour (U.S. News & World Report). Assume that available data indicate wages are normally distributed with a standard deviation of $2.25. 1) What is the probability that wages are between $15.00 and $20.00 per hours?
Answer:
[tex]P(15<X<20)=P(\frac{15-\mu}{\sigma}<\frac{X-\mu}{\sigma}<\frac{20-\mu}{\sigma})=P(\frac{15-17.15}{2.25}<Z<\frac{20-17.15}{2.25})=P(-0.96<z<1.27)[/tex]
And we can find the probability with this difference and using the normal standard table:
[tex]P(-0.96<z<1.27)=P(z<1.27)-P(z<-0.96)= 0.898-0.169 = 0.729[/tex]
Step-by-step explanation:
Let X the random variable that represent the wages, and for this case we know the distribution for X is given by:
[tex]X \sim N(17.15,2.25)[/tex]
Where [tex]\mu=17.15[/tex] and [tex]\sigma=2.25[/tex]
We want to find this probability:
[tex]P(15<X<20)[/tex]
And we can use the z score formula given by:
[tex]z=\frac{x-\mu}{\sigma}[/tex]
Using this formula we have:
[tex]P(15<X<20)=P(\frac{15-\mu}{\sigma}<\frac{X-\mu}{\sigma}<\frac{20-\mu}{\sigma})=P(\frac{15-17.15}{2.25}<Z<\frac{20-17.15}{2.25})=P(-0.96<z<1.27)[/tex]
And we can find the probability with this difference and using the normal standard table:
[tex]P(-0.96<z<1.27)=P(z<1.27)-P(z<-0.96)= 0.898-0.169 = 0.729[/tex]
1/4+3/8+1/2+5/8+7/8
Answer: 1/4+3/8+1/2+5/8+7/8
= 21/8
Hope this helps :)))
Answer:
21/8
Step-by-step explanation:
Suppose f '' is continuous on (−[infinity], [infinity]). (a) If f '(−5) = 0 and f ''(−5) = −1, what can you say about f ? At x = −5, f has a local maximum. At x = −5, f has a local minimum. At x = −5, f has neither a maximum nor a minimum. More information is needed to determine if f has a maximum or minimum at x = −5. (b) If f '(1) = 0 and f ''(1) = 0, what can you say about f ? At x = 1, f has a local maximum. At x = 1, f has a local minimum. At x = 1, f has neither a maximum nor a minimum. More information is needed to determine if f has a maximum or minimum at x = 1.
Answer:
Step-by-step explanation:
a) The first derivative helps considering f decreases or increases. Also, when f'(x) = 0, the function gets local max/min depends on how it acts.
The second derivative helps determining the concave up/down.
At x = -5, f"(-5) = -1 <0 That means the function f have concave down. Also, it shows f increases before -5 and decreases after -5.
Hence f'(-5) = 0 shows f gets maximum at -5.
b) At the point where f" =0, the function has a reflecting point and we need more information to determine if f has a local max/min there.
Using concepts of critical points, it is found that:
a) At x = −5, f has a local maximum.
b) At x = 1, f has neither a maximum nor a minimum.
-----------------------
A critical value of a function f(x) is a value of [tex]x^{\ast}[/tex] for which: [tex]f^{\prime}(x^{\ast}) = 0[/tex].
The second derivative test is also applied:
If [tex]f^{\prime\prime}(x^{\ast}) > 0[/tex], [tex]x^{\ast}[/tex] is a minimum point.If [tex]f^{\prime\prime}(x^{\ast}) < 0[/tex], [tex]x^{\ast}[/tex] is a maximum point.If [tex]f^{\prime\prime}(x^{\ast}) = 0[/tex], [tex]x^{\ast}[/tex] is neither a maximum nor a minimum point.Item a:
[tex]f^{\prime}(-5) = 0, f^{\prime\prime}(-5) = -1[/tex], thus, a maximum point, and the correct option is:At x = −5, f has a local maximum.
Item b:
[tex]f^{\prime}(1) = 0, f^{\prime\prime}(1) = 0[/tex], thus, neither a maximum nor a minimum point, and the correct option is:At x = 1, f has neither a maximum nor a minimum.
A similar problem is given at https://brainly.com/question/16944025
HELP! the function f(x)=200/x+10 models the cost per student of a field trip when x students go on the trip. how is the parent function f(x)=1/x transformed to create the function f(x)=200/x+10
Answer:
stretch of 200 shift up 10 units
Step-by-step explanation:
f(x)=1/x to 200/x+10
Multiply by 200 means a stretch of 200
f(x) = 200/x
Now shift up 10 units
f(x) = 200/x + 10
Answer:
It moves up 10 units
Step-by-step explanation:
f(x) =1/x to 200/x + 10
= 200/x
If we shift up 10 units, we get:
f(x) = 200/x + 10
Hope this helps!
Which figure has two bases and one lateral face that is rectangular? cone cylinder rectangular prism rectangular pyramid
Answer: Cylinder
Step-by-step explanation:
Two bases first: that rules out cone and rectangular pyramid.
One lateral face: the only one with that is cylinder.
Hope that helped,
-sirswagger21
The figure which has two bases and one lateral face that is rectangular is, ''Cylinder.''
What is mean by Triangle?Any triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.
Given that;
The shape have two bases and one lateral face that is rectangular.
We know that;
In a Cylinder,
It is a three-dimensional solid that contains two parallel bases connected by a curved surface.
And, The bases are usually circular in shape. The perpendicular distance between the bases is denoted as the height “h” of the cylinder and “r” is the radius of the cylinder.
Thus, The figure which has two bases and one lateral face that is rectangular is, ''Cylinder.''
Learn more about the triangle visit;
brainly.com/question/1058720
#SPJ6
a line has a slope of -3/4 and passes through the point (-5, 4). what is the equation of the line?
Answer:
y = -3/4x-1/4
Step-by-step explanation:
The slope intercept form of a line is
y = mx+b
where m is the slope and b is the y intercept
y = -3/4x +b
We have a point (-5,4)
4 = -3/4 (-5) +b
Changing to a common denominator
16/4 = 15/4 +b
subtracting 15/4 from each side
16/4-15/4 = -15/4 +15/4 +b
1/4 = b
y = -3/4x-1/4
Answer:
book
Step-by-step explanation:
kmgktn
find the mean of the following numbers 7,21,2,17,3,13,7,4,9
Answer:
9.222222222
Step-by-step explanation:
7+21+2+17+3+13+7+4+9 = 83
7+21+2+17+3+13+7+4+9 = 83 83÷9 = 9.222222222
_____________________________
Hey!!
Solution,
Given data=7,21,2,17,3,13,7,4,9
summation FX= 83
N(total no. of items)=9
Now,
Mean=summation FX/N
= 83/9
=9.23
So the answer is 9.23
__________________________
Die A has 4 red faces and 2 black faces. Die B has 2 red faces and 4 black faces. A coin is flipped once. If it were heads, only die A is used (die B is discarded). If it were tails, only die B is used (die A is discarded). We do not get to know which die was chosen.
a) The first roll of the chosen die gives red. What is the probability that the second roll (with the same die) will be red?
b) The first two rolls of the die were both red. What is the probability that the third roll (with the same die) will be red?
Answer:
a) 5/9
b) 1/3
Step-by-step explanation:
a) P(Die A or Die B) = P(red and red with Die A) + P(red and red with Die B)
= 4/6 × 4/6 + 2/6×2/6
= 5/9
b) P(Die A or Die B) = P(red and red and red with Die A) + P(red and red and red with die B)
= 4/6×4/6×4/6 + 2/6×2/6×2/6
= 1/3
