How does the volume of an oblique cone change if the height is reduced to 2/5 of its original size and the radius is doubled?
Answers
V=1/3πr^2h
r=2r
h=2/5h
thus;
V=1/3*π*(2r)^2(2/5h)
=8/15πr^2h
This implies that the new volume will be 8/15 of the original volume
Answer:
Option (D) is correct.
Step-by-step explanation:
Let the initial original height of the cone is h and radius is r.
The volume of original cone is given by
[tex]V=\frac{1}{3}\times \pi r^{2}\times h[/tex]
Now the new height be h' = 2/5 h and radius r' = 2r
So, the new volume be
[tex]V'=\frac{1}{3}\times \pi r'^{2}\times h'[/tex]
[tex]V'=\frac{1}{3}\times \pi\times 2r^{2}\times \frac{2}{5}h[/tex]
[tex]V=\frac{8}{15}\times \pi \times r^{2}h[/tex]
Related Questions
Which relationship is always true for the angles x, y, and z of triangle MNP?
A. x + z = y
B. y + z = x
C. x + y + z = 180 degrees
D. x + y + z = 90 degree
Answers
-the answer would be C: "x+y+z= 180 degrees"
-and here is proof so you know you won't get the answer wrong
- hope you do good on your test, have a good day :)
Help please! In the figure line a and line b are parallel based on the figure match each given angle with its congruent angles
Answers
∠2 and ∠3 are vertical angles, ∠3 and ∠7 are corresponding angles, and ∠7 and ∠6 are vertical angles.
∠3, ∠7, ∠2: angles congruent to ∠6
∠2 and ∠3 are vertical angles, ∠3 and ∠7 are corresponding angles, ∠7 and ∠6 are vertical angles.
∠4, ∠8, ∠5: angles congruent to ∠1
∠1 and ∠4 are vertical angles, ∠4 and ∠8 are corresponding angles, ∠8 and ∠5 are vertical angles.
Answer: copy the guy on top of me but the last one for PLATO users is <3,<6,<2 is angles congruent to <7
Step-by-step explanation: bec I said so
Evaluate the function rule to find the range of each function for the domain {-3, 0, 5}. f(x) = x² − 6x + 4
A. {-5, -4, -1}
B. {-5, -1, 4}
C. {-1, 4, 31}
D. {4, 31, 59}
Please I beg of you!
Answers
Domain image, f(x) =x^2 - 6x + 4
-3 (-3)^2 - 6(-3) + 4 = 9 + 18 + 4 = 31
0 (0)^2 - 6(0) + 4 = 0 - 0 + 4 = 4
5 (5)^2 - 6(5) + 4 = 25 - 30 + 4 = - 1
So, we got the images -1, 4, and 31 and that is that is the range {-1, 4, 31}
Answer: option C. {-1, 4 , 31}
In an upcoming race, the top 3 finishers will be recognized with the same award. Ryan is one of 12 people entered in the race.
If all racers are equal in skill, what is the probability that Ryan will be one of the top 3 racers?
Answers
Answer: The required probability is 25%.
Step-by-step explanation: Given that in an upcoming race, the top 3 finishers will be recognized with the same award and Ryan is one of 12 people entered in the race.
We are to find the probability that Ryan will be one of the top 3 racers, if all racers are equal in skills.
Let S denote the sample space of the experiment for selecting a racer and A denote the event of selecting the top 3 finishers.
Then, according to the given information, we have
n(S) = 12 and n(A) = 3.
So, the probability of event A is given by
[tex]P(A)=\dfrac{n(A)}{n(S)}=\dfrac{3}{12}=\dfrac{1}{4}\times100\%=25\%.[/tex]
Thus, the required probability is 25%.
7x1,000,000+
3x100,000+
5x10,000+
6x1.00+
2x100+3x10+7+1
Answers
7350244
Factor each expression 1)4a^2-16ab^3+8ab^2c 2) n^2+8n+15 3) g^2-9g+20 4) z^2-7z-30 5) 4y^3-36y
Answers
1)
[tex]4a^2-16ab^3+8ab^2c=4a(a-4b^3+2b^2c)[/tex]
2)
[tex]n^2+8n+15\\ =n^2+5n+3n+15\\ =n(n+5)+3(n+5)\\ =(n+5)(n+3) [/tex]
3)
[tex]g^2-9g+20\\ =g^2-5g-4g+20\\ =g(g-5)-4(g-5)\\ =(g-5)(g-4) [/tex]
4)
[tex]z^2-7z-30\\ =z^2-10z+3z-30\\ =z(z-10)+3(z-10)\\ =(z-10)(z+3) [/tex]
5)
[tex]4y^3-36y\\ =4y(y^2-9)\\ =4y(y-3)(y+3) [/tex]
Rationalize the denominator.
10/√24x
write it in simplest form
Answers
[tex]\frac{ \sqrt{24x} }{\sqrt{24x}} =1[/tex] and the expression has the same value when multiplied by 1.
Multiply the terms:
[tex]\frac{10}{ \sqrt{24x} } * \frac{ \sqrt{24x} }{\sqrt{24x}} =\frac{ 10\sqrt{24x} }{24x}[/tex]
Simplify to get the final answer:
[tex]\frac{ 10\sqrt{24x} }{24x}=\frac{ 5\sqrt{24x} }{12x}[/tex]
Need help fast!
The table shows the relationship between the number of drops of food color added to different number of cups of cake frosting. Look at the first picture.
Which point below shows an equivalent ratio in this situation? Look at the second picture.
A. Point B, because if cups of frosting are 50, then drops of food coloring will be 200
B. Point B, because if drops of food coloring are 50, then cups of frosting will be 200
C. Point J, because if cups of frosting are 40, then drops of food coloring will be 10
D. Point J, because if drops of food coloring are 40, then cups of frosting will be 10
Answers
This is because the proportion of frosting to food coloring is 1:4, and if the answer to A is simplified (50:200), the ratio would be the same.
Answer:
Option A. will be the answer.
Step-by-step explanation:
From the given table we will find the relation first and the we will try to find the point with the same relation in the graph.
From the given table ratio of Cups of frosting and Drops of food color is = [tex]\frac{\text{Cups of frosting}}{\text{Drops of food color}}[/tex]
= [tex]\frac{2}{8}[/tex]
= [tex]\frac{1}{4}[/tex]
Or 1 : 4
Now the point B shows the ratio between food color and frosting = [tex]\frac{\text{Cups of frosting}}{\text{Drops of food color}}[/tex]
= [tex]\frac{\text{x-coordinates}}{\text{y-coordinates}}[/tex]
= [tex]\frac{50}{200}[/tex]
= [tex]\frac{1}{4}[/tex]
The same ratio 1 : 4
Option A. will be the answer.
Find two positive numbers a and b (witha≤b) whose sum is 88 and whose product is maximized.
Answers
a + b = 88
ab = y
a = 88 - b
y = (88 - b)*b
y = -b^2 + 88b
Take the derivative and set equal to 0
y' = -2b + 88 = 0
2b = 88
b = 44
a=44
both numbers are 44
To find two positive numbers a and b whose sum is 88 and whose product is maximized, we can use the concept of quadratic equations. By taking the derivative of the product function and setting it equal to zero, we can find the maximum value. Plugging that value back into the product function will give us the maximum product.
Explanation:To find two positive numbers a and b whose sum is 88 and whose product is maximized, we need to use the concept of quadratic equations. Let's assume a as x and b as 88-x. The product of the two numbers can be expressed as the quadratic equation P(x) = x(88-x). To maximize the product, we need to find the maximum value of P(x). We can use calculus to find the maximum value by taking the derivative of P(x) and setting it equal to zero. Solving that equation will give us the value of x, and plugging it back into P(x) will give us the maximum product.
Let's go through the steps:
Write the quadratic equation: P(x) = x(88-x).Take the derivative of P(x) and set it equal to zero: P'(x) = 88-2x = 0.Solve for x: x = 44.Plug x back into P(x) to find the maximum product: P(44) = 44(88-44) = 1936.So, the two positive numbers a and b are 44 and 88-44, which is 44 as well. Their sum is 88 and their product is maximized at 1936.
help. Find mBAC in circle O. (The figure is not drawn to scale.)
A. 170
B. 95
C. 47.5
D. 42.5
Answers
Answer: The answer is (C) 47.5.
Step-by-step explanation: In the given figure, O is the centre of a circle, where AC is the diameter and OB is the radius. We are to find the measure of ∠BAC.
We have
[tex]m\angle AOB+m\angle BOC=180^\circ\\\\\Rightarrow m\angle BOC=180^\circ-85^\circ\\\\\Rightarrow m\angle BOC =95^\circ.[/tex]
∠BOC and ∠BAC are angles at the centre and at the circumference subtended by the arc BC, so
[tex]m\angle BAC=\dfrac{1}{2}\times m\angle BOC=\dfrac{1}{2}\times 95^\circ=47.5^\circ.[/tex]
Thus, (C) is the correct option.
literal equations, please help! this one is confusing to me.
Answers
aby - b = c
First, we bring the -b term to the right hand side by adding b left and right:
aby -b+b = c+b
The -b and +b cancel out, so we get:
aby = c + b
Then, we divide left and right hand side by ab:
aby/ab = (c+b)/ab
Again, the ab/ab on the left cancels out (it is 1), so we get:
y = (c+b)/ab
And we're done!
So you have to know that it is allowed to add or subtract something (anything) to/from the left and right hand side of an equation. Likewise, you have to know that it is allowed to multiply or divide by something, as long as it isn't 0.
A scatter plot is made with the data shown.
Time (hr)
1
2
3
4
5
6
7
8
9
Distance from Destination (mi)
320
280
240
200
160
120
80
40
0
What type of association will the scatter plot for this data represent between the time, in hours, and the distance from the destination, in miles?
No association
Negative linear association
Positive nonlinear association
Positive linear association
Answers
This is a negative linear association because when ever the x (top line) is increasing and the y (bottom line) is decreasing, that shows that you are going farther to the end of the x axis and lower down the y axis.
Negative linear association is the type of association will the scatter plot for this data represent between the time, in hours, and the distance from the destination, in miles
What is Graph?Graph is a mathematical representation of a network and it describes the relationship between lines and points.
The scatter plot for this data will represent a negative linear association between the time, in hours, and the distance from the destination, in miles.
As the time in hours increases, the distance from the destination in miles decreases, and this relationship is a straight line that slopes downwards from left to right which indicates a negative linear association.
Therefore, Negative linear association is the type of association will the scatter plot for this data represent between the time, in hours, and the distance from the destination, in miles.
To learn more on Graph click:
https://brainly.com/question/17267403
#SPJ3
The process of moving a figure to a different location is called:
mapping.
transformation.
isometry.
None of the choices are correct.
Answers
If runners in a long distance race were to run straight from the starting line to the finish line they would run 13 kilometers. However, the road they run makes them travel longer than that. They must run 5 kilometers south and then head west "x" kilometers for the remainder of the race. How far do the runners travel?
Answers
5^2 +x^2 = 13^2
25 + x^2 = 169
x^2 = 144
x = sqrt(144) = 12
they run west for 12 KM
12+5 = 17 total km
I don't know the answer can someone pls help me
Answers
line QP =
11.5*(11.5 +24) = 11.5 * 35.5 = 408.25
SqRT(408.25) = 20.205
round answer to 20 units
[tex] n^{2} =PN(PN+MN)[/tex]
where your PQ is [tex] n^{2} [/tex]
So our formula, filled in and solving for PQ is this:
[tex] n^{2}=11.5(11.5+24) [/tex]
and [tex] n^{2} =11.5(35.5)[/tex]
and n = 20.2 or 20 rounded. That's the last choice above
f(x)=5x^2 + 9x-4 g(x)= -8x^2-3x-4 find (f+g)(x)
Answers
Please help !
(cos Θ − cos Θ)^2 + (cos Θ + cos Θ)^2
Answers
_____________________________________________
Explanation:
_____________________________________________
(cos Θ − cos Θ)² + (cos Θ + cos Θ)²
= 0² + (cos Θ + cos Θ)² ;
= 0 + (2 cos Θ)² = (2 cos Θ)(2 cos Θ) ;
= 4 (cos Θ)² = 4 cos² Θ .
_____________________________
Answer: The required simplified form is [tex]4\cos^2\theta.[/tex]
Step-by-step explanation: We are given to simplify the following trigonometric expression :
[tex]T=(\cos \theta-\cos\theta)^2+(\cos \theta+\cos \theta)^2.[/tex]
To simplify, first we need to evaluate the terms within the brackets.
The simplification is as follows :
[tex]T\\\\=(\cos \theta-\cos\theta)^2+(\cos \theta+\cos \theta)^2\\\\=0^2+(2\cos\theta)^2\\\\=0+4\cos^2\theta\\\\=4\cos^2\theta.[/tex]
Thus, the required simplified form is [tex]4\cos^2\theta.[/tex]
Factor out the greatest common factor of 5ab^2+10ab
Answers
GCF is : 5ab
Answer: 5ab
Step-by-step explanation:
The given polynomial : [tex]5ab^2+10ab[/tex]
The prime factorization of [tex]5ab^2= 5\times a\times b\times b[/tex]
The prime factorization of [tex]10ab= 5\times2\times a\times b[/tex]
We can see that the greatest common factor of [tex]5ab^2\text{ and }10ab[/tex] is [tex]5\times a\times b[/tex]
Hence, the greatest common factor of [tex]5ab^2+10ab[/tex] = 5ab
What is the following product?
Answers
_______________________________________________________
Explanation:
_______________________________________________________
Note that: ⁴√7 = 7^(1/4) .
As such: " (⁴√7) * (⁴√7) * (⁴√7) * (⁴√7) " = (⁴√7)⁴ = [ 7^(1/4) ] ^ (4) ;
→ [ 7^(1/4) ] ^ (4) = 7^ [ (1/4) * (4)] = 7¹ = 7 .
_______________________________________________________
The answer is: " 7 " .
_______________________________________________________
Check the attachment.
Hope it helps you :)
Points A and B lie on a circle centered at point O. If OA = 5 and length of ABowncircumference=14, what is the area of sector AOB? Use the value π = 3.14, and choose the closest answer.
Answers
This question can simply be answered directly. To solve this, we should recall that the formula of a circle is:
Area of circle = π r^2 where r is the radius of the circle
Now we are given that segment OA is equivalent to 5 units. Segment OA is also the diameter of that circle therefore d = 5.
Now let us convert the formula knowing that radius is one half the diameter:
r = d / 2
Area of circle = π (d / 2)^2
Area of circle = π d^2 / 4
Substituting:
Area of circle = π (5)^2 / 4
Area of circle = 3.14 * 25 / 4
Area of circle = 19.625 = 19.6 square units
Answer:
The answer would be 19.6 for plato Users
Step-by-step explanation:
When positive integer x is divided by 11, the quotient is y and the remainder is 4. when 2x is divided by 8, the quotient is 3y and the remainder is 2. what is the value of 13y – x ?
Answers
[tex]\dfrac{2x}8=3y+\dfrac28\iff2x=24y+2[/tex]
[tex]\implies 2x-x=(24y+2)-(11y+4)[/tex]
[tex]\implies x=13y-2[/tex]
[tex]\implies 13y-x=2[/tex]
Part 1: what are the conditions for using the standard deviation formula when conducting a significance test? be specific about p versus p-hat. part 2: what are the conditions for approximating with a normal distribution?'
Answers
The difference between p and p-hat is that p represents that true standard deviation of the population while p-hat is only an approximation using a sample of the population.
The conditions that must be met when approximating a normal distribution are that the samples must be independent of each other and that number of samples must be at least 30.
To use the standard deviation formula in a significance test, the sample must be random and the population standard deviation should typically be unknown, while approximation with a normal distribution requires a sufficiently large sample size and the success-failure condition for proportions. Choosing the correct distribution depends on whether the standard deviation is known and the sample size.
Explanation:Conditions for Using the Standard Deviation Formula and Approximating with a Normal Distribution
For conducting a significance test using the standard deviation formula, certain conditions must be met:
The sample must be randomly selected.If surveying a proportion, we use \( \hat{p} \) for samples and \( p \) for populations.If calculating a sample standard deviation, the population standard deviation should be unknown.The sample size should be sufficiently large if the population distribution is not normal (usually n > 30).To approximate the sample distribution with a normal distribution, particularly when conducting hypothesis testing:
The sample size must be large enough (typically n > 30).The sample should be randomly selected and should represent the population.For proportions, the sample should meet the success-failure condition where \( np \geq 10 \) and \( n(1-p) \geq 10 \).The conditions for a hypothesis test often include:
Stating the null and alternative hypotheses.Deciding on a significance level (e.g., \( \alpha = 0.05 \)).Knowing whether population parameters are known, which determines the choice of test statistic.Finding the p-value and comparing it with the significance level to make a decision.Examples of Hypothesis Testing with Different Conditions
If you know the population standard deviation, you might use the z-distribution for hypothesis testing.If the population standard deviation is unknown but the sample size is large, the t-distribution might be the appropriate choice.The F-statistic is used when comparing two variances, such as two standard deviations of test scores.If an eagle and a bumblebee are traveling at 8 km/hr, which has more momentum explain
Answers
Write the ratio in lowest terms: 4415 feet to 22245 feet
Answers
since they both end with 5 divide each number by 5
4415 = 883
22245/5 = 4449
there is no number that can go into 883 evenly
so the lowest term
would be 883/4449
The correct ratio in lowest terms is [tex]\(\frac{883}{4449}\)[/tex].
To find the ratio in lowest terms, we first write the ratio of the two given lengths:
[tex]\[ \frac{4415 \text{ feet}}{22245 \text{ feet}} \][/tex]
Next, we divide both the numerator and the denominator by their greatest common divisor (GCD) to simplify the ratio. The GCD of 4415 and 22245 can be found by using the Euclidean algorithm or by inspection.
We can start by dividing both numbers by 5:
[tex]\[ \frac{4415 \div 5}{22245 \div 5} = \frac{883}{4449} \][/tex]
Now, we check if 883 and 4449 have any common divisors other than 1. Since 883 is a prime number and does not divide evenly into 4449, we have found the simplest form of the ratio.
Thus, the ratio of 4415 feet to 22245 feet in lowest terms is [tex]\(\frac{883}{4449}\)[/tex].
Gina mixed paint to make her favorite shade of purple. She filled up one third of the container with red paint. Then she filled the remaining space with 4 Liters of blue paint.How many milliliters of paint did Gina mix
Answers
The volume of a rectangular prism varies jointly with the length and width of the figure when the height remains constant. The volume of a rectangular prism is 672 cubic centimeters. The figure has a length of 8 centimeters and a width of 14 centimeters. A second prism has a length of 12 centimeters and a width of 8 centimeters. What is the volume of the second prism? 576 cubic centimeters 768 cubic centimeters 784 cubic centimeters 1,344 cubic centimeters
Answers
1st Prism = 8*14 = 112
672/112 = 6
2nd prism = 8*12=96
96*6 = 576 cubic cm
answer is 576 cubic centimeters
Answer:
The correct option is 1.
Step-by-step explanation:
The volume of a rectangular prism varies jointly with the length and width of the figure when the height remains constant.
Let the height of both rectangular prism be h cm.
The volume of a prism is
[tex]V=l\times b\times h[/tex]
Where, l is length, b is breadth or width and h is height.
The volume of a rectangular prism is 672 cubic centimeters. The figure has a length of 8 centimeters and a width of 14 centimeters.
[tex]672=8\times 14\times h[/tex]
[tex]672=112h[/tex]
Divide both sides by 112.
[tex]\frac{672}{112}=h[/tex]
[tex]6=h[/tex]
The value of h is 6 cm. It means the height of both prism is 6 cm.
A second prism has a length of 12 centimeters and a width of 8 centimeters. So, the volume of second prism is
[tex]V=12 \times 8\times 6[/tex]
[tex]V=576[/tex]
The volume of second prism is 576 cubic centimeters. Therefore the correct option is 1.
Select the inequality that corresponds to the given graph. graph of an inequality with a dashed line through the points negative 3 comma 0 and 0 comma 4 and shading below the line
A. 4x-3y>-12
B. x+4y>4
C. 4x-2y<-8
D. 2x+4y=>-16
Answers
The detail about dashed line is important because it expresses an equality with a symbol < or >. The data points that coincide with that line is not part of the solution but just stand as a boundary, hence, I used dashed line and hollow points. If it were ≥ or ≤, then we use solid lines and dots. With that, we can already eliminate choice D.
Next, we test the inequality. Let's choose a point within the shaded region. Suppose the point is (1,0) denoted by the red dot. If it is part of the solution, then the inequality will be proven true.
A. 4x-3y>-12
4(1) - 3(0) > -12
4 > -12, this is true
B. x+4y>4
1 + 4(0) > 4
1 > 4, this is not true
C. 4x-2y<-8
4(1) -2(0) < -8
4 <-8, this is not true
∴The answer is A.
Answer:
b
Step-by-step explanation:
i took the test
You are getting a line-up ready for a school kickball game. you have 55 girls and 55 boys. the rules state each child must kick the same number of times and alternate girl-boy or boy-girl. how many ways can a line-up be made for one round of kicking
Answers
To solve this problem,
we must first imagine out that the sequence of the children is either
GBGBGB.... or BGBGBG....
So there are 2
possible sequence all in all. Now to solve for the total arrangements per
sequence, the
girls can be arranged in n! ways in their alloted spots, and so can the boys n!
in their alternate spots, therefore:
Total arrangements = 2 * n! * n!
If n = 55
Total arrangements = 2 * 55! * 55!
Total arrangements = (The answer is very big ~almost infinite)
If n = 5
Total arrangements = 2 * 5! * 5!
Total arrangements = 28,800
So I believe the correct given is 5 boys and 5 girls and there are a total of 28,800 arrangements.
By the empirical rule, what percentage of the area under the normal curve lies to the left of mu, the average? put your answer as a percentage.
Answers
When the curve is plotted against the normalized coordinate z, the curve is symmetric about z=0, which coincides with μ.
Because the total area under the curve is 1, each half of the curve about the line of symmetry has an area of 0.5.
Ths means that 50% of the normal curve lies to the left of μ.
Answer: 50%
The population of a town is decreasing at a rate of 1.1% each year. If there are 3,000 people in the town right now, how many people will be living in the town in 10 years? Round your answer to the nearest whole number.
Answers
total = 3000*(1-0.011)^10
1-0.011 = 0.989
total = 3000*(0.989)^10
0.989^10 = 0.895288314
3000* 0.895288314 = 2685.86
rounded to nearest whole number = 2686
there will be 2686 people
P=Ae^-rt
P ?
A 3000
R 0.011
T 10 years
P=3,000×e^(−0.011×10)
P=2,687.5 round your answer to get
P=2688