The volume of the smaller cone is 19.6cm³
How to determine the volume of the smaller coneFrom the question, we have the following parameters that can be used in our computation:
Side length = 2 cmVolume = [?] cm³Side length = 3 cmVolume = 66 cm³The above parameter mean that
Smaller cone
Side length = 2 cm
Volume = [?] cm³
Large cone
Side length = 3 cm
Volume = 66 cm³
The ratio of the cones can be represented as
Ratio = Side length³ : Volume
So, we have
2³ : Volume of smaller cone = 3³ : 66
Evaluate the exponents
8 : Volume of smaller cone = 27 : 66
Express as fraction
Volume of smaller cone/8 = 66/27
So, we have
Volume of smaller cone = 8 * 66/27
Evaluate
Volume of smaller cone = 19.6
Hence, the volume is 19.6cm³
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Check which of the following are the solutions of the equation 5x – 4y = 20.(i) (4, 0)(ii) (0, 5)(iii) (-2,5/2)(iv) (0, –5)(v) (2,-5/2)
(A) (4,0), (D) (0, -5), and (E)(2, -5/2) are the solutions of the given equation 5x – 4y = 20.
What are equations?The equals sign is a symbol used in mathematical formulas to denote the equality of two expressions.
The typical form for linear equations with two variables is Ax+By=C.
For instance, the linear equation 2x+3y=5 is in standard form.
So, we have the equation:
5x – 4y = 20
(A) (4,0)
=5x−4y
=5(4)−4(0)
=20
=RHS
(4,0): YES
(B) (0,5)
=5x−4y
=5(0)−4(5)
=−20
≠RHS
(0,5): NO
(C) (−2, 5/2)
=5x−4y
=5(−2)−4(5/2)
=−10−10
=−20
(−2, 5/2): NO
(D) (0, -5)
=5x−4y
=5(0)−4(−5)
=20
=RHS
(0, -5): YES
(E) (2, -5/2)
=5x−4y
=5(2)-4(-5/2)
=10+10
=20
=RHS
(2, -5/2): YES
Therefore, (A) (4,0), (D) (0, -5), and (E)(2, -5/2) are the solutions of the given equation 5x – 4y = 20.
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Express each set in roster form. You may need to use the internet or some other reference source. C={x|x+6=10}
The roster form of the set C={x|x+6=10} is C={4}
A set is mathematically represented in a straightforward way using roster notation. The components (or members) of a set are listed in a row inside the curly brackets in the roster form. If the set comprises more than one element, a comma is used in a roster notation to indicate the separation of every two elements. Since each person is counted separately, the roster form is also known as an enumeration notation.
In the given set, the value of x is such that when it is added with 6 the result is 10.
∴x+6=10⇒x=10-6=4
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Given the following exponential function, identify whether the
change represents growth or decay, and determine the
percentage rate of increase or decrease.
y = 3300(0.949)^x
The function simulates exponential decay, and it degrades by 5.1% for every increment in x.
What is exponential growth & exponential decay?Explosive increase and decay are common in situations where quantities change rapidly. It has been suggested that exponential development and decay follow a geometric progression. Quantities that change exponentially rather than continually are referred to be exponentially growing or decaying.
As per the given data in the question,
An exponential function with the formula y = a[tex]r^x[/tex] is the function that is given.
a = 330
r = 0.949
The function indicates exponential growth if the base r is larger than 1. The function shows exponential decline if indeed the base r is far less than 1. In this instance, the function depicts exponential decline because the base r is smaller than 1, or 0.949.
If we want to describe the rate of reduction as a percentage, we can remove the base r by 1 and multiply it by 100.
The rate of reduction as a percentage in this instance is:
1 - 0.949 = 0.051 ×100
= 5.1%.
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the traffic flow rate, in cars per hour, past a certain point on a highway is where is in hours and is 8 am. how many cars pass by during the time interval from 8 am to 9 am?
Following integration, we may estimate that between 6 and 8 am, 2080 automobiles will pass through the crossing.
What is integration?In mathematics, an integral assigns numerical values to functions to represent concepts like volume, area, and displacement that result from combining infinitesimally small amounts of data.
Integration is the action of locating integrals.
So, the number of automobiles that cross an intersection each hour is:
r(t) = 400 + 800t - 120t²
Integration should be carried out to establish the number of cars traveling through the intersection between 6 am and 8 am.
[tex]\begin{aligned}\int_{t_1}^{t_2} r d t & =\int_0^2 400+800 t-120 t^2 d t \\& =\left[400 t+400 t^2-40 t^3\right]_0^2 \\& =400 \times 2+400 \times 2^2-40 \times 2^3 \\& =800+1600-320 \\& =2080\end{aligned}[/tex]
Therefore, following integration, we may estimate that between 6 and 8 am, 2080 automobiles will pass through the crossing.
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Correct question:
The traffic flow rate (cars per hour) across an intersection is r ( t ) = 400 + 800 t − 120 t 2 , where t is in hours, and t =0 is 6am. How many cars pass through the intersection between 6 am and 8 am?
I don't understand how to figure out the product:
Write 91 as the product of prime factors in ascending order
Then, work out the HCF of 91 and 130
91 as a product of its prime factors will be 7 and 13.
The highest common factor of 91 and 130 is 13.
How to calculate the factor?The process of factorization simony has to do with the division of arithmetic algebraic expressions into the sum of their factors. in this case, multiplying the variables will yield the original expression. It means the writing of a number into smaller or simpler numbers that give the original number.
The factor of 91 include 1, 7, 13 and 91
The factor of 130 include 1, 2, 5, 10, 13 65, and 130.
The highest factor is 13.
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9,15,25, Find the 10th term
On solving thr provided question, by help of arithmetic progression, we got to know that a10 = 207
what is arithmetic progression?There are two approaches to define arithmetic progressions (AP):
The difference between any two successive terms in an arithmetic sequence must always be equal, and it is sometimes referred to as a series in which all terms except the first are created by adding a predetermined number to the preceding term.
9,15,25..............
15-9 = 6
25-15 = 10
a4 - 25 = 14 => a4 = 39
a5-39 = 18 => a5 = 57
a6-57 = 22 => a6 79
...
...
...
...
...
a10 - 169 = 38 => a10 = 207
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adam is racing around a circular running track. the time he takes to run each lap is 5 seconds less than he took for the previous one. he completes the first lap in 1 minute and 58 seconds. how long (in seconds) does he take to run his seventh lap?
Time taken by Adam to complete his seventh lap of the circular track as per given data is equal to 1minute 28seconds.
As given in the question,
Time taken by Adam to complete hi first lap of circular track = 1 min 58 sec
First term t₁ = 1 minute 58seconds
Time taken by each successive lap is 5seconds less then the previous lap
Common difference 'd' = -5seconds
let time taken to complete the seventh lap be t₇
t₇ = t₁ + ( 7 - 1 ) d
⇒ t₇ = 1 minute 58 seconds + ( 6 ) (- 5seconds)
= 1 minute 58 seconds - 30seconds
= 1 minute 28 seconds
Therefore, the time taken by Adam to complete his seventh lap is equal to
1 minute 28 seconds.
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50 POINTS Giselle wants to buy the newest book in her favorite series. She has some money saved but does not want House all her savings on the book. Giselle’s grandma offers to pay some of the cost of the book for every weed she pulls in her grandma’s garden. The graph shows the cost to Giselle for the purchase of the book after pulling x weeds in her grandma’s garden.
Select True or False to describe each statement.
SELECT True or False
The following are the answer to each statement;
The book is $18 - TrueGiselle can earn up to $18 pulling weeds for her grandma - FalseGiselle's grandma pays her $1 for every 5 weeds she pulls - TrueGiselle does not have to use any of her own money towards the purchase of the book when she pulls 90 weeds - TrueGiselle only needs to pull 18 weeds to not use any of her own money - FalseHow to interpret graph?1. The book is $18
The statement is true because the beginning of the graph represents cost before she picks any weeds.2. Giselle can earn up to $18 pulling weeds for her grandma.
This is not true because the graph shows that she is still able to earn more money from picking weeds.3. Giselle's grandma pays her $1 for every 5 weeds she pulls
This is true because the price change from $18 to $17 is $1 for 0 weeds to 5 weeds.4. Giselle does not have to use any of her own money towards the purchase of the book when she pulls 90 weeds.
This is true because the amount earned for 90 weeds is equivalent to the money needed to buy the book.5. Giselle only needs to pull 18 weeds to not use any of her own money
Giselle will need to pull 90 weeds in order to not spend her own money. The statement is false.Read more on graph:
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2) At a concert, 35% of the audience members were teenagers. If the number of audiences at the concert was 1800, what was the number of teenager members?
Answer:
630
Step-by-step explanation:
35% of 1800 = 0.35 × 1800 = 630
identify the equation of the line in slope-intercept form when:slope = -8y-intercept = 5
Answer:
y = - 8x + 5
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
here m = - 8 and c = 5 , then
y = - 8x + 5 ← equation of line
Rewrite <8,-5> In coordinate notation
The vector <8,-5> when expressed in coordinate notation is (8, -5)
How to express the vector in coordinate notation?From the question, we have the following parameters that can be used in our computation:
Notation = <8, -5>
The above expression is in vector notation
To express the vector notation in a coordinate notation, we simply express the <> as ()
So, we have the following representation
(8, -5)
Hence, the coordinate notation is (8, -5)
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calculate least squares solution using svd a matrix has the singular value decomposition what is the solution to the least-squares problem that has minimal norm ?
The Least-squares problem that has minimal norm can be given using factorization.
The least squares method is used to find the best fit for a set of data points by minimizing the sum of the offsets from the plotted curve. Singular value decomposition (SVD) is a factorization of a real or complex matrix.
It is a widely used technique to decompose a matrix into several component matrices, exposing many of the useful and interesting properties of the original matrix. The singular value decomposition, guaranteed to exist, is A=UΣV.
When we have the equation system Ax=b, we calculate the SVD of A as A=UΣVT. The matrices U and VT have a very special property. They are unitary matrices. One of the main benefits of having unitary matrices like U and VT is that if we multiply one of these matrices by its transpose (or the other way around), the result equals the identity matrix.
The singular value decomposition (SVD) of matrix A is very useful in the context of least squares problems. It is also very helpful for analyzing the properties of a matrix.
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Look at the triangle. It is given that CD bisects ACB and that ABC is isosceles with AC = BC.
Answer options for each are:
Line AD = Line BD
Given
CPCTC
Definition of Midpoint
Definition of Angle Bisector
Reflexive Property of Congruence
SAS
SSS
ASA
Solve 2v² + 4y = 6 by factoring.
The solutions are v =
and v=
On factorizing 2v² + 4v = 6 the obtained solutions of the quadratic equation are v = 1 and v = -3.
What is factorization by splitting middle term?
The method of Splitting the Middle Term by factorization is where you divide the middle term into two factors. We know that composite numbers can be expressed as the product of prime numbers.
Rule to factorize trinomial expression where coefficients are real numbers, is to split b (the coefficient of x) into two real numbers such that the algebraic sum of these two numbers is b and their product is c, then factorize by grouping method.
According to the given question:
Factorizing 2v² + 4v = 6 by Splitting the Middle Term method
2v² + 4v = 6
2v² + 4v - 6 = 0
2v² + 6v - 2v - 6 = 0
2v(v+3) - 2(v+3) = 0
(2v-2)(v+3) = 0
Therefore the solutions are
2v - 2 = 0 v +3 = 0
v = 1 v = -3
Hence on factorizing 2v² + 4v = 6 the obtained solutions of the quadratic equation are v = 1 and v = -3
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which of the following factors is a factor of 3x^3+18x^2+27x
The factor of the given expression is (C) (x + 3).
What are the factors?In mathematics, a divisor of an integer n, often termed a factor of n, is an integer m that may be multiplied by some number to generate n.
In this scenario, one also asserts that n is a multiple of m.
A factor is a number that is multiplied by another number to produce the desired result.
A product is a solution to a multiplication problem.
Think of a multiplication problem as components being combined to find a product.
So, we have:
3x^3+18x^2+27x
Now, take the factors out as follows:
3x^3+18x^2+27x
3x(x²+6x+9)
3x(x+3)²
Factors: (x + 3)
Therefore, the factor of the given expression is (C) (x + 3).
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Complete question;
Which of the following is a factor of 3x3 + 18x2 + 27x?
a. 9x
b. x3
c. x + 3
d. x - 3
4. The Windsor-Detroit International Freedom Festival hosts one of the largest fireworks displays in the world. The fireworks are set off over the Detroit River. The path of a particular firework rocket is modelled by the relation h=-4.9(t-2)+169.6, where h is the rocket's height above the water, in metres, and t is the time, in seconds.
a) How long will the rocket take to reach its maximum height? What is the maximum height?
b) A firework rocket will stay lit for an average of 5 s. What will the height of a rocket be 5 s after it is launched?
a) It takes 2 seconds for the rocket to reach the maximum height, and this maximum height is of 169.6 metres.
b) The height of the rocket five seconds after it was launched is of 125.5 metres.
How to obtain the vertex of the quadratic equation?The vertex-form definition of a quadratic function is defined as follows:
y = a(x - h)² + k.
In which the parameters are given as follows:
h is the x-coordinate of the vertex.k is the y-coordinate of the vertex.a is the leading coefficient.In the context of this problem, the height function is defined as follows:
h(t) = -4.9(t - 2)² + 169.6.
Hence the coordinates of the vertex are given as follows:
h = 2 -> maximum height at 2 seconds.k = 169.6 -> maximum height of 169.6 metres.As the leading coefficient is negative, the parabola is concave down and the vertex represents a maximum.
The height at a time of five seconds is of:
h(5) = -4.9(5 - 2)² + 169.6 = 125.5 metres.
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Many high schools now have drug-testing programs for athletes. The main goal of these programs is to reduce the use of banned substances by students who play sports. It is not practical to test every athlete for drug use regularly. Instead, school administrators give drug tests to randomly selected student athletes at unannounced times during the school year. Students who test positive face serious consequences, including letters to their parents, required counseling, and suspension from athletic participation. Drug test aren't perfect. Sometimes the tests say that athletes took a banned substance when they did not. This is known as a false positive. Other times, drug tests say that athletes are "clean" when they did take a banned substance. This is called a false negative. Suppose that 16% of the high school athletes in a large school district have taken a banned substance. The drug test used by this district has a false positive rate of 5% and a false negative rate of 10%. If a randomly chosen athlete tests positive, what is the chance that the student actually took a banned substance. Use what you have learned in this chapter to help answer the following questions about the district's drug-testing program. A. What is the probability that a randomly chosen athlete tests positive for banned substances? B. If two athletes are randomly selected, what's the probability that at least one of them tests positive? C. What's the probability that a randomly selected athlete did not take a banned substance, given they tested positive? Based on your answer, do you think an athlete who tests positive should be suspended from athletic competition for a year? Why or why not? D. What's the probability that a randomly selected athlete took a banned substance given the student tested negative? Explain why it makes sense for the drug-testing process to be designed so that this probability is less than the one you found in Question 4. E. The district decides to immediately retest and athlete who tests positive. Assume that the results of an athlete's two tests are independent. Find the probability that a student who gets a positive result on both tests actually took a banned substance (hint: took the banned substance given two positive tests). Based on your answer, do you think that an athlete who tests positive twice should be suspended from athletic competition for a year. Why or why not?
Students who test positive face serious consequences, including letters to their parents,
Find the common Diff/Ratio with missing terms
The common ratio of the sequence which have first term, = 3 and third term = 192 is calculated to be 6
How to find the common ratio of the geometric sequenceThe common ratio of the sequence is calculated by comparing the preceding terms as done below
first term = a = 3
second term = a * r = 3r
third term = second term * r
= a * r * r
= 3r * r
= 3r²
The given data shows that, third term = 192
3r² = 192
divide through by 3
3r² / 3 = 192 / 3
r² = 64
r = √64
r = 8
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In a circle, an angle measuring 8.7 radians intercepts an arc of length 3.9. Find the radius of the circle to the nearest 10th.
Answer:
r = .5 units
Step-by-step explanation:
8.7 R is an improper FRACTION of the 2 pi R of the entire circle ....set up a ratio:
8.7 / (2 pi) = 3.9 / x where x is the entire circumference measurement
x = 3.9 / (8.7 / (2 pi) ) = 2.82 units
To find the radius circumf = 2 pi r
2.82 = 2 pi r shows r = .5 units
Quill bought one package each of red, blue, and gold paper, each package had the same number of sheets. He bought a total of 165 sheets of paper, but used 4 sheets of each color. How many sheets of each color remain?
Answer:
153
Step-by-step explanation:
165/3 = 55 sheet of each color
55-4 = 51
51 x 3 = 153
Shawn is typing a paper for class. He can type 1 2/7 pages in 1/3 of an hour. How many pages can Shawn type in one hour? A. B. C. D.
Shawn can type [tex]1\frac{6}{21}[/tex] pages in an one hour.
What is typing speed?
How many words a person can correctly type in one minute. He types at a 60 wpm rate.
Given:
Shawn is typing a paper for class. He can type 1 2/7 pages in 1/3 of an hour.
We have to find how many paged he can type in one hour.
First to convert improper fraction 1 2/7 into a fraction.
⇒ [tex]1\frac{2}{7} = \frac{7*1+2}{7} = \frac{9}{7}[/tex]
So, Shawn can type 9/7 pages in 1/3 of an hours.
i hour = 3/3
So, Shawn can type
9/7 x 3/3 = 27/21 = [tex]1\frac{6}{21}[/tex] pages in one hour.
Hence, Shawn can type [tex]1\frac{6}{21}[/tex] pages in an one hour.
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Someone please answer this my question is in the picture I will give you brainliest and your getting 50 points no fraud answers.
Step-by-step explanation:
I will help you sir.
Given
Opposite Sides are Congruent
Reflexive
SSS
CPCTC
(06.01 lc) a car traveling in a straight line from its starting position at a speed of 65 miles per hour for 3 hours is represented by the function v(t), where t is the number of hours traveled. what units describe the area under the curve of v(t)?
The required area under the curve of function v(t) is 195 square miles, which depicts the total distance traveled by car during the 3 hours.
The area under the curve of the function v(t) represents the total distance traveled by the car over the given time period.
The function v(t) is defined as the speed of the car (in miles per hour) at any given time t (in hours). Since the speed is constant at 65 miles per hour, the graph of v(t) will be a straight horizontal line at y = 65.
To find the distance traveled, we need to multiply the speed (in miles per hour) by the time (in hours):
Distance = Speed * Time
Following the given case, the speed is 65 miles per hour, and the car traveled for 3 hours:
Distance = 65 miles/hour * 3 hours = 195 miles
So, the area under the curve of v(t) is 195 square miles, which represents the total distance traveled by car during the 3 hours.
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Remata it’s 3 more than 6 times as old as her daughter Isabella. The sumo their ages is 38. What are Renata and Isabella’s ages, respectively.
Answer:
The answer to you question is 18 and 20
18 and 20
determine whether or not the vectors U=(1, 1, 2), v=(2, 3, 1), and w=(4, 5, 5) in R³ are linearly dependent
The u(1, 1, 2), v(2, 3, 1), and w(4, 5, 5) supplied vectors are linearly dependent.
What is a Vector?A vector is a quantity with both magnitude and direction in physics. It is often depicted by an arrow with the same direction as the amount and a length proportionate to the size of the quantity. A vector lacks position, but has magnitude and direction. A vector is therefore unaffected by displacement parallel to itself as far as its length is unaltered.
As per the given information in the question,
The given vectors are:
u = (1, 1, 2)
v = (2, 3, 1) and,
w = (4, 5, 5)
If there are three scalars that are not all zero and that are dependent on a set of vectors (u, v, and w), they have been shown to be linearly dependent.
au + bv + cw = 0
⇒ a(1, 1, 2) + b(2, 3, 1) + c(4, 5, 5) = (0, 0, 0)
⇒ (a + 2b + 4c, a + 3b + 5c, 2a+ b + 5c) = (0, 0, 0)
So,
a + 2b + 4c = 0 (i)
a + 3b + 5c = 0 (ii)
2a+ b + 5c = 0 (iii)
From equation (i) and (ii)
b = -c
From equation (i)
a - 2c + 4c = 0
⇒ a = -2c
Let's assume that c = 1
So,
a = -2 and,
b = -1
Then, from the obtained values,
-2u - v + w = 0
As a result, there is a set of non-zero values for a, b, and c such that:
au + bv + cw = 0
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Find the solutions by factoring 9x^2-16=0
Answer: x= 4/9
Step-by-step explanation:
9x^2-16=0
9x^2 = 16
9x = 4
x= 4/9
Just number 4 pleaseee
Answer:
blip
Step-by-step explanation:
blipgg
What is the summation of all the roots of the equation [tex]x^{2022}[/tex] = 1
Answer:
x = 1 or x = -1
Step-by-step explanation:
The only number square root and get 1 is 1 and -1. Because 2022 is an even number, so -1 will work in this case, and the final answer will be positive 1!
If you can please give me a Brainliest, thank you and have a good day!
help me and thank you so much
Answer:
BRO IS GERMAN LOL
Step-by-step explanation:
Are the ratios 3:4 and 11:20 equivalent
Answer:
nah
Step-by-step explanation:
