A right circular cone has a radius of x+4 and a height 5 units less than its radius. Express the volume of the cone as a polynomial function. The volume of a cone is V=13πr2h for radius r and height h. Enter π as pi.
Answers
The equation of the volume function is V(x) = 1/3(x + 4)²(x - 1)
How to determine the volume function?The given parameters are
Radius, r = x + 4
Height, h = 5 units less than the radius
This means that
h = r - 5
So, we have
h = x + 4 - 5
Evaluate
h = x - 1
The volume of a cone is calculated as
V = 1/3πr²h
Substitute the known values in the above equation
V = 1/3 * (x + 4)² * (x - 1)
This gives
V = 1/3(x + 4)²(x - 1)
Express as a function
V(x) = 1/3(x + 4)²(x - 1)
Hence, the function is V(x) = 1/3(x + 4)²(x - 1)
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Related Questions
If the odds against an event are 4:7, then the probability that the event will fail to occur is
Answers
The odds against an event is 4:7
Unfavourable elements for the event = 4
Favourable elements for the event = 7
Total = 4 + 7 = 11
Hence the probability that the event will fail = 4/11.
The prime factor trees for 14 and 15 are
shown.
a) Write down the lowest common
multiple (LCM) of 14 and 15 as the
product of its prime factors.
b) Hence, work out the lowest common
multiple (LCM) of 14 and 15.
2
14
7
3
15
5
Answers
Answer:
14 = 2 * 7
15 = 3 * 5
LCM = 2 * 3 * 5 * 7 = 210
can you please help me with my homework and I have a picture of it. 2 raised to the power 3
Answers
The power 3 means "multiplying 3 copies" of (in our case) 2 ;
[tex]2^3=2\times2\times2[/tex]which is equal to 8.
Answer:
8
Step-by-step explanation:
for a lower tail test, the p-value is the probability of obtaining a value for the test statistic at least as a. small as that provided by the sample. b. large as that provided by the sample. c. small as that provided by the population. d. large as that provided by the population.
Answers
For a lower tail test, the p-value is the probability of obtaining a value for the test statistic is at least as small as that provided by the sample.
Probability is the probability that something will happen. Whenever the outcome of an event is uncertain, we can speak of the probability, or likelihood, of a particular outcome. Probabilistic analysis of events is called statistics.
The lower-tailed test is a one-tailed test in which the critical region of the distribution is one-sided (leftmost) and tests whether a sample is less than a specified value.
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1. Kylie mowed Mr. Johnson's lawn for
4 weeks. Every week Mr. Johnson
paid Kylie $15.43. How much money
did Kylie earn after the four weeks?
$71.62
c. $60.72
b. $61.72
d. $70.62
Answers
Answer:
The answer is b. $61.72
Step-by-step explanation:
Since she mowed the lawn for 4 weeks, and each week Kylie earned $15.43, then 4 x 15.43 = $61.72 after 4 weeks.
B. $61.72
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Which table has a constant of proportionality between y and c of 3/4?
Answers
Answer:
answer Is A.............
Which equation is perpendicular to
5-10y=6
and passes through (2.1)
Answers
Answer: x=2
Step-by-step explanation: Because there is only one variable in this equation, it makes a straight line. so to get a line, just do x= blank, but you need a point to go through (2,1), so x-2 is your equation.
I need help please!!
Answers
The most appropriate choice for slope will be given by -
1) Initially, as x increases, y also increases
2) Slope of the graph between x = 3 and x = 5 is 2
3) Slope of the graph between x = 5 and x = 9 is -1
4) Greatest value of y is y = 4 and it occurs when x = 5
What is slope of a line?
Slope of a line is equal to the tangent of the angle that the line makes with the positive direction of x axis.
If [tex]\theta[/tex] is the angle that the line makes with the positive direction of x axis, slope = tan [tex]\theta[/tex]
Suppose [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex]be two points on a line then the slope of the line is calculated by the formula
slope = [tex]\frac{y_2 - y_1}{x_2 - x_1}[/tex]
Here,
1) Initially, as x increases, y also increases
2) Slope of the graph between x = 3 and x = 5 = [tex]\frac{4 - 0}{5 - 3}[/tex]
= [tex]\frac{4}{2}[/tex]
= 2
3) Slope of the graph between x = 5 and x = 9 =
[tex]\frac{4 - 0}{5 - 9}\\-\frac{4}{4}\\-1[/tex]
4) Greatest value of y is y = 4 and it occurs when x = 5
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HELP please
Giving brainlyest
Answers
The equation of the line that contains (-4, 6) and (7, -5) in point slope form is y + 5 = - 1(x - 7).
How to represent equation in point slope form?The point slope form can be represented as follows:
y - y₁ = m(x - x₁)
where
m = slopex₁ and y₁ are the coordinates.Therefore, the equation of the line that contains (-4, 6) and (7, -5) can be found in point slope form as follows:
Hence,
m = -5 - 6 / 7 + 4
m = - 11 / 11
m = -1
Therefore, using (7, -5)
y + 5 = - 1(x - 7)
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Pic below!! Find the surface area of a cube with side length of three meters.
Answers
Solve the problem. Express your answer to the correct number of significant figures.
6.221 × 7.11 − 13.7 =
Answers
We need to know about significant figures to solve this question. The value of the expression is 30.53131
Significant figures are the number of digits in a value that contribute to the degree of accuracy of the value. In the given expression we have three decimal numbers that have different significant figures, we need to solve the expression to get the answer with the right number of significant numbers. When a number starts with zero, the zeros are not significant, when a decimal number ends with zero, the zeroes are not significant.
6.221x7.11-13.7=44.23131-13.7=30.53131
Therefore the solution of the expression is 30.53131
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Which point is a solution to this system of inequalities?
y < 1/2x - 3y + 2x > 6
A. (7-8)
B. (2-3)
C. (5,-2)
D. (4,1)
Answers
Option C is correct. The (5,-2) point solves the given system of inequalities y < 1/2x - 3 and y + 2x > 6.
What exactly is an inequality?An inequality in mathematics is a relationship that makes a non-equal comparison between two numbers or other mathematical expressions. It is most commonly used to compare the sizes of two numbers on a number line.The given system of inequalities is as follows:
y < 1/2x - 3, y + 2x > 6
Substituting (7,-8) in these inequalities,
y < 1/2x - 3
y < 0.5
-8 < 0.5 is true
y + 2x > 6
-8 + 14 > 6
6 > 6 is false
So this is incorrect option.
Similarly, substituting (2,-3) in these inequalities,
y < 1/2x - 3
y < -3
-3 < -2 is true
y + 2x > 6
1 > 6 is false
So this is incorrect option.
Substituting (5,-2) in these inequalities,
y < 1/2x - 3
-2 < -0.5 is true
y + 2x > 6
8 > 6 is true
So, this is correct option.
Therefore, (5,-2) point is a solution to the given system of inequalities y < 1/2x - 3 and y + 2x > 6. So, Option C is correct.
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Parking for 4 hours costs $10. Parking for 5 hours costs $12. Is this a proportional relationship, and if so, what is the constant of the proportionality
Answers
No, this is not a proportional relationship.
Proportional relationships are relationships between two variables where their ratios are equivalent.
In this scenario the ratio between 4 hours and $10 parking cost comes out to be 10/4=2.5
But in the second case the ratio between 5 hours and $12 paring cost comes out to be 12/5=2.6
Since the ratios don't come out to be equal therefore this is not a proportional relationship .
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2. Big TV prices Here are prices and screen sizes (in inches, measured diagonally) for 7 different sizes of one brand of LED HD television.47 Use technology to calculate the equation of the least- squares regression line relating y = price to x = screen size. Screen size Price 60 1000 55 800 50 700 47 600 42 430 39 400 32 300
Answers
The general formula for the least-squares regression is:
[tex]y=a+bx_i[/tex]Where
a represents the y-intercept
b represents the slope
To estimate the y-intercept and the slope of the regression line you have to apply the following formulas:
[tex]b=\frac{\Sigma xy-\frac{\Sigma x\Sigma y}{n}}{\lbrack\Sigma x^2-\frac{(\Sigma x)^2}{n}\rbrack}[/tex][tex]a=\bar{y}-b\bar{x}[/tex]First, calculate the sums and the means for both variables.
X= screen size
Y= price
n=7
[tex]\begin{gathered} \Sigma x=60+55+50+47+42+39+32 \\ \Sigma x=325 \end{gathered}[/tex][tex]\begin{gathered} \Sigma x^2=60^2+55^2+50^2+47^2+42^2+39^2+32^2 \\ \Sigma x^2=15643 \end{gathered}[/tex][tex]\begin{gathered} \bar{x}=\frac{\Sigma x}{n} \\ \bar{x}=\frac{325}{7} \\ \bar{x}=46.43 \end{gathered}[/tex][tex]\begin{gathered} \Sigma y=1000+800+700+600+430+400+300 \\ \Sigma y=4230 \end{gathered}[/tex][tex]\begin{gathered} \bar{y}=\frac{\Sigma y}{n} \\ \bar{y}=\frac{4230}{7} \\ \bar{y}=604.29 \end{gathered}[/tex][tex]\begin{gathered} \Sigma xy=60\cdot1000+55\cdot800+50\cdot700+47\cdot600+42\cdot430+39\cdot400+32\cdot300 \\ \Sigma xy=210460 \end{gathered}[/tex]Calculate the slope of the line:
[tex]\begin{gathered} b=\frac{\Sigma xy-\frac{\Sigma x\Sigma y}{n}}{\Sigma x^2-\frac{(\Sigma x)^2}{n}} \\ b=\frac{210460-\frac{325\cdot4230}{7}}{15643-\frac{325^2}{7}} \\ b=\frac{210460-196392.85}{15643-15089.29} \\ b=\frac{14067.75}{553.71} \\ b=25.41 \end{gathered}[/tex]Once you have calculated the slope, you can calculate the y-intercept:
[tex]\begin{gathered} a=\bar{y}-b\bar{x} \\ a=604.29-25.41\cdot46.43 \\ a=604.29-1179.7863 \\ a=-575.23 \end{gathered}[/tex]The regression line for the price with respect to the screen size is:
[tex]y=-575.23+25.41x[/tex]Which binomial is a factor of
x² + 2x - 15?
O A. (x+15)
O B.(x-3)
O c.(x - 1)
O D. (x - 5)
Answers
Binomial is a factor of ( x² + 2x - 15) is (x − 3) .
Why does a binomial qualify as a factor?Despite the fact that many distinct expression types can be categorized as binomials, not all of them can be factored. A binomial must have one of the following in order to be factorable: a difference of two squares, a difference of cubes, a sum of cubes, or a greatest common factor.
In math, what is a binomial?Having two terms makes a polynomial a binomial. Binomials include, for instance, x 2 x -2 x2 and x 6 x -6 x6. This article will go over multiplying these binomials.
Separate the expression into groups using (x^2+3x)+ (5x-15)
Factor x from (x^2-3x)
x(x-3)
Subtract 5 from 5x-15.
5(x-3)
=> x(x-3)+5(x-3)
Remove the common term (x-3) (x-3)(x+5) since (x-3) and (x+5) are binomials of (x2+2x-15).
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Kinsley is thinking of a secret number, she tells her brother the number she's thinking of is divisible by 3, then tells her friends it's divisible by 17, if Kinsley is telling the truth to both of them, what could be the number she is thinking of?
Answers
Answer:
51
Step-by-step explanation:
17 x 3 = 51. To check this answer, you can do
51 ÷ 17 = 3
51 ÷ 3 = 17
What is the monthly payment for a $4,000 two-year loan with an APR of 4%?
Answers
A loan calculator is an automated instrument that enables you to comprehend what your potential monthly loan payments and total loan cost might be. Online, you can find a variety of loan calculators, such as those for mortgages or other kinds of specialized loans.
What is the cost of a $4000 loan every month?The amount due each month is $4000.
Detailed explanation:
Given: $4168.79 in total interest has been paid for a loan with a two-year term at 4% interest compounded monthly.
Identify: What is the loan's monthly payment?
Answer: $4168.79 in total interest for a two-year loan compounded monthly.
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Please help me solve this
Answers
On solving the expression 1/2 - 1/10 we get 2/5
What is fraction?In Mathematics, fractions are represented as a numerical value, which defines a part of a whole. Example - 5/9. Here, (5) is called numerator and (9) is called denominator.
Given is the following expression -
1/2 - 1/10
We have -
1/2 - 1/10
Multiplying the denominator and numerator in 1/2 by 5, we get -
5/10
Now, the expression becomes -
5/10 - 1/10
(5 - 1)/10
4/10
2/5
Therefore, on solving the expression 1/2 - 1/10 we get 2/5.
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PLEASE HELP!! These two shapes are similar. True or False?
(Be sure to use the two rules of similarity to make your choice)
A- True, because the corresponding side lengths are proportional and the corresponding angles are congruent.
B- False, because the corresponding side lengths are congruent but the angles are not proportional.
C- False, because the corresponding side lengths are congruent but the angles are not proportional.
D- True, because the corresponding side lengths and corresponding angles are the same size.
Answers
Answer:
True, because the corresponding side lengths are proportional and the corresponding angles are congruent.
Step-by-step explanation:
The statement (A) True, because the corresponding side lengths are proportional and the corresponding angles are congruent is correct.
What is the similarity law for triangles?It is defined as the law to prove that two triangles have the same shape, but it is not compulsory to have the same size. The ratio of the corresponding sides is in the same proportions and the corresponding angles are congruent.
It is given that:
The two triangles are shown in the picture.
As we know from the definition of a similar triangle, two triangles have the same shape, but it is not compulsory to have the same size.
The ratio of the corresponding sides is in the same proportions and the corresponding angles are congruent.
As we can see in the picture, the relevant angles are congruent and the corresponding side lengths are proportionate.
The triangles are similar.
Thus, the statement (A) True, because the corresponding side lengths are proportional and the corresponding angles are congruent is correct.
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Elijah put 2x+3 dollars in the bank the first week. The following week he doubled the first week’s savings and put that amount in the bank. The next week, he doubled what was in the bank and put that amount in the bank. He now has $477 in the bank. How much money did he put in the bank the first week?
Answers
Answer:
$53
Step-by-step explanation:
You want to know Elijah's initial deposit if his deposits were ...
first week: 2x+3second week: addition = double the first weekthird week: addition = double the total so far; total is $477BackwardIf x2 is the amount in the bank after the deposit of week 2, the amount deposited in week 3 is 2(x2). The total after that deposit is 477, so we have ...
x2 +2(x2) = 477
x2 = 477/3 = 159
Working back another week, we figure ...
If x1 is the amount in the bank after the initial deposit, the amount deposited the following week was 2(x1). Then the total amount in the bank after that deposit is ...
x1 +2(x1) = 159
x1 = 159/3 = 53
Elijah put $53 in the bank the first week.
__
Additional comment
We're not asked for the value of x, so the expression 2x+3 doesn't come into play in this problem. (We can see that 2x+3 = 53 ⇒ x = 25.)
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help me a=1/7(b+c-d-d)
Answers
The simplified equation of the equation given as a=1/7(b+c-d-d) is a = b/7 + c/7 - 2/7d
How to simplify the equation?From the question, the equation is given as
a=1/7(b+c-d-d)
Rewrite the above equation properly
So, we have the following representation
a = 1/7(b + c - d - d)
Evaluate the like terms in the above equation
So, we have the following equation
a = 1/7(b + c - 2d)
Open the brackets in the above equation
So, we have the following equation
a = 1/7 * b + 1/7 * c - 1/7 * 2d
Evaluate the products in the above equation
So, we have the following equation
a = b/7 + c/7 - 2/7d
The above equation cannot be further simplified
So, we leave it like that
Hence, the simplified equation of a=1/7(b+c-d-d) is a = b/7 + c/7 - 2/7d
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what is the answer to -3(4-5b+7)
Answers
Answer:
-33+15n
Step-by-step explanation:
You will have to first distribute the -3.
-3*4 is equal to -12
-3*-5b is equal to 15b Note: -*-=+
-3*7 is equal to -21
Once you get those numbers you will have a equation like this
-12+15b-21
Combine like terms and you will get -33+15n as you answer
Express your answer as a polynomial in standard form.
f(x) = 2x² + 3x + 12
g(x) = 5x - 6
Find: (gof)(x)
Answers
The answer as a polynomial in standard form is 50x² - 45x +66.
What are polynomials?A polynomial is an expression in mathematics that solely uses the operations of addition, subtraction, multiplication, and powers of positive-integer variables. It consists of indeterminates and coefficients. The polynomial x2 4x + 7 is an illustration of a single indeterminate x polynomial. Sums of terms with the pattern k x n—where k is any positive integer and n is an arbitrary number—are known as polynomials. A polynomial is something like 3x+2x-5. Polynomials: An introduction In this video, basic terms such terms, degrees, standard form, monomial, binomial, and trinomial are covered. Using mathematical operations like addition, subtraction, multiplication, and division, a polynomial is an equation made up of variables, constants, and exponents (No division operation by a variable).
g(x) = 5x - 6
So,
f(x) = 2(5x - 6)² + 3(5x - 6) + 12
= 2( 25x² + 36 - 60x ) + 15x - 18 + 12
= 50x² + 66 - 45x
= 50x² - 45x +66
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Find the unknown value please helppp
Answers
Answer:
30
Step-by-step explanation:
To get from 15 to 5, you multiply 15 times 1/3, so do the reciprocal to get from x to 10. So, 10 times 3 is 30.
as you can see 5 times 3 equals to 15 therefore times 10 with 3 makes 30.
The residents of a village want to paint a sign that shows the
The residents of a village want to paint a sign that shows the elevation of their village relative to the sea. Their altimeter shows +2,100 feet. What should their signboard read?
A.
2,100 feet above sea level
B.
2,100 feet below sea level
C.
-2,100 feet above sea level
D.
+2,100 feet below sea level
Answers
A. 2,100 feet above sea level
B. 2,100 feet below sea level
C. -2,100 feet above sea level
D. +2,100 feet below sea levelEXPLANATIONDepth above water levels refers to a location's peak just above ocean.
If indeed the height is positive (+) then the depth might well just above water level and if negative (-) therefore the depth will be lower than the water level.
Please help mee,
It’s what I’m doing in technology class
Answers
Area of square with side = 4cm is : 16cm²
Area of rectangle with height = 2cm and width = 3cm is : 6cm²
Explanation :To find the area of square:
A square is a two-dimensional figure with equal-sized sides. Because all of the sides are equal, the area is length times width, which equals side side. As a result, the area of a square is side square.Area = a×a
= a²
To find the area of rectangle :
In the rectangle opposite sides are equal .The area of a rectangle is calculated once the length and width are known. A rectangle's area can be calculated by multiplying its length and width.Area = l x b
Given sides of square a = 4cm .
Area = a²
Area = 4²
= 16 cm²
Given sides of rectangle ,
l = 3cm
b = 2cm
Area = l × b
= 3 × 2
= 6 cm²
Area of square is 16 cm²
Area of rectangle is 6 cm²
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Eva is making smoothies. Each smoothie uses scup of yogurt. How many
cups of yogurt does she need to make 4 smoothies? Express your answer in
simplest form.
Answers
Cups of yogurt she needs to make 4 smoothies is 20 cups
What is Fraction?
An element of a whole or, more broadly, any number of equal pieces, is represented by a fraction. When used in conversational English, a fraction indicates the number of components of a particular size, as in one-half, eight-fifths, and three-quarters.
Given,
5cups of yogurt is used to make 1 smoothie
We have to find out that how cups of yogurt will it take to make 4 smoothies
1 smoothie = 1 x 5cups
4smoothies = 4 x 5cups
= 20 cups
Hence, 20 cups of yogurt is needed to make 4 smoothies
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5.
Amelia buys 6 cans of beans for $1.50 each. She also buys a
pineapple. The total cost of the items is $12.30, What is the cost of
the pineapple?
Answers
Angelica's bouquet of a dozen roses contains 5 white roses. The rest of the roses are pink. What fraction of the
bouquet is pink roses? There are 12 roses in a dozen.
O
O
O
5
12
12
517
775
Answers
Answer: 7/12
Step-by-step explanation:12/12-5/12=7/12
-9y+2(5y-2)
Preciso da resposta o Mais rápido possível
Answers
Answer:
y-4
Step-by-step explanation:
