The rate of change of the volume of the sphere is 100,530.96 mm^3/s
How to calculate rate of change of the volume of the sphere?
Given,
radius = r = 80 / 2 = 40 mm
rate of change radius = [tex]\frac{dr}{dt}[/tex] = 5 mm/s
Formula to calculate volume of the sphere is
[tex]V = \frac{4}{3}\pi r^{3}[/tex]
Differentiating the volume formula and we get new formula to calculate rate of change of the volume.
[tex]\frac{dV}{dt} = \frac{4}{3}\pi 3r^{2}\frac{dr}{dt}[/tex]
Simplify to
[tex]\frac{dV}{dt} = 4\pi r^{2}\frac{dr}{dt}[/tex]
Now, we put the given value to formula and calculate it
[tex]\frac{dV}{dt} = 4\pi (40)^{2}(5)[/tex]
[tex]\frac{dV}{dt} = 100,530.96[/tex] mm^3/s
Thus, the rate of change of the volume of the sphere is 100,530.96 mm^3/s
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F(x)=x² + 7
Find
a) F (10)
6) F(-3)
The value of f(10) = 107 and f(-3) = 16.
The function is defined as in mathematics, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable). An example of this would be y=x2. You only get one output for y if you enter anything for x. Considering that x is the input value.
Given that f(x)=x² + 7
We do determine the values of F (10) and F(-3)
Now f(10)
= (10)2 +7
= 100 +7
= 107
Now f(-3)
= (-3)2 +7
= 9 +7
= 16
Therefore the value of f(10) = 107 and f(-3) = 16
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Suppose the math club is going on a field trip. Members will be riding in vans that will hold 7 people each including the
driver. More than 28 people will be going on the field trip. Do not put spaces in your answers.
Write an inequality to model this situation using V as the variable.
Solve the inequality.
What is the least number of vans needed to make the trip?
Since more than 4 vans will be required in total, at least 4 vans should be reserved.
What is inequality?In mathematics, "inequality" refers to a relationship between two expressions or values that are not equal to one another. In mathematics, inequalities specify the relationship between two non-equal values. Equal does not imply inequality. The "not equal symbol ()" is typically used to indicate that two values are not equal. The expression 5x 4 > 2x + 3 resembles an equation, but the equals sign has been replaced by an arrowhead. It is an illustration of inequality. This shows that the left part, 5x 4, is bigger than the right part, 2x + 3.
Here,
Since the total number of people is at least 28, then the total number of people must be 28 or more, so
7v≥28
v≥4
The total number of vans needed will be more than 4 that is at least 4 vans should be booked.
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hello am new here,so I want u guys to help me with the question and good workings and it is urgent.
using sine rule
In a triangle ABC the value of side a is 13.12 cm.
What is a triangle?A triangle is a three-sided closed-plane figure formed by joining three noncolinear points. Based on the side property triangles are of three types they are Equilateral triangle, Scalene triangle, and Isosceles triangle.
We know in a ΔABC, a/sinA = b/sinB = c/sinC.
GIven, In a ΔABC A = 29°, B = 36°, b = 15.8 cm.
∴ a/sinA = b/sinB.
a/sin(29°) = 15.8/sin(36°).
a/0.49 = 15.8/0.59.
a = (15.8×0.49)/0.59
a = 7.742/0.59.
a = 13.12.
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Find the sum of the interior angle measures of a regular polygon with 19 sides.
Answer:
Step-by-step explanation:
3060
ASAP! exponent rules
Answer: P and Q could both be equal to -1
Jared had two numbers to multiply. They were written as 64⋅3.He thought that it would be easier to multiply them as 3⋅64.What property would he be using?
Answer:
He is using the commutative property of multiplication.
PLS HELP URGENT!!!
Q.1: (Q.1 IN FIRST IMAGE!!)
The population of a specific species of nocturnal mammal is decreasing at a rate of 3.5%/year. The graph models the number of mammals x years after they were originally counted.
Identify and interpret the key features of the exponential function modeled in terms of this situation.
Select EACH correct answer.
Question 1 options:
The y-intercept represents the number of mammals when they were originally counted.
The line y = 0 is an asymptote of the graph.
The y-intercept.is 75.
The y-intercept is 120.
The asymptote indicates that the number of mammals counted when the study began was 120.
The asymptote indicates that as years pass, the number of mammals will approach 0.
The line x = 0 is an asymptote of the graph.
Q.2 ( IMAGE IN SECOND )Once an antibiotic is given, number of bacteria decreases at a rate of 15%/day. There were about 15,000 bacteria prior to the treatment. The graph models the number of bacteria after x days of treatment.
What are the key features of the exponential function modeled in terms of this situation and how can they be interpreted?
Select each correct answer.
Question 2 options:
The line y = 0 is an asymptote of the graph.
The x-intercept is 30.
The line x = 0 is an asymptote of the graph.
The asymptote indicates that there will never be more than 15,000 bacteria.
The y-intercept is 15,000.
The y-intercept represents the number of bacteria when treatment began.
The asymptote indicates that as time increases, the number of bacteria approaches 0.
Q.3 ( Q.3 IN THIRD IMAGE) A local farmer had a mouse problem in his barn. He estimated there were about 800 mice to start with. He adopted some cats and noticed that the number of mice was decreasing by 8%/wk. The graph models the number of mice x weeks after the farmer adopted the cats.
Identify and interpret the key features of the exponential function modeled in terms of this situation.
The features for each of the exponential functions are listed as follows:
1.
The y-intercept represents the number of mammals when they were originally counted.The line y = 0 is an asymptote of the graph.The y-intercept is 120.The asymptote indicates that as years pass, the number of mammals will approach 0.2.
The line y = 0 is an asymptote of the graph.The y-intercept is 15,000.The y-intercept represents the number of bacteria when treatment began.The asymptote indicates that as time increases, the number of bacteria approaches 0.3. The key features are listed as follows:
y-intercept of 800, which is the number of mice when the study began.The line y = 0 is the asymptote of the graph, indicating that as the number of weeks increase, the number of mice approaches 0.What are the features of exponential functions?The features to the graphs of the exponential functions are listed as follows:
y-intercept: Initial value of the output variable, that is, the value of y when the function crosses the y-axis.horizontal asymptote: value that the output variable approaches as the input variable goes to infinity.More can be learned about exponential functions at
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Choose Yes or No to tell whether the expression represents a 20% discount off the price of an item that originally cost d dollars. 0.8d Choose... d – 0.2 Choose... d – 0.2d Choose... 1 – 0.2d Choose...
The expression that represents a 20% discount off the price of an item that originally cost d dollars include:
0.8d
d - 0.2d
What is an expression?Expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both.
In this case, the cost of the item is d. Since there's a 20% discount, the new cost will be:
= d - (20% × d)
= d - 0.2d
= 0.8d
The cost is 0.8d.
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What is the coefficient of this number written in scientific notation?
(3.6 x 10^5)
Enter the coefficient only. Don't change to standard form!
The coefficient would be 3.6
based on the information given above is it possible to compute the probability that a randomly selected cookie has a weight less than 14 g?
0.1367 percent of randomly chosen cookies will weigh less than 14 grams.
Given data;
Is it possible to calculate the likelihood that a randomly selected cookie weighs less than 14g using the information provided above?
Let,
X = Average cookie weight in a pack of 30
E (X) = μ = 15
Var (X) = σ²/n
= 1²/30 = 0.0333
⇒ Standard Deviation (X) = √0.0333 = 0.1826
P(X ≤ 14.8) = (X-15 / 0.1826 < 14.815/0.1826)
= P(14.815 - 0.1826)
= P(Z-1.1)
= 0.1367
Hence, the probability that a randomly selected cookie has a weight less than 14g is 0.1367
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A local farmer had a mouse problem in his barn. He estimated there were about 800 mice to start with. He adopted some cats and noticed that the number of mice was decreasing by 8%/wk. The graph models the number of mice x weeks after the farmer adopted the cats.
Identify and interpret the key features of the exponential function modeled in terms of this situation.
Select each correct answer.
Question 3 options:
The asymptote indicates that as the number of weeks the farmer has had the cats increases, the population of mice approaches 0.
The y-intercept represents the number of mice the farmer had in the barn at the time he adopted the cats.
The line x = 0 is an asymptote of the graph.
The point (0,30) contains the x-intercept.
The line y = 0 is an asymptote of the graph.
The y-intercept is 800.
The asymptote indicates that there were never more than 800 mice in existence.
The asymptote tells us the number of mice will approach zero as cats increased y-intercept shows the number of mice with zero cats and the asymptote is y = 0 thus option (A),(B), and (E) is correct.
What is a graph?The graph is a geometrical representation of a function and can be plotted by taking x's and y's corresponding values within the interval.
For example plot of y = x³ ,y = sinx.
The given graph of the number of mice in the number of weeks the cat adopted.
The asymptote of the graph is y = 0.
The asymptote tells that the number of the mouse will become zero when the number of cats becomes infinite.
Hence "The asymptote tells us the number of mice will approach zero as cats increased y-intercept shows the number of mice with zero cats and the asymptote is y = 0".
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In the next several games, the pitcher threw a total of 384 pitches and used a fastball 240 times. What decimal should Juanita use to update her report?
Juanita should use the decimal to update her report.
The decimal that Juanita can use to update her report is 1.6.
What is a decimal?A decimal is a number with a whole and a fractional part. Decimal numbers are between integers and represent numerical value for whole plus some fraction of a whole.
The decimal numeral system is the most widely used system for representing both integer and non-integer numbers. It is the Hindu-Arabic numeral system's extension to non-integer numbers. Decimal notation refers to the method of representing numbers in the decimal system.
In this case, the the pitcher threw a total of 384 pitches and used a fastball 240 times. The decimal will be:
= Number of throws / Fastball
= 384 / 240
= 1.6
The decimal is 1.6.
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The fraction 3/5 fits into 2 1/5 more or less than 1? That means the quotient is more or less than 1?
The fraction 3/5 fits into 2 1/5 more than once. The quotient is more than one.
We are given two fractions. The first fraction is 3/5, which is a simple fraction. The second fraction is 2 1/5, which is a mixed fraction. We will first convert the mixed fraction into a simple fraction.
F = 2 1/5
F = (2*5 + 1)/5
F = 11/5
We need to find out if the quotient is more or less than one. So we will divide the second fraction by the first fraction. Let the quotient be represented by the variable "Q".
Q = (11/5)÷(3/5)
Q = (11/5)×(5/3)
Q = 11/3
Q = 3.667
We can see that the quotient is more than one. Hence, the fraction 3/5 fits into 2 1/5 more than once.
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Answer:
the fraction 3/5 fits into 2 1/5 more than 1 time. That means the quotient is greater than.
Step-by-step explanation:
(3+6n³ + 3n) - (3n+3n³-2n¹)
Answer:
3n³ + 2n + 3
Step-by-step explanation:
(3+6n³ + 3n) - (3n+3n³-2n¹)
3 + 6n³ + 3n - 3n - 3n³ + 2n
3n³ + 2n + 3
A random number generator is used to select a number from 1 to 100. What is the probability of selecting the number 153?
Answer:
0
Step-by-step explanation:
153 isn't between 1-100 making the probability 0
what is the smallest positive integer a such that the intermediate value theorem guarantees a zero exists between 0 and a?
The smallest positive integer that the intermediate value theorem guarantees a zero exists between 0 and a is 3.
What is the intermediate value theorem?
Intermediate value theorem is theorem about all possible y-value in between two known y-value.
x-intercepts
-x^2 + x + 2 = 0
x^2 - x - 2 = 0
(x + 1)(x - 2) = 0
x = -1, x = 2
y intercepts
f(0) = -x^2 + x + 2
f(0) = -0^2 + 0 + 2
f(0) = 2
(Graph attached)
From the graph we know the smallest positive integer value that the intermediate value theorem guarantees a zero exists between 0 and a is 3
For proof, the zero exists when x = 2 and f(3) = -4 < 0 and f(0) = 2 > 0.
Your question is not complete, but most probably your full questions was
Given the polynomial f(x)=− x 2 +x+2 , what is the smallest positive integer a such that the Intermediate Value Theorem guarantees a zero exists between 0 and a ?
Thus, the smallest positive integer that the intermediate value theorem guarantees a zero exists between 0 and a is 3.
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The temperature today in Chicago is 50°E
Instead of using the standard conversion
formula °C = x(°F - 32), Tommaso uses his
9
grandmother's rule, which is easier but gives
an approximate value: "Subtract 32 from the
value in °F and multiply the result by 0.5."
Error = (10-9)°C & Error percentage = 10%.
Given that temperature today in Chicago is 50°F
Standard conversion formula
°C = [tex]\frac{5}{9} *(T^{0}F-32)[/tex] - 1
Given T = 50°F
Put the value in equation 1
[tex]^{0}C = \frac{5}{9} *(50-32) \\\\= \frac{5}{9}*18\\ \\= \frac{90}{9}[/tex]
= 10°C
Tommasa's grandmothers rule is to subtract 32 from the value in °F and multiply the result by 0.5
i.e. [tex]^{0}C = 0.5(T^{0} F-32)[/tex] - 2
Given temperature is T = 50°F
Put the value of T in equation 2
[tex]^{0}C = 0.5*(50-32)[/tex]
= 0.5 * 18
= 1/2 * 18
= 9°C
Temperature obtained by standard conversion Formula is 10°C and the temperature obtained by Tammaso's grandmother rule is 9°C.
So error = (10-9)°C
= 1°C
Error percentage = [tex]\frac{1}{10}*100[/tex]
= 10%
Hence the answer is Error = (10-9)°C & Error percentage = 10%.
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In triangle EFG, m∠E = 84.3° and m∠F = 36.4°. Determine the measure of the exterior angle to ∠G.
47.9°
59.3°
121.1°
120.7°
By applying the exterior angle property, the measure of the exterior angle to ∠G in triangle EFG is 120.7°
What is the exterior angle property?In Mathematics, the exterior angle property can be defined as a theorem which states that the measure of an exterior angle in a triangle is equal in magnitude to the sum of the measures of the two remote or opposite interior angles of that triangle.
To determine the value of ∠G in triangle EFG (ΔEFG), we would have to apply exterior angle property.
Then, the exterior angle property can be used to model triangle EFG (ΔEFG) is given by:
∠G = m∠E +m∠F
Now Substituting the given parameters into the formula, we have
∠G = 84.3° + 36.4°.
∠G = 120.7°.
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In the diagram below, GH is parallel to DE. If the length of DE is the same as the
length of GF, DF = 13, and GH = 5, find the length of GF. Figures are not
necessarily drawn to scale. State your answer in simplest radical form, if necessary.
Using the properties of similar triangle and parallel lines we calculate the length of GF as √65 units.
It is given that GH is parallel to DE or GH || DE in the trapezium GHDE .
Therefore in the triangles ΔFDH and ΔFDE , we can say that
ΔFDH is similar to ΔFDE by angle angle angle axiom of similarity.
Now using the properties of similar triangles we can say that :
FG / DF = GH / DE
Now let us consider the length of GF be x.
Therefore DE = x
Now using the properties of similar triangles and substituting the values we get:
x / 13 = 5 / x
or, x² = 65
or, x = √65
Therefore the length of DE and GF is equal to √65.
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What does the transformation f(x)—>f(1/3x) do to the graph of f(x)?
The transformation f(x)—>f(1/3x) due to the graph of f(x), will be dilation horizontally and vertically.
What is Transformation of Function?
Transformation of functions refers to the graph's curve moving to the left, right, up, or down, expanding, contracting, or reflecting. Just dilation, out of these three transformations, alters the size of the original shape; the other two only adjust the position.
A translation happens when each point on a graph (which represents a function) travels in the same direction and by the same amount. There are two kinds of function translations.
Stretching or compressing is a dilation. The x-values on a graph are all scaled up by the same amount when a dilation that is parallel to the x-axis occurs. The y-values are all increased by the same scale factor if it is dilated parallel to the y-axis.
f(x) to become f(1/3x), Then it will go dilation "vertically and horizontally".
Referring to the graph mentioned below we can conclude the same.
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bobby spent 40% of his allowance on art supplies last month, with two-thirds of this amount spent on paintbrushes alone. if his monthly allowance is $75, how much did bobby spend on paintbrushes last month?
Bobby spent $20 out of $75 of his monthly allowance on paintbrushes.
What is monthly allowance?
Giving someone money on a regular basis to help them pay for the things they need is known as giving them an allowance.
Main Body:
total monthly allowance = $75
Now Bobby spent 40% on his art supplies,
which means we need to calculate 40% of 75.
⇒(40/100)*75
⇒30
so Bobby spent $30 on art supplies.
now according to question,
Bobby spent 2/3 on paintbrushes
⇒2/3 of art supplies
⇒(2/3 )*30
⇒$20
Hence Bobby spent $20 on his paintbrushes.
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Wich rule best represents the dilation that was applied to the quadrilateral ABCD to create quadrilateral A'B'C'D'?
Answer:
Step-by-step explanation:
It A (x,y) (0.4x,0.4y)
Write down two expressions for the
perimeter of this shape, one with
brackets and one without.
t + 5
P (with brackets) =
P (without brackets) =
[2]
[2]
The expression for the perimeter of the square with and without brackets is 4(t + 5) and 4t + 20, respectively.
We are given a shape. The shape is a square. The side length of the square is equal to (t + 5). We have to find the expression for the perimeter of the square. A perimeter is a closed route that covers, surrounds, or outlines a two-dimensional form or length. Let the perimeter of the square be denoted by the variable "P".
The expression for the perimeter of the square in brackets is given below:
P = 4(t + 5)
The expression for the perimeter of the square without brackets is given below:
P = 4t + 20
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What are the missing values?
The ratio table's missing values are 6: 3, 24:12, and 18:9.A ratio shows how many of one number there are of another. Two numbers are expressed as x: y, which is equivalent to x/y, to represent their ratio.
What does ratio mean?A ratio shows how many of one number there are of another. Two numbers are expressed as x: y, which is equivalent to x/y, to represent their ratio.
where each of the two variables, x and y, is a separate quantity.
Additionally, the combined total is given as x + y.
Therefore, Peoples = 6, 18 and Benches = 3, 12
Now,
These ratios are equivalent: 6: 3, x: 12, and 18: y.
Ascertain the values of x and y.
Given that all ratios are equal.
so we obtain;
⇒ 6 : 3 = x : 12
⇒ 6 / 3 = x / 12
⇒ 6 × 12 / 3 = x
⇒ x = 24
And, ⇒ 6 : 3 = 18 : y
⇒ 6 × y = 18 × 3\s⇒ y = 18 × 3 / 6\s⇒ y = 9
Therefore, the ratio table's missing values are 6: 3, 24:12, and 18:9.
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solve for y and then graph the solution: -25 < 4y + 3 < 19
So, for this question, there are two answers possible that you could put in.
-25 < 4y + 3 < 19 in inequality form: -7<y<4
-25 < 4y + 3 < 19 in interval notation form: (-7,4)
The graph that goes alongside it should be attached to this answer as well.
Hope this helps! :)
2x + 3y = 30 solve for y
I will name you the Brainliest if you answer!
Choose the ordered pair that is a solution of the inequality y ≤ −3x − 5.
(2, 3)
(0, 0)
(−1, −3)
(0, −1)
Answer:C. (1,-3)
E. (2,5)
Step-by-step explanation:
whats eleven decreased by k ?
Answer:
11-k
Step-by-step explanation:
if you are asking what is as a equation its 11-7 because decreased means minus
The required mathematical expression for the given statement is 11-k.
What are expressions?A mathematical statement containing variables, numbers and related by at least one mathematical operator is considered as an expression.
Given that, a statement, what's eleven decreased by k,
Converting it into a mathematical expression,
Here, a value k is being extracted or subtracted by 11, that mean, the expression should be like k is being subtracted by 11.
That is = 11-k
Hence, the required mathematical expression for the given statement is 11-k.
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A farmer grows 128 red tomatoe plants and 102 yellow tomato plants each plants about 32 tomatoes the farmer plants to sell each tomatoes for $2 explain how to find a reasonable as the meal for the total of money is the farmers market
The total amount of money that farmer will make to sell the tomatoes for $2 per tomato will be $14720.
What is the arithmetic operator?Arithmetic operators are four basic mathematical operations in which summation, subtraction, division, and multiplication involve.,
Summation = addition of two or more numbers or variable
Multiplication = to multiply any two or more numbers or variables called multiplication.
The number of red tomato = 128 × 32
The number of yellow tomato = 102 × 32
The total cost will be,
2(128 × 32) + 2(102 × 32)
⇒ 2(4096) + 2(3264)
⇒8192 + 6528
⇒$14720
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change each decimal to fraction then determine whether the decimal is terminating.
1. 2
8
2. 8
10
3. 1
6
4. 4
9
5. 8
11
6. 14
11
7. 3
7
Answer:
ok ask your teacher
Step-by-step explanation: