The rate of increase of the radius of the balloon at the instant when the radius is 30 cm is 0.0167 cm/min and when the radius is 60 cm, it is 0.0021 cm/min.
(a) At the instant when the radius of the balloon is 30 cm, the rate of increase of the radius of the balloon is
Rate of Increase of radius = (Change in Volume/ Change in Time) / (4/3 × π × (radius)^3)
= (800 cm3/min) / (4/3 × π × (30 cm)^3)
= 0.0167 cm/min
(b) At the instant when the radius of the balloon is 60 cm, the rate of increase of the radius of the balloon is
Rate of Increase of radius = (Change in Volume/ Change in Time) / (4/3 × π × (radius)^3)
= (800 cm3/min) / (4/3 × π × (60 cm)^3)
= 0.0021 cm/min
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Oranges are 2 pounds for $1.00. Apples are $2.00 per pound. Chris
bought 5 pounds of oranges and 3 pounds of apples. How much did Chris pay
for all the fruit?
Chris has to pay $8.5 for all the fruit.
given:
Oranges are 2 pounds for $1.00. Apples are $2.00 per pound. Chris
bought 5 pounds of oranges and 3 pounds of apples.
cost of apples is $2 per poundtotal apple purchase by Chris = 3 pounds
the total cost of apples (3 * $2 )= $6
cost of 2-pound orange is = $1.00total cost for 5 pounds of orange will be $2.5
the total cost of fruits is the cost of apples plus the cost of orange
= ($6+$2.5)= $8.5
therefore, the total amount to be paid by Chris is $8.5
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I am having a hard time starting this problem, can I get some help please.
Answer:
C
Step-by-step explanation:
The answer is 390
six-sided die is tossed 3 times. The probability of observing three ones in a row is:
Select one:
a. 1/6
b. 1/27
c. 1/216
d. 1/3
.
Answer:
c. [tex]1/216[/tex]
Step-by-step explanation:
The probability of rolling a one is 1/6.
Using the multiplication principle, the desired probability is [tex](1/6)^3=1/216[/tex].
solv the following equation and a explanation
We can simplify the inequality |x + 3| > 2 to get the compound inequality:
-1 < x
-5 > x
Thus, the correct option is B.
How to solve the inequality?Here we have the following inequality:
|x + 3| > 2
The absolute value part can be "separated" into a compound inequality, we can rewrite this as:
|x + 3| > 2
-2 > x + 3
2 < x + 3
Now we can solve these two inequalities for x, we will get:
-2 > x + 3
-2 - 3 > x
-5 > x
The second inequality gives:
2 < x + 3
x - 3 < x
-1 < x
Then the compound inequality is:
-1 < x
-5 > x
Then the correct graph is the one in option B.
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Select all equations that depict one of the properties of exponents. Select all that apply.
The properties of exponents are (ab)^x = a^xb^x, b² × b^x = b^(2+x), and x⁻² = 1/x². Hence options A, D, E are correct.
What is the property of exponent?
When referring to a mathematical phrase that denotes that a number will be multiplied by itself n times, the terms power and exponent are frequently used interchangeably. That is a valid definition of power, however, in mathematics, the word exponent expressly refers to the amount. n that specifies the number of times it will be multiplied by itself.
There are six properties of the exponent. The properties are
Product of Powers (x^m)(x^n) = x^(m+n)
Power to a Power (x^m)^n = x^(mn)
Quotient of Powers (x^m)/(x^n) = x^(m-n)
Power of a Product (xy)^m = x^m× x^n
Power of a Quotient (x/y)^n = x^n/y^n
Negative exponent x^(-n)= 1/x^n
According to the Power of a Product:
(ab)^x = a^xb^x
According to the Negative exponent:
7⁻³ = 1/7³
According to the Product of Powers:
b² × b^x = b^(2+x)
According to the Negative exponent:
x⁻² = 1/x².
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Helpp I need this asap
Explain how to modify the graphs of f(x) and g(x) to graph the solution set to the following system of inequalities. How can the
solution set be identified?
ysx²-3
y>-x² +2
Shaded portion gives the solution set of following in inequality.
What is inequality?
An inequality in mathematics is a relationship that allows us to contrast two (or more) mathematical expressions.
A difference between two values indicates whether one is more than, less than, or not equal to the other.
For example The strict inequalities like
a > b - “greater than”,
a < b - “less than”.
They are called Strict inequalities, since in each case a and b are not equal.
Here y ≤ [tex]x^2-3[/tex]
for the point (0, 0)
⇒ 0 ≤ 0 - 3
⇒ 0 ≤ -3
which is false thus region is opposite to origin
For y > [tex]x^2+2[/tex]
⇒ 0 > [tex]0^2+2[/tex]
⇒ 0 > 2
which is false thus the region is opposite to origin
Thus shaded portion is solution to given inequality
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Maggie made the following quilt from 64 square pieces of fabric.
A square array of eight squares wide by eight squares long. The length of the total square is seven and fifty-two hundredths feet.
What is the side length of each square piece of fabric? Enter your answer in the box.
The side length of each square piece of fabric is 0.343 feet
How to determine the side length of each square piece of fabric?From the question, we have the following parameters that can be used in our computation:
Square quilt
The readings from the quilt are given as
Area of quilt = seven and fifty-two hundredthsNumber of squares = 64Individual shapes = squareUsing the above as a guide, we have the following:
Number of squares * Area of Individual shapes = Area of quilt
Substitute the known values in the above equation, so, we have the following representation
64 * Area of Individual shapes = seven and fifty-two hundredths feet
Rewrite as
64 * Area of Individual shapes = 7.52
Divide both sides by 64
Area of Individual shapes = 0.1175
Take the square roots
Length of square = 0.343
Hence, the length is 0.343 feet
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Use the rules of exponents and your understanding of roots to find the exact value of the following expressions.
The values of exponent 5, √15, 2 and ∛2.
What are exponent?There are various exponential laws. Numerous mathematical problems involving repeated multiplication operations can be solved using all of the exponent rules. The operations of multiplication and division are made simpler and easier to solve by the laws of exponents.
Given,
The important laws of exponents are given below:
xᵃ ₓ xᵇ = x ᵃ⁺ ᵇ
xᵃ/xᵇ = x ᵃ⁻ ᵇ
(xᵃ)ᵇ = x ᵃᵇ
a⁻ⁿ = 1/aⁿ
a⁽¹/ⁿ⁾ = [tex]\sqrt[n]{a}[/tex]
1: [tex]25^{\frac{1}{2} }[/tex]
25 = 5 x 5 = 5²
[tex]( 5^{2}) ^{\frac{1}{2} }[/tex] = 5 using formula (xᵃ)ᵇ = x ᵃᵇ
2: [tex]15^{\frac{1}{2} }[/tex]
= [tex]\sqrt{15}[/tex] using a⁽¹/ⁿ⁾ = [tex]\sqrt[n]{a}[/tex]
3: [tex]8^{\frac{1}{3} }[/tex]
8 = 2 x 2 x2 = 2³
[tex]( 2^{3}) ^{\frac{1}{3} }[/tex] = 2 using formula (xᵃ)ᵇ = x ᵃᵇ
4: [tex]2^{\frac{1}{3} }[/tex]
= ∛2 using a⁽¹/ⁿ⁾ = [tex]\sqrt[n]{a}[/tex].
Hence values are 5, √15, 2 and ∛2.
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Determine whether the polygons with the given vertices are congruent or similar. Use transformations to explain your reasoning. a. Q(2, 4), R(5, 4), S(6, 2), T(1, 2) and W(6, -12), X(15, -12), Y(18, -6), Z(3, -6) b. A(-6, 6), B(-6, 2), C(-2, -4) and D(9, 7), E(5, 7), F(-1, 3)
The polygons, regarding congruence and similarity, are classified as follows:
a. Similar polygons.
b. Congruent polygons.
How to classify the triangles as similar of congruent?A dilation happens when the coordinates of the vertices of an image are multiplied by the scale factor, changing the side lengths of a figure.
If the transformation is a dilation, the triangles are similar, otherwise the triangles are congruent, as the dilation is the only transformation that changes the side lengths.
For item a, we have that the coordinates of WXYZ are multiples of QRST, meaning that a dilation with a scale factor of k = 3 was part of the transformation, hence the polygons are similar.
For item b, the only change was in the position, hence the side lengths are constant and thus the triangles are congruent.
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A man took a life insurance policy for 2 728 000 FRW on his 25th
birthday. He paid a premium of 35 740 FRW yearly. He died at the age of
65 years. The company paid into his estate the whole amount of his
insurance policy. How much more than his premium contribution did
the company pay into the man’s estate?
The difference between the amount paid by the company and the premium contribution is given as follows:
FRW 1 298 400.
How to obtain the difference?The difference is obtained applying the proportions in the context of the problem, which is the yearly payment, for the time.
The insurance was purchased on the 25th birthday, and the person died with 65 years old, hence the time period is given as follows:
65 - 25 = 40 years.
He paid a premium of 35 740 FRW yearly, hence the total amount paid is given as follows:
40 x 35 740 = 1,429,600.
A man took a life insurance policy for 2 728 000 FRW on his 25th birthday, hence the difference is calculated as follows:
2,728,000 - 1,429,600 = FRW 1 298 400.
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Situations and Sequence Types
This lesson's goal is to get pupils writing equations to create sequences given tables or visual patterns.
What do you meant by Situations and Sequence Types?Arithmetic sequences, geometric sequences, quadratic sequences, and special sequences are the four primary categories of distinct sequences you need to be familiar with. A sequence is an ordered list of components that follows a predetermined pattern.
As an illustration, the sequence 3, 7, 11, 15,... is one because it follows a pattern where each term is created by adding 4 to the word before it. Simple to complicated, prerequisite learning, whole to portion, and chronology are the sequencing concepts outlined by Print (1993 as quoted in Edith Cowan University, 2001) for content.
The acceptance of these four guidelines as the standards for content sequencing has increased. I consume 1 cookie the first time, then 1/2 the second. I'll eat half of the previous serving every time after that.
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How do you describe the graph of linear equation in terms of its intercept and?
The slope-intercept form of the equation is y = - mx + b.
The equation of a line can be expressed in a variety of ways. Although they may differ in appearance, all of them describe the same line because multiple equations can describe the same line. However, all linear equations describing the same line are equivalent.
The formula y = mx + b can be used to represent any straight line. Any straight line equation, known as a linear equation, can be expressed as y = mx + b, where m denotes the line's slope and b its y-intercept. The value of y at the line's intersection with the y-axis is its y-intercept.
Given a graph of the equation, choose two points on the line and use them to calculate the slope in order to put the equation in slope-intercept form. This is the answer to the equation's question. Next, determine the y-coordinates, intercept's which should be of the type (0,b). The value in the equation is the y-coordinate.
Thus, the equation derived from the graph is as follows:
Since we are aware that the slope here is negative,
Therefore Our formula is y = -mx + b.
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Which problem could be solved using this equation?
12x + 3 = 39
A. Three eggs fewer than some dozen make a total of 39 eggs. How many dozens are there?
B. One dozen regular milk cartons and some 3-packs of chocolate
milk make a total a of 39 cartons.
How many 3-packs are there?
C. An order with 12 books and 3 magazines is in a box of a 39 items.
How many other items are in the box?
D. Three inches and some number of feet have a total measurement a
of 39 inches. How many feet are there?
Answer:
C is the corect answer
Step-by-step explanation:
12x+3=39
12x=39-3
12x=36
x=36:12
x=3
12×3=36
36+3=39
a + 3 1/4 = 5 2/9 what is a
Answer:
a=-1/4
Step-by-step explanation:
a+3 1/4 =5 2/9
change to improper fraction
a+13/4 = 47/9
make sure that both fractions have the same denominator
a+(13/4)9=(47/9)4
a+117/36=108/36
make sure that variable is alone on one side
a=108/36-117/36
a=-9/36= -1/4
a=-1/4
Step-by-step explanation:
a+3 1/4 =5 2/9
change to improper fraction
a+13/4 = 47/9
make sure that both fractions have the same denominator
a+(13/4)9=(47/9)4
a+117/36=108/36
make sure that variable is alone on one side
a=108/36-117/36
a=-9/36= -1/4
each apple got 1.32 per pound.if Evenly bought 3 pounds ,how much did she pay?
The amount paid by Evenly will be $3.96.
How to calculate the expression?An expression is simply used to show the relationship between the variables that are provided or the data given regarding an information. In this case, it is vital to note that they have at least two terms which have to be related by through an operator.
Some of the mathematical operations that are illustrated in this case include addition, subtraction, etc.
Since each apple got 1.32 per pound. When Evenly bought 3 pounds. The amount paid will be:
= 1.32 × 3
= $3.96
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what is the inequality represented by the following graph.
Answer:
x > 2
Step-by-step explanation:
3. It is given that y is directly proportional to at Write down the value of n when (1)y m² is the area of a square of length x m
(ii) y em' is the volume of a cube of length x cm
The value of n when y m is the area of a square of length x m, is 2
The value of n when y cm is the volume of a cube of length x cm, is 3
How to find the value of nFor area of square, the formula is given by
= length * length
assuming the length is equal to x
= x * x
= x²
comparing with given formula shows that n = 2
For volume of a cube of length x cm, the formula is given by
= length * length * length
= x * x * x
= x³
comparing with given formula shows that n = 3
complete question
It is given that y is directly proportional to x".
Write down the value of n when
(i) y m? is the area of a square of length x m,
(ii) y cm is the volume of a cube of length x cm.
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The point a has coordinates (-4,10) and the point b has coordinates (3,11). The line l passes through a and b .Find an equation of l.
The equation y = x / 7 + 74 / 7 is the line that passes through points (- 4, 10) and (3, 11).
How to determine the equation of line from the knowledge of two points on a plane
In this question we must derive the equation of the line that passes through two points: (x₁, y₁) = (- 4, 10), (x₂, y₂) = (3, 11). Algebraically speaking, lines are described by equations of the form:
y = m · x + b
Where:
m - Slopex - Independent variable.b - Intercepty - Dependent variable.And the slope of the line can be calculated by secant line formula:
m = Δy / Δx
Where:
Δx - Change in independent variable.Δy - Change in dependent variable.First, determine the slope of the line:
m = (11 - 10) / [3 - (- 4)]
m = 1 / 7
Second, determine the intercept of the line:
b = y - m · x
b = 11 - (1 / 7) · 3
b = 11 - 3 / 7
b = 74 / 7
Third, write the equation of the line:
y = x / 7 + 74 / 7
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I need help on this imagine math question last one due tonight!
the length of the side of square a is 50% of the length of square b
Answer:
so the length of square b is 50%.
road to white house assignment math HELP
PLEASEEE
The value of the difference of the value of functions at x = 4 and -5 can be obtained as -39.
What is a function?A function y = f(x) can be defined as a one to one relation between sets X and Y. The set X is called the domain and Y is called the range of the function.
The given functions are f(x) = 3/2x + 2 and g(x) = 2x² - 3
Then, the value of given functions at x = 4 and -5 can be calculated as,
f(4) = 3/2 × 4 + 2 = 8.
And, g(-5) = 2 × -5² - 3 = 47
Thus, the value of f(4) - g(-5) can be calculated as,
⇒ f(4) - g(-5) = 8 - 47 = -39
Hence, the required value can be obtained as -39.
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x+3=4x
solve for x
please i need it for a test
Answer:
x=1
Step-by-step explanation:
x+3=4x
x-4x+3=0
-3x=-3
x= -3/-3
x=1
Answer:
X = 1
Hope this helps!!
Solve the following system:
4x+3y=-2 and 6y=-4-8x
Answer:
0=0
Step-by-step explanation:
6(4x+3y)=6(-2)
3(8x+6y)=3(-4)
24x+18y=-12
24x+18y=-12
0=0
Percy puts $600.00 into an account to use for school expenses. The account earns 4%
interest, compounded annually. How much will be in the account after 5 years?
- P(1 + A)”, ' where A is the balance (final amount), P is the principal
Use the formula A = P
(starting amount), r is the interest rate expressed as a decimal, n is the number of times per
year that the interest is compounded, and t is the time in years.
Round your answer to the nearest cent.
$
Percy will have an amount of $730 in her account.
What is interest?Interest is the price you pay to borrow money or the cost you charge to lend money.
Given that, Percy puts $600.00 into an account to use for school expenses. The account earns 4% interest, compounded annually, for 5 years,
Formula for CI =
[tex]A = P(1+r)^{t}[/tex]
Where, A = amount
P = principal
r = rate
t = time
Therefore,
A = 600(1+0.04)⁵
A = 600(1.04)⁵
A = 600 × 1.2166529
A = 729.99 ≈ 730
Hence, he will have $730 in her account after 5 years.
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Which numbers are solutions to the inequality 2x – 1 > x 2? check all of the boxes that apply.
Solutions to the given inequality are numbers 4 and 5. Thus, the answer is (e) and (f).
To find the solution, first, we solve the inequality for x:
2x - 1 > x + 2
2x - x > 2 + 1
x > 3
Hence, the answer is any number that is greater than 3.
Therefore, the solutions are numbers 4 and 5.
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The complete question is:
Which numbers are solutions to the inequality 2x - 1 > x + 2? Check all of the boxes that apply.
(a) 0
(b) 1
(c) 2
(d) 3
(e) 4
(f) 5
Help with nested triangle problem asap! <3
Solve for z!
The depth of water at a boat dock varies with the tides. The depth is 5 feet at low tide and. 13 feet at high tide. On a certain day, low tide occurs at 4 a.m. and high tide at 10 a.m. if y represents the depth of the water, in feet, x hours after midnight , use a sine function of the form y= A sin(Bx - C) +D
The sine function that models the depth of the tide in this problem is given as follows:
y = 4sin(π/6(x - 0.71)) + 13.
How to define the sine function?The general format for the sine function in this problem is given as follows:
y = A sin(Bx - C) + D.
In which the parameters of the function are given as follows:
A: amplitude.B: The period is of 2π/B.C: phase shift.D: vertical shift.The depth is 5 feet at low tide and 13 feet at high tide, hence the amplitude is calculated as follows:
2A = 13 - 5
2A = 8
A = 8/2
A = 4.
A sine function, with no vertical shift and amplitude of 4, would oscillate between -4 and 4, while this function oscillates between 5 and 13, hence the vertical shift is given as follows:
D = 13.
On a certain day, low tide occurs at 4 a.m. and high tide at 10 a.m, which means that half the period is of 6 hours, hence the period is of 12 hours and the coefficient B is calculated as follows:
2π/B = 12
B = π/6.
Without phase shift, the low tide would happen at x = 3π/2 a.m. = 4.71 a.m., while it happens at 4 a.m., hence the phase shift is given as follows:
c = 4.71 - 4 = 0.71.
Hence the function is defined as follows:
y = 4sin(π/6(x - 0.71)) + 13.
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Identify the percent of change as an increase or a decrease.
5/4 to 3/8
Responses
Increase
Increase
Decrease
Decrease
Question 2
Find the percent of change. Round to the nearest tenth of a percent if necessary.
The percentage of the change is 70% decrease
How to identify the percentage change as increment or decrementFrom the question, we have the following parameters that can be used in our computation:
Initial value = 5/4
Final value = 3/8
3/8 is less than 5/4
This means that the percentage is a decrease
What is the percentage change?We have
Initial value = 5/4
Final value = 3/8
The percentage change is then calculated as
Percentage change = (Final value - Initial value)/Initial value * 100%
Substitute the known values in the above equation, so, we have the following representation
Percentage change = (3/8 - 5/4)/(5/4) * 100%
Evaluate
Percentage change = -70%
Hence, the percentage change is 70% decrease
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The entities on which data are collected are population samples elements None of the above
c). The entities on which data are collected are called elements.
Data collection is a process of gathering information from different sources which is later used for analysis and interpretation. Data is usually collected from elements, which are individual units like people, organizations, or any other physical or virtual entity.
Each element has a set of characteristics or attributes which are collected to form the data. For example, if data is being collected from people, the attributes would include age, gender, occupation, income, etc. This data is then collected and stored in some form that can be used for further analysis.
Data can also be collected from populations, which are a collection of elements or a group of elements with certain features in common. In this case, the data collected is the average of all the elements in the population, rather than data from individual elements.
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Why are Fortune 500 companies engaging, in blogging? What sources capital for a project by raising many small amounts from a large number of individuals, typically via the Internet?
A popular way for people to share information and thoughts with others online is through blogging.
A blog is a conversation or informational website published on the World Wide Web that is composed of discrete, frequently informal diary-style text posts, according to the definition of a blog provided by Wikipedia.
This has given rise to a brand-new trend where everyone may now voice their opinions on a given subject.
Other phenomena and artefacts, such as analogue signals, poetry, photographs, music, or other sounds, as well as electrical currents, transmit information in a more continuous manner than do digital signals and other data, which employ discrete signs or algebras to do so.
Information itself is not knowledge, but how it is interpreted is crucial. Raw information can also take the shape of structured data. A collection of data may contain information that may be extracted through analysis by analysts who are experts in their field.
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