Using Sphere geometry formulas , 2.45 ft/min is increasing rate of spherical ballon when the diameter is 1.5 feet.
Sphere is a three dimensional form of circle .
let V and D be volume and diameter of the sphere. we have given that ,
Volume increasing rate of spherical ballon (dV/dt)
= 3.7 ft³/min
diameter of sphere at time of increasing = 1.5 feet
the increasing rate of spherical ballon is dD/dt.
Now, Volume of sphere (V) = 4/3π³ ft³
or we know that D = r/2 so,
V = 4/3 π (D)³×8 ft³
differentating both sides we get ,
dV/dt = 32/8π 3D³dD/dt
=> 3.7 = 32/3 (3.14)(1.5)²dD/dt
=> dD/dt= 2.45 feet/min
Hence, 2.45 ft/min is the rate of the diameter of the balloon increasing when the diameter is 1.5 feet.
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If the half life of a radioactive
substance is 5.3 years and there are
8.4 grams present initially, when will
there be 1 gram remaining?
[?] years
Use the function f(t) = Pert and round
your answer to the nearest year.
Enter
Joan has $ 60 to buy her friends a gift bag. The gift bags are $ 4 each. The function f ( x ) = − 4 x + 60 represents the amount of money Joan has left in her budget after purchasing x number of gift bags. Complete the statements. The solution for f ( x ) = 72 is x = [DROP DOWN 1] which [DROP DOWN 2] a viable solution in this scenario.
DROP DOWN 1
-3
-15
3
15
DROP DOWN 2
is
is not
The solution for f ( x ) = 72 is x = -3 ; which is not a viable solution in this scenario.
What is the solution for the function instance as given in the task content?It follows from the task content that the solution for the function instance, f(x) = 72 is to be determined according to the given function.
Since the given function is; f ( x ) = − 4 x + 60;
The solution for f (x) = 72 can be determined as follows;
72 = - 4 x + 60
- 4x = 72 - 60
- 4x = 12
x = 12/-4
x = - 3
On this note, since x = -3 which is negative; it follows that it is not a a viable solution in this regard.
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Part 2 - Find the error(s) and solve the problem correctly.
The error made in the calculation was improper use of quotient rule of logarithm
How to solve the logarithm equation correctlyThe problem will be solved by using the rules of logarithm as done below
logₐ 2x + 2 ( logₐ x - logₐ y )
expanding the parenthesis
logₐ 2x + 2logₐ x - 2logₐ y
applying exponential rule of logarithm
logₐ 2x + logₐ x² - logₐ y²
applying product rule of logarithm
logₐ (2x * x²) - logₐ y²
logₐ (2x³) - logₐ y²
applying quotient rule of logarithm
logₐ (2x³/ y²)
The error was that the quotient rule of logarithm was not properly applied
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One dimension of a rectangle is 3 more than twice the other dimension. Let x be the
shortest dimension. Write an equation for the area of the rectangle.
A= x + 2x + 3
A = x(2x + 3)
A= 3x +2
A= 2x +3
The area of the rectangle with one dimension sizes three more than twice the other dimension is A= x(2x+3)
We assume that there is rectangle ABCD with lines AB and CD are parallel with each other. Meanwhile lines BC and DA are parallel with each other. We could ssume that lines BC and DA are the shortest lines.
Please take a look at the picture below.
Based on the formula of rectangle, the area of rectangle could be calculated using the multiple between the longest line and the shortest line.
It could be written based on the rectangle we have into such formula:
A = AB × BC
A = CD × DA
A = AB × DA
A = CD × BC
If we input the rules from the question, then we could find the relationship between the shortest and the longest lines. Hence:
AB = CD = 2(BC) + 3
AB = CD = 2(DA) +3
if we assume that the shortest line is x, then we will get the formula:
BC = DA = x ...(1)
AB = CD = 2x+3 ...(2)
If we input equation (1) and (2) into the rectangle area formula, we will get the result:
A = AB × BC
A = (2x+3)
A = x(2x+3)
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Solve the equation
2x²+ 8x - 1 = 0
by completing the square.
Give your answers correct to 2 decimal places.
Answer:
x = 0.08
Step-by-step explanation:
2x²+ 8x - 1 = 0
4x + 8x - 1 = 0
12x - 1 = 0
Add 1 to the -1 and to the 0 too
12x = 1
Divide both side
x = 0.08
What is the equation of this line in standard form?
A - 9x−8y=23
B - 8x−9y=−23
C - 8x−9y=23
D
8x−7y=−25
Answer:
The correct answer is B
Step-by-step explanation:
I went a weird way to get this. I wrot the line in the slope intercept form and then converted it to the standare form.
For the slope intercept form I need a slope and a y interctp. I used the two points given to find the slope. The slope is the change in y over the change in x. From the points the y values are 3 and -1. The x values are 1.2 and -4
[tex]\frac{3 - -1}{\frac{1}{2}- - 4 }[/tex] = [tex]\frac{3+1}{\frac{1}{4}+4 }[/tex] = [tex]\frac{4}{\frac{9}{2} }[/tex]
4 ÷[tex]\frac{9}{2}[/tex] = [tex]\frac{4}{1}[/tex] x [tex]\frac{2}{9}[/tex] = [tex]\frac{8}{9}[/tex]
[tex]\frac{8}{9}[/tex] is the slope
Now to find the y intercept
I will use
slope [tex]\frac{8}{9}[/tex] (m)
y = -1 from the point (-4,-1) given
x = -4 from the point (-4,-1) given
y=mx + b
-1 = [tex]\frac{8}{9}[/tex](-4) + b
-1 = [tex]\frac{-32}{9}[/tex]x + b Add [tex]\frac{32}{9}[/tex] to both sides
[tex]\frac{23}{9}[/tex] = b
y = [tex]\frac{8}{9}[/tex]x + [tex]\frac{23}{9}[/tex] Multiply all the way thorugh by 9
9y = 8x + 23 Subtract 9y from both sides
0 = 8x -9y + 23 Subtract 23 from both sides
-23 = 8x -9y
or
8x -9y = -23
Hot dogs are sold in packages of 10. Hot dog buns are
sold in packages of 8. What is the least number of
packages of each that need to be purchased so every
hot dog you buy for a picnic will have a bun?
Answer:
4 Hot dogs packages and 5 hot dog buns packages.
Step-by-step explanation:
This question seems to be regarding the LCM or the least common multiple. Least common multiple is found by figuring out the first time when both numbers, in this case 10 and 8 have the multiple. You can do this by setting up a table with the multiples of each number.
8 | 16 | 24 | 32 | 40
10 | 20| 30 | 40
We can see that the LCM is 40 so we can see that we need 4 Hot Dog packets and 5 buns packets.
PLEASE HELP. I need both the x and y and the length of DF
The value of x is 17, y is 2 and length of DF is 20.
Basic Proportionality Theorem (can be abbreviated as BPT) states that, if a line is parallel to a side of a triangle which intersects the other sides into two distinct points, then the line divides those sides in proportion.
For x
DG = GE ( Given )
DG + GE = DE
DE = 2(DG)
DG/DE = 1/2
hence GH/EF = 1/2
By Basic Proportionality Theorem ( BPT )
(x – 3) / 28 = 1/2
after cross multiplication
2(x – 3) = 28
2x – 6 = 28
2x = 34
x = 17
For y
By Basic Proportionality Theorem (BPT) to side DF
DF = 2(DH)
DH/DF = 1/2
(y + 8) / (y + 8 + x – 7) = 1/2
after cross multiplication
2(y + 8) = y + 8 + x – 7
put x = 17
2(y + 8) = y + 8 + 17 – 7
2(y + 8) = y + 18
2y + 16 = y + 18
2y = y + 2
2y – y = 2
y = 2
DF = 2(2+8)
= 2(10)
= 20
Hence, x is 17, y is 2 and DF is 20.
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1.Find the y-intercept of (2,4) and (4, 8) and
2.What is the slope of the points that go through (2,4) and (4, 8)
3.Upload a picture of the slope intercept form of the points (2,4) and (4, 8)
Answer:
1. Y = 2x
2. 2
3.
Step-by-step explanation:
2. Slope = (y2- y1)/(x2-x1)
(8-4)/(4-2)
4/2
2
3.
The purchase price of an iPad is $610. If the sales tax rate is 6.5%, what is the amount of sales tax?
Answer:
Step-by-step explanation:
$603.5
Answer:39.65
Step-by-step explanation:
turn 6.5% to 0.065
610 x 0.065=39.65
The edges of a rectangular solid have these measures: 1. 5 feet by 1½ feet by 3 inches. What is its volume in cubic inches?.
Volume of the rectangular solid in cubic inches for the given measures of edges 1. 5 feet by 1½ feet by 3 inches is equal to 972 cubic inches.
As given in the question,
Given measures of edges of the rectangular solid is equal to :
1. 5 feet by 1½ feet by 3 inches
Length = 1.5 feet
Conversion 1 feet = 12 inches
1.5 feet = 1.5 × 12
= 18 inches
Width = 1½ feet
= 3/2 feet
= ( 3/2 ) × 12
= 18 inches
height = 3 inches
Volume of the rectangular solid = length × width × height
= 18 × 18 × 3
= 972 cubic inches
Therefore, volume of the rectangular solid in cubic inches for the given measures of edges 1. 5 feet by 1½ feet by 3 inches is equal to 972 cubic inches.
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Patrick has a rectangular backyard at his new house. After he built a square brick patio, he planted grass in the rest of the yard, as shown below. The grass area is 656 square feet. Two measurements of the grass region are shown in the diagram below. What is the side length of the square patio? Note: The figure is not drawn to scale.
Answer:
Step-by-step explanation:
Answer:
Step-by-step explanation:
2x4+6+5x8=_______________
will mark brainiest
The simplification of the given expression will be 54.
What is a numerical expression?A numerical expression is algebraic information stated in the form of numbers and variables that are unknown. Information can is used to generate numerical expressions.
Given that the expression is 2 x 4 + 6 + 5 thex 8
To solve the given expression we have to first solve the multiplication operation.
2 x 4 + 6 + 5 x 8
8 + 6 + 40
Now add the terms;
8 + 6 + 40
= 54
Hence, the simplification of the given expression will be 54.
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a
b
c
d
which is the right answer
The function is odd because f(-x) = -f(x)
What is a Function?
A function is an expression, rule, or law in mathematics that describes a connection between one variable (the independent variable) and another variable (the dependent variable).
Solution:
For a function to be even it must satisfy the condition that,
f(-x) = f(x)
else,
if f(-x) = -f(x), then the function is odd
we are given with the function f(x) = [tex]4x^{3}[/tex]
replacing x by (-x)
f(-x) = 4(-x)^3
f(-x) = -4x^3
this implies that, f(-x) = -f(x)
Therefore, the function is an odd function
So, option D is correct
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which graph represents y=-2x
A graph which represents the linear function y = -2x is: graph B.
What is a graph?In Mathematics, a graph can be defined as a type of chart that is typically used for the graphical representation of data points or ordered pairs on both the horizontal and vertical lines of a cartesian coordinate, which are the x-axis and y-axis respectively.
Generally speaking, the graph of any proportional relationship is characterized by a straight line with the data points passing through the origin (0, 0) because as the values on the x-axis (x-coordinate) either increases or decreases, the values on the y-axis (y-coordinate) increases or decreases simultaneously.
In this context, we can reasonably infer and logically deduce that the relationship between x-values and y-values in the graph of y = -2x is proportional as it passes through the origin (0, 0).
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dan goe from birmingham to coventry by bu. he take 5 minute to walk from hi houe to the bu top in birmingham. he take 20 minute to walk from the bu top in coventry to work. dan ha to get to work by 10.30 am. what i the latet time dan hould leave hi houe to get to work on time?
The latest time Dan should leave his house to get to work on time will be 10: 05 am.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.
Dan goes from Birmingham to Coventry by Bu. Be goes for 5 moments to stroll from greetings houe to the bu top in Birmingham. He goes for 20 moments to stroll from the Bu top in Coventry to work. Dan has to get to work by 10.30 am.
The total time is given as,
⇒ 5 + 20
⇒ 25 minutes
The latest time Dan should leave his house to get to work on time will be given as,
10: 30 am
- 00: 25
10: 05 am
The latest time Dan should leave his house to get to work on time will be 10: 05 am.
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wich is the smallest angle in MNO?
For the given triangle MNO, as per the given measurements the smallest angle among all the three angles is ∠M.
As given in the question,
In the given triangle MNO,
Measure of the sides of the triangle are as follow:
MN = 18 yd
NO = 17 yd
MO = 19 yd
Arrange them in ascending order we have,
17 < 18 < 19
NO < MN < MO
From the given measurement of the sides of the triangle , smallest side is NO.
Angle opposite to side MN = ∠O
Angle opposite to side NO = ∠M
Angle opposite to side MO = ∠N
Angle opposite to the smallest side is the smallest angle.
∠M is the smallest angle.
Therefore, for the given triangle MNO, as per the given measurements the smallest angle among all the three angles is ∠M.
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Can someone help me with this
table student is in 3nf. student studentid ssn name class d111 111-11-1111 connor freshman d222 222-22-2222 trevor freshman d333 333-33-3333 connor sophomore d444 444-44-4444 parker sophomore d555 555-55-5555 connor sophomore group of answer choices true false
Functional dependency SSN --> Name exists in the table STUDENT is TRUE, The correct option is (A)
due to the fact that a student ID is a primary key in a table and that (StudentID, SSN) can also combine to form a composite key that can be used to identify a record in a table in a unique way. The augmented functional dependency between the StudentID and SSN enables you to locate additional data in the table. However, using only StudentID will also assist you in finding data in the table.
Since it could be a candidate key, this is true because it can be used in part of augmented functional dependency.
Thus, the SSN matches the name in the STUDENT table.
So, SSN ----> Name holds in STUDENT table.
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(complete question)
Observe the table STUDENT:
STUDENT
StudentID SSN Name Class
D111 111-11-1111 Connor Freshman
D222 222-22-2222 Trevor Freshman
D333 333-33-3333 Connor Sophomore
D444 444-44-4444 Parker Sophomore
D555 555-55-5555 Connor Sophomore
Functional dependency SSN --> Name exists in the table STUDENT.
True
False
-3(x + 4) + 5x simplify
Answer:
Answer: 2x-12
Step-by-step explanation:
First, you distribute and then combine like terms. :)
Answer:
Step-by-step explanation:
Step 1 : Distribute
The distributive property is a rule in mathematics that is used to help simplify equations by using brackets
-3(x+4) + 5x
-3x - 12 + 5x
Step 2 : combine similar tribes
Similar terms are terms in algebra that have the same variables or constants in algebra. Similar terms of the algebraic form above are. Similar terms are terms in algebra that have the same variables or constants in algebra.
-3x - 12 + 5x
2x - 12
Step 3 : common factor
Common factor is the same factor of two or more numbers. For example, the factors of the numbers 18 and 12 can be determined in the following way. So, the common factors of these two numbers are 2, 3, and 6.
2x - 12
2 (x-6)
Completion
2(x-6)
Which of the following is an example of a data set with 5 values for which the standard deviation is zero. a) -2.-1.0.1.2 b) 4.4.4.4.4 c) -5,-3.0.3.5 d) 1,2,3,4,5
The standard deviation for the dataset (4, 4, 4, 4, 4) is zero (0)
To find a data set with 5 values for which the standard deviation is zero,
⇒ (4, 4, 4, 4, 4)
For the above dataset;
Mean μ = 4
Number of samples n = 5
Standard deviation σ = [tex]\sqrt{\frac{sumof(xi - x)^2}{n} }[/tex]
= [tex]\sqrt{\frac{(4-4)^2+(4-4)^2+(4-4)^2+(4-4)^2+(4-4)^2}{5} }[/tex]
= 0
Therefore, for the dataset (4, 4, 4, 4, 4) the standard deviation is zero(0).
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The regular price of swimming lessons is $20 per hour. The sale price for new students is 75% of the regula
price. What is the sales price?
The federal unemployment tax act (futa) is a payroll tax paid by employers on employee wages. The tax is 6. 0% on the first $7,000 an employee earns each year. If walmart has 1. 5 million employees in the u. S. , about how much does it pay in futa taxes annually?.
The amount of tax that Walmart pay annually in FUTA is $630 million .
In the question ,
it is given that ,
the amount that an employee earns in 1 year(E) = $7000
the tax rate (r) = 6%
number of employees in Walmart = 1.5 million = 1.5 × 10⁶
So , the amount of tax paid by Walmart in Federal Unemployment Tax Act(FUTA) can be calculated using the formula
Amount = r × n × E
Substituting the values of r , n , E in the amount formula ,
we get ,
Amount = 0.06 × 1.5 × 10⁶ × 7000
= 630,000,000
= 630 million .
Therefore , The amount of tax that Walmart pay annually in FUTA is $630 million .
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A base-10 three digit number $n$ is selected at random. Which of the following is closest to the probability that the base-9 representation and the base-11 representation of $n$ are both three-digit numerals?
A. 0.3 B. 0.4 C. 0.5 D. 0.6 E. 0.7
The probability that the representation in base-9 and the representation in base-11 are both three-digit numbers is 0.6753 which is approximately 0.7 option E.
Given,
We require the following inputs to determine the probability that both the base-9 representation and the base-11 representation are three-digit numbers:
The lowest base 10-based 3-digit base-11 numberThe largest three-digit base 9 in base 10 number.The total amount of 3-digit base-10 numbersThe base-11's lowest 3-digit number is 100.
The comparable number is 121 when expressed in base 10.
888 is the biggest 3-digit base-9 number.
The corresponding number is 728 when expressed in base 10.
As a result, there are the following possibilities:
Possibilities = 728 - 121 + 1
Possibilities = 608
The total number of 3-digit base-10 numbers is
Count = 999 - 100 + 1
Count = 900
The necessary probability is:
P = 608/900
Evaluate
P = 0.6753 ≈ 0.7
Therefore,
The probability that the representation in base-9 and the representation in base-11 are both three-digit numbers is 0.6753 which is approximately 0.7 option E.
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Can you guys help me please bc I tried this and I got it wrong .
Answer:
[tex]\frac{1}{3}[/tex]
Step-by-step explanation:
you multiply the denominator with the denominator and the numerator with the numerator
[tex]\frac{5}{6}x\frac{2}{5}[/tex]
[tex]\frac{5x2}{6x5}[/tex]
[tex]\frac{10}{30}[/tex]
[tex]\frac{1}{3}[/tex]
Hopes this helps please mark brainliest
Convert years to days. 7 years = x |_ *( days year) days)
I ment middle school not high
Answer:
2555 days
Step-by-step explanation:
1 year is 365 days, and 365 x 7 = 2555.
A wholesale food supplier charges x dollars for each bag of flour and y dollars for each bag of sugar. Bakery A purchases seven bags of flour and five bags of sugar for a total cost of $260.45. Bakery B purchases five bags of flour and three bags of sugar for a total cost of $171.35. What is the cost of each bag of flour? Each bag of sugar?
The cost of each bag of flour is $ 18.85 and the cost of each bag of $ 25.7 which a wholesale food supplier charges for each bag of flour and for each bag of sugar.
Given that:
The cost of each bag of flour = x dollars
The cost of each bag of sugar = y dollars
Bakery A purchases seven bags of flour and five bags of sugar for a total cost of $260.45.
Bakery B purchases five bags of flour and three bags of sugar for a total cost of $171.35.
Making equation from both the above statements. We get,
7x + 5y = 260.45 ...... (1)
5x + 3 y = 171.35 ....... (2)
Multiplying equation (1) by 5 and equation (2) by 7. We get the value,
35x + 25y = 1302.25 ....... (3)
35x + 21y = 1199.45 ........ (4)
Subtracting equation (4) from (3). We get,
4y = 102.80
=> y = $ 25.70
Putting the value of y in equation (1). We get,
7x + 25.70 x 5 = 260.45
7x = 260.45 - 128.5
7x = 131.95/7
=> x = $ 18.85
Hence, we can say that a wholesale food supplier charges 18.85 dollars for each bag of flour and 25.7 dollars for each bag of sugar.
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a) How many times does the line y = -6 intersect with the circle x² + y² = 36 ?
b) Hence, use a single word to describe what the line is to the circle.
Answer:
a) Once,b) Tangent.Step-by-step explanation:
Part AGeneral equation of circle:
(x - h)² + (y - k)² = r², where (h, k) is center and r- radiusComparing with the general equation we see that the circle x² + y² = 36 has:
Center at the origin,Radius of 6 units.The circle radius of 6 units, so y = - 6 has only one common point.
Part BSince there is only one common point of the circle and line, the line is tangent to the circle.
Solve the equation. 3 + |t + 4| = 10
Question 9 options:
[-3, 11]
[-11, 3]
[3, 11]
[-3, -11]
Answer:
b) [-11, 3]
Step-by-step explanation:
Given equation,
→ 3 + |t + 4| = 10
Now the value of t will be,
→ 3 + |t + 4| = 10
→ 3 + t + 4 = 10 || → 3 -(t + 4) = 10
→ t + 7 = 10 || → -t - 1 = 10
→ t = 10 - 7 || → -t = 10 + 1
→ [ t = 3 ] || → [ t = -11 ]
Hence, value of t is 3 (or) -11.
Two Tofurkys will serve six people. How many people will fourteen Tofurkys serve?
Answer:
7
Step-by-step explanation: