The air is filled inside the balloon at the rate of 1600π cm³/sec.
What is termed as the rate of change?The momentum of a variable is represented by the rate of change, which is used to arithmetically define the percentage change in value over a specified period of time.The amount of air blown through will be evaluated in volume per unit of time. That is the rate at which volume changes with respect to time.The rate during which air is blown into the balloon is identical to the rate that the volume of a balloon grows.
Volume of the spherical balloon;
V = (4/3)πr³
Given is dr/dt = 4 cm/sec.
To calculate the volume change with respect to time.
dV/dt when r = 10 cm.
Differentiate V = (4/3)πr³ with respect to t.
d(V)/dt = (d/dt)(4/3)πr³
dV/dt = (4/3)π. 3r² dr/dt
dV/dt = 4πr² dr/dt
Put the values.
dV/dt = 4π(10)² .(4)
dV/dt = 1600π cm³/sec
Thus, air is filled inside the balloon at the rate of 1600π cm³/sec.
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Your answer 6 points Dawn has 3 1/4 cups of cinnamon. She uses 1/2 cup of cinnamon in each batch of rolls she bakes. How many batches of rolls can Dawn make with the cinnamon she has? 1 5/8.3 7/866 1/2
She uses 1/2 cup in each batch.
So, if she has 3 1/4 cups in total, we have to divide this total by 1/2 to know how many batchs she can make:
[tex]\frac{\text{Total}}{\text{Batch}}=\frac{3+\frac{1}{4}}{\frac{1}{2}}=\frac{\frac{3\cdot4}{4}+\frac{1}{4}}{\frac{1}{2}}=\frac{12+1}{4}\cdot2=\frac{13}{2}=\frac{12}{2}+\frac{1}{2}=6+\frac{1}{2}[/tex]She can make 6 1/2 batches.
please help asap for 50 points. The Smith and Jones manufacturing company keeps a third of its cash in the bank, which pays 0.5% interest, and the other two-thirds in long-term investments that give 3.5% interest. If the company earned a total of $37,500 in interest last year, how much cash did they keep in the bank?
Based on the calculation below, the amount of cash that the Smith and Jones manufacturing company kept in the bank was $500,000.
How do we calculate amount kept in the bank?Let x represents the amount of cash that Smith and Jones manufacturing company has.
Therefore, we have:
Interest amount from bank = Cash * A third * Bank interest rate = x * (1/3) * 0.5% = x0.0017
Interest amount from long-term investments = Cash * Two-third * Long-term investments interest rate = x * (2/3) * 3.5% = x0.023
Total interest earned = Interest amount from bank + Interest amount from long-term investments = $37,500 ...................... (1)
Substituting all the relevant values into equation (1) and solve for x, we have:
x0.0017 + x0.023 = $37,500
x0.025 = $37,500
x = $37,500 / 0.025
x = $1,500,000
Amount kept in the bank = Cash * A third = $1,500,000 * (1 / 3) = $500,000
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A certain video game console uses 154 watt-hours of energy each hour.
The console used 276 hours last year.
How many watt-hours of energy did the console use?
***Show the equation you used to solve this problem.
Use any method to solve this problem. You must show all your work.
By taking a product, we can see that the total energy consumed by the console is 42,504 watt-hours.
How many watt-hours of energy the console used?Here we know that the console uses 154 watt-hours of energy each hour.
So, if you use it for x hours, the energy consumed is given by the product:
E = ( 154 watt-hours)*x
In this case, we know that the console is used for 276 hours, then we can write:
E = (154 watt-hours)*276 = 42,504 watt-hours.
Which is the product between the hourly consumption and the number of hours used.
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Yasmin is taking a multiple choice test with a total of 20 points available. Each question is worth exactly 1 point. What would be Yasmin's test score (out of 20) if she got 2 questions wrong? What would be her score if she got x questions wrong?
Answer:
• score with two questions wrong = 18
• score with x questions wrong = (20 - x)
Step-by-step explanation:
The question is divided into two parts.
The first part asks us to calculate the marks that would be scored out of 20 if someone got 2 questions wrong. To do this we simply have to subtract 2 from 20 to get the score:
score = 20 - 2
= 18
Therefore, Yasmin's score would be 18.
The second part asks us to calculate the marks that would be scored if someone got x questions wrong instead. As we did in the first part, we have to take away x from 20 in order to get the score:
score = 20 - x,
where x can be any whole number.
Therefore, Yasmin's score would be (20-x).
Joshua has 245 feet of fence. His rectangular yard is 54 feet by 78 feet. Does Joshua have enough fence for his yard?
We can calculate the perimeter of the rectangular yard to find out how much fence Joshua needs:
[tex]P=2(78+54)=2(132)=264ft[/tex]since the perimeter of the yard is 264 yards, then Joshua does not have enough fence for his yard, since he only has 245 t of fence, and he needs 264ft
A student writes the inequality representing the graph as y ≥ –2(x – 10)2 + 200.
The inequality is
because testing the point (5, 100) simplifies to the inequality
Answer:
A student writes the inequality representing the graph as y ≥ –2(x – 10)2 + 200.
The inequality is
✔ incorrect
because testing the point (5, 100) simplifies to the inequality
✔ 100 ≥ 150
.
Step-by-step explanation:
A student writes the inequality representing the graph as y ≥ –2(x – 10)2 + 200.
The inequality is
✔ incorrect
because testing the point (5, 100) simplifies to the inequality
✔ 100 ≥ 150
.
The inequality is incorrect because testing the point (5, 100) simplifies to the inequality 100 ≥ 150.
What is an inequality?An inequality can be defined as a mathematical relation that is typically used for comparing two (2) or more numerical data and variables in an equation based on any of the following arguments (symbols):
Greater than (>).Greater than or equal to (≥).Less than (<).Less than or equal to (≤).Next, we would evaluate and simplify the given inequality in order to determine its solution as follows:
y ≥ –2(x – 10)² + 200.
At point (5, 100), we have:
100 ≥ –2(5 – 10)² + 200.
100 ≥ –2(-5)² + 200.
100 ≥ –2(25) + 200.
100 ≥ –50 + 200.
100 ≥ 150 (incorrect and false).
In conclusion, the given inequality is incorrect because 100 cannot be greater than or equal to 150.
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Compete Question;
A student writes the inequality representing the graph as y ≥ –2(x – 10)² + 200.
The inequality is ______ because testing the point (5, 100) simplifies to the inequality _____.
what is the answer to 9,379-4,312
Answer:
5,067
Step-by-step explanation:
9,379-4,312=5,067
Answer:
5,067
sometimes writing the problem like this
9,379
- 4,312
can help. :)
I REALLY NEED HELP PLEASE THIS WORK IS FOR MONDAY.can y’all please help me:(
Answer:
B. the answer is 4
Step-by-step explanation:
Start by dividing miles by gallons.
So for Mitra: Divide 469.8 and 14.5 --- 469.8/14.5= 32.4
For Adira: Divide 355 and 12.5 355/ 12.5 = 28.4
Now, we just subtract the answers to find the difference.
32.4-28.4 = 4.
4 is the difference.
Nine years from now, Jack will be three times as old as he was eleven years ago. How old is he now?
Answer:
John is 16 years old now.
Check:
1) 16+5 = 21
2) 16-9 = 7
3) 21 = 7*3
Step-by-step explanation:
Hope it helps! =D
896 X 4
Two answers
Answer:
3584
Step-by-step explanation:
[tex]896[/tex]×[tex]4[/tex] =[tex]3584[/tex] (refer as table of 896).
hope it help :)
Determine which integer will make the inequality 4x + 6 < 2x + 12 false.
S:{1}
S:{−1}
S:{4}
S:{−4}
Answer:
s:{4}
Step-by-step explanation:
4(4)+6<2(4)+12
16+6<8+12
32<20
which is the only false one
Find the equation of the line that goes through the points (2, 10) and (-1, -2).
Answer:
y=4x+1
Step-by-step explanation:
Step 1: plot your points
Step 2: draw a line through them
Step 3: find the slope (RISE/RUN) = 12/3 = 4
Step 4: find the y-int = 1
y=mx+b where x and y are variables, m is the slope and b is the y-int
y = 4x + 1
Hope that helps
Question 4 (10 point)
Answer:
25
Step-by-step explanation:
25 is the square root of 625
Answer:
25
Step-by-step explanation:
[tex]\sqrt{625} = \sqrt{25^{2} } = 25[/tex]
A student receives the following grades with and A worth 4 points, a B worth 3 point, a C worth 2 points, and a D worth 1 point. What is the students weighted mean grade point score?
B in 2 three-credit classes
D in 1 three-credit class
A in 1 four-credit class
C in 1 four-credit class
Mean grade point is ___
2.33 is the student's GPA using the average weighted mean.
What is Mean?The mathematical average of a group of two or more numbers is called the mean. There are two different types of means that can be calculated: the arithmetic means and the geometric mean. The arithmetic mean is calculated by adding all of the numbers in a set and dividing by the total number of numbers in the set.So, the weighted average is calculated by multiplying each grade by its weight and dividing the result by the total weights.
In three three-credit classes, the student earned three Bs.A D in three-credit course results in a grade of 1, weighted at 3.Consequently, a C earns a grade of 2, which has a weight of 4.Consequently, a C earns a student two credits and a weight of 2.It is as follows:
[tex]M=\frac{3 \times 3 \times 3+1(3)+2(4)+2(2)}{9+3+4+2}=\frac{12}{18}=2.33[/tex]
Therefore, 2.33 is the student's GPA using the average weighted mean.
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Please help me!! I was absent when class learned this but teacher is still making me do homework!!! I have no idea how to do this!! Please help!! Need now!!
Answer:
a. (2x−9)(x+3)
b. (2x+11)(2x−11)
c. (3x−2)(2x+5)
d. (3x+4)(x+1)
e. (5x+3)(x−9)
f. (2x+5)(2x−7)
g. 4(3x+5)(3x−5)
h. 3(2x+5)(2x+5)
Step-by-step explanation:
Answer:
Lol, I recommend you ask your teacher later how to factor :]
It's kinda hard to explain. Tell me if I got any wrong :]
Step-by-step explanation:
Ouch. Well, here I go:
a) (2x-9)(x+3)
b) (2x-11)(2x+11)
c) (3x-2)(2x+5)
d) (x+1)(3x+4)
e) (x-9)(5x+3)
f) (2x-7)(2x+5)
g) (6x-10)(6x+10)
h) (6x+15)(2x+5)
:]
Write a function store_digits that takes in an integer n and returns a linked list where each element of the list is a digit of n.
def store_digits(n):
"""Stores the digits of a positive number n in a linked list.
>>> s = store_digits(1)
>>> s
Link(1)
>>> store_digits(2345)
Link(2, Link(3, Link(4, Link(5))))
>>> store_digits(876)
Link(8, Link(7, Link(6)))
"""
"*** YOUR CODE HERE ***"
1 = Link.empty
while n > 0:
1 = Link(n % 10, 1)
n //= 10
return 1
Store Digits
In some programming languages you have to declare a variable before using them or define the information that will be stored in it, e.g., a number. However, in Python we just need to type the name of our variable, followed by an equals sign and a value to assign to it.
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Select the correct answer.
This graph represents a quadratic function.
Answer:
a = - 1
Step-by-step explanation:
given the zeros of a parabola x = a and x = b , then the factors are
(x - a) and (x - b) , then the equation is
y = a(x - a)(x - b) ← a is a multiplier
here the zeros are x = - 3 and x = 3 , then factors are
(x - (- 3) ) and (x - 3) , that is (x + 3) and (x - 3) and the equation is
y = a(x - 3)(x + 3)
to find a substitute any other point on the curve into the equation
using (0, 9 ) , then
9 = a(0 - 3)(0 + 3) = a(- 3)(3) = - 9a ( divide both sides by - 9 )
- 1 = a
To win a trivia game, Nevan must score 90 points.
Each correct answer is worth 1 3/4 points, and each incorrect answer is worth −1/4 points.
If he gets 58 questions correct and 22 questions incorrect, does Nevan win? How many points does he score?
Answer: no he does not win he got 67 points not 90 or more
Step-by-step explanation:
Question
Suppose J=[−1428].
What is the value of ∣∣J∣∣?
Enter your answer in the box.
Answer: |J|= -16
Step-by-step explanation:
The value of ∣J∣ is -16.
What is matrix?A collection of numbers lined up in rows and columns to form a rectangular array is called a matrix. The elements, or entries, of the matrix are the numbers.
Given:
[tex]J = \left[\begin{array}{ccc}-1&4\\2&8\end{array}\right][/tex]
To find the value of ∣J∣:
We have to find the determinant of matrix J.
Multiply the numbers along the diagonal from top-left to bottom-right.
Multiply the numbers along the diagonal from bottom-left to top-right.
The second product is subtracted from the first.
Get the 2-by-2 determinant's value via simplifying.
∣J∣ = {(-1x8) - (2x4)}
∣J∣ = {-8 - 8}
∣J∣ = -16
Therefore, the value of ∣J∣ is -16.
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Sanjay a is making punch. he uses 1/3 c of pineapple juice for every 3/4 c of orange juice. how many cups of pineapple juice does he need if he uses 3 c of orange
Sanjay a is making punch. he uses 1/3 c of pineapple juice for every 3/4 c of orange juice Then 4/3 cups of pineapple juice does he need if he uses 3 c of orange
equation of direct proportion between x and y
x1/y1 = x2/y2
as per given ,
let x= quantity of pineapple juice and y= quantity of orange juice
x1= 1/3 , y1 = 3/4
x2 = ? and y2 =3
x1/y1 = x2/y2
(1/3)/ (3/4) = x2/3
4/9= x2 /3
4/3 = x2
Hence ,Sanjay a is making punch. he uses 1/3 c of pineapple juice for every 3/4 c of orange juice Then 4/3 cups of pineapple juice does he need if he uses 3 c of orange
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10. Find the area of the shaded region.
17 yd
5 yd
7 yd
6 yd
7 yd
4 yd
Answer:
176 yd²
Step-by-step explanation:
You want the shaded area of a parallelogram that has a trapezoid-shaped white area.
Parallelogram areaThe area of a parallelogram is given by the formula ...
A = bh
The parallelogram shown has a base of 17 yd and a height of 7 yd +6 yd. Its area is ...
A = (17 yd)(7 yd +6 yd) = 221 yd²
Trapezoid areaThe area of the white space cut from the parallelogram is given by the formula ...
A = 1/2(b1 +b2)h
where b1 and b2 are the parallel bases of the trapezoid, and h is the distance between them.
A = 1/2(7 yd +8 yd)(6 yd) = 45 yd²
Shaded areaThe shaded area is the difference of these two areas:
shaded area = 221 yd² -45 yd² = 176 yd²
The area of the shaded region of the parallelogram is 176 yd².
Ellos ____ en la casa. (To express location)
Answer: Estan
Step-by-step explanation: I know spanish
What is x^3 pls help
Answer:
its x^3 or 1
Step-by-step explanation:
there's nothing else you can do with it
also it might be 1 because x by itself is 1 so x^3 is considered 1^3
Diane deposits the same amount of money into a bank account every month. The table below shows the amount of money in the account after different amounts of time.
Giv the table below:
Time (Months) 6 8 10 12
Money (Dollars) 476 606 736 866
(a) We are asked to find the amount that is alreafy in the account when Diane started depositing.
The amount that will be in the account before Diane started depositing will be
86 dollars.
(b) To get the rate if the money increase or decrease:
606 - 476
2
= 130/2
= 65
The money increases by 65
HELP PLS 60 POINTS , Math Law Identification.
The first law is called the Law of Detachment. The law states that if p → q and p is true, then q is true.
The second law is the Law of Syllogism. It states that If p → r and q → r, then p → r is true.
What is the use of the Law of Detachment?It is to be noted that the Law of Detachment is the most often employed deductive reasoning theory.
In other words, if a conditional statement and its hypothesis are true, the conclusion is likewise true. In other words, the conclusion may be "separated" from the conditional.
In the above instance, p is synonymous with having a cat; while q is synonymous with it chasing a rat.
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the average life of a certain type of small motor is 10 years with a standard deviation of 2 years. the manufacturer replaces free of charge any motor that fails during a warranty period. if she is willing to replace only 3% of the motors that fail, how long should should the warranty period last? assume that the lifetime of a motor follows a normal distribution.
using the normal distribution, the warranty period of motor last at 6.24 years.
According to given question , the average life of motor = 10 years and standard deviations = 2 years .
let X be the time period in which the warranty period of motor last . X ~ N( μ, σ²) where u is mean and s is standard deviations. X ~ N( 10, 2²) ⁼ N(μ, σ²)
it is given that only 3% number of motors are replaced and 3% = 0.03
Using normal distribution , P( X≤ x)= P(( X - μ )/ σ ≤ (x- μ)/σ ) = P ( Z ≤ (x- μ ) / σ ) =0.03
Z = (X- μ) / σ => X = Z (σ) + μ
p (Z ≤ -1.88) = 0.03 so, Z-value is - 1.88..
put all the value of variables in above formula we get , -1.88 ( 2) + 10 = X => X = - 3.76 + 10
=> X = 6.24
Thus , the motor's warranty period lasted about 6.24 years.
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Torque is a measure of how much to tighten a bolt. The torque specification for a
small-block Chevy V8 is 70 foot-pounds with an error of 0.02 foot-pounds. Write
and solve an absolute value equation to find the minimum and maximum torque
required for the bolts.
The absolute value equation is |x - 70| = 0.02, while the minimum and maximum torque are 69.98 and 70.02 foot pounds
How to determine the absolute value equation?From the question, the given parameters are:
Specification = 70 foot pounds
Margin of error = 0.02 foot pounds
The absolute value equation of the scenario is then calculated as
|x - Specification| = Margin of error
Substitute the known values in the above equation
So, we have
|x - 70| = 0.02
Solving the equation, we have
x - 70 = 0.02 and x - 70 = -0.02
Add 70 to all sides
x = 70.02 and x = 69.98
Hence, the range is 69.98 to 70.02
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Write a story about temperatures that this expression could represent: 27+(-11)
Draw a number line diagram and write an expression to represent this situation: “On Tuesday at lunchtime, it was 29ºC. By sunset, the temperature had dropped to 16ºC.”
(this is summit learning btw)
The temperature “On Tuesday at lunchtime, it was 29ºC
i.e., 29 - 16.
Given,
Write a story about temperatures that this expression could represent:
27+(-11)
Now, According to the question:
1. The temperature is 27 degree C in the morning and reduced 11 degree C in the evening , the difference in temperature is 27 + (-11)
2. “On Tuesday at lunchtime, it was 29ºC. By sunset, the temperature had dropped to 16ºC.”
Again, Similarly
= 29 - 16
About Number line,
Draw a number line and allocate a point 16 degree C on the left side
and, 29 allocate a point on the right side.
Hence, The temperature “On Tuesday at lunchtime, it was 29ºC
i.e., 29 - 16.
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Shelley's cup of tea cooled down
1
2
of a degree in 10 minutes. At what rate is her tea cooling down?
Shelley's cup of tea is cooling down at the rate of 1.2 degree per minute.
According to the question,
We have the following information:
Shelley's cup cooled down 12 degrees in 10 minutes.
In order to find the rate of cooling down of the cup of tea, we will divide the degrees of the cooling by the total number of minutes.
So, we have the following expression:
Rate of cooling down of Shelley's cup = Total degrees the cup cooled down/total time taken
Rate of cooling down of Shelley's cup = 12/10
Rate of cooling down of Shelley's cup = 1.2 degree per minute
Hence, the rate of cooling down of Shelley's cup is 1.2 degree per minute.
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Answer:
1/20
Step-by-step explanation:
Find the rate in degrees per minute. Divide
1
2
of a degree by 10 minutes.
To divide by 10, multiply by its reciprocal,
1
10
.
1
2
÷10
=
1
2
1
10
=
1
20
Shelley's tea is cooling down at a rate of
1
20
of a degree per minute.
Drag and drop the answer into the box to match each point to its coordinates. Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse. Point A Point B Point C
The answer should be dragged and dropped into the box to match each point to its coordinates as follows;
Point A ⇔ (2 1/4 , 1 1/2).
Point B ⇔ (-1 1/4 , 1 1/2).
Point C ⇔ (-2 1/2 , 1/4).
What is an ordered pair?In Mathematics, an ordered pair is sometimes referred to as a coordinate and it can be defined as a pair of two (2) elements or data points that are commonly written in a fixed order within parentheses as (x, y), which represents the x-coordinate (abscissa) and the y-coordinate (ordinate) on the coordinate plane of any graph.
How to identify the coordinates points and quadrants?In Mathematics and Geometry, a quadrant simply refers to the area that is occupied by the values on the x-coordinate (x-axis) and y-coordinate (y-axis) of a cartesian coordinate.
Based on the cartesian coordinate (grid) below, the coordinates points and quadrants should be identified as follows;
Point A ⇔ (2 1/4 , 1 1/2) → quadrant 1.
Point B ⇔ (-1 1/4 , 1 1/2) → quadrant 2.
Point C ⇔ (-2 1/2 , 1/4) → quadrant 2.
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Missing information:
The question is incomplete and the complete question is shown in the attached picture.