Answer:
The time it would take to inflate the balloon to approximately two-thirds of its maximum volume is approximately 46.90 minutes
Step-by-step explanation:
The given parameters are;
The diameter of the balloon = 55 feet
The rate of increase of the radius of the balloon when inflated = 1.5 feet per minute
We have;
dr/dt = 1.5 feet per minute = 1.5 ft/min
V = 4/3·π·r³
The maximum volume of the balloon = 4/3 × 3.14 × 55³ = 696556.67 ft³
When the volume is two-thirds the maximum volume, we have;
2/3 × 696556.67 ft³ = 464371.11 ft³
The value of the radius, r₂ at that point is found as follows;
4/3·π·r₂³ = 464371.11 ft³
r₂³ = 464371.11 ft³ × 3/4 = 348278.33 ft³
348278.333333
r₂ = ∛(348278.33 ft³) ≈ 70.36 ft
The time for the radius to increase to the above length = Length/(Rate of increase of length of the radius)
The time for the radius to increase to the above length ≈ 70.369 ft/(1.5 ft/min) ≈ 46.90 minutes
The time it would take to inflate the balloon to approximately two-thirds of its maximum volume ≈ 46.90 minutes.
Which pair of points has a slope of 4? Question 4 options: (0, 4), (4, 0) (3, 0), (–1, –1) (0, –3), (1, 1) (1, 4), (–1, 4)
Use the binomial theorem to expand the binomial (x + -2y)8.
x8 + 8x6y + 28x7y2 + 56x5y4 + 70x5y4 + 56x3y7 + 28x2y +
8xy + y 8
x8 + 8x7y + 28x6y2 + 56xy3 + 70x4y4 + 56x3y5 + 28x2y6 +
8xy7 + y8
x8 + 16x7y + 112x6y2 + 448x5y3 + 1,120x4y4 +
1,792x3y5 + 1,792x2y6 + 1,024xy7+ 256y8
256x8 + 1,024x7y + 1,792x6y2 + 1,792x5y3 + 1,120x4y4 +
448x3y5 + 112x2y6 + 16xy7 + y8
Answer:
256x8y8256+2x8y8+56x3y7+28x7y2+126x5y4+x8+1048x7y+1932x6y2+2240x5y3+2310x4y4+2296x3y5+1932x2y6+1048xy7+y8+8x6y+56xy3+28x2y+8xy
Step-by-step explanation:
A totem pole that is 90 feet tall casts a shadow that is 45 feet long. At the same time, a 6 – foot tall man casts a shadow that is x feet long. Find the length of the shadow.
Answer:
x=90+45/6
x=135/6
x=22.5
The length of the shadow of the 6-foot tall man is 3 feets
Actual Length :
Length of pole = 90 feets Length of man = 6 feetsLength of shadow :
Pole shadow = 45 feets Shadow of man = xUsing the relation :
(Pole length/shadow) = (man's height / shadow) (90 / 45) = (6 / x) Cross multiply :90x = 270x = 270 / 90 x = 3Therefore, the shadow of the man is 3 feets long.
Learn more : https://brainly.com/question/18112348
Each type of ball represents a different digit (0-9) that
remains consistent across the three equations.
Figure out the number that matches each of the balls
and explain your reasoning.
Answer:
I think the
basketball = 2
football = 4
soccer ball = 0
Step-by-step explanation:
Why because
2+2 = 4 and + =
2×2 = 4 and × =
4+0 = 4 and +⚽ =
Which means that even if basketball is getting added or multiplied it will get the same answer and 2 will gets same answer (4) when it's multiplied or added. In conclusion = 2 = 4 and ⚽ = 0
What is the solution of 2d=a-b/b-c when you solve for a
Answer:
2d(b-c)+b=a
Step-by-step explanation:
First you start off with the equation given
2d=(a-b)/(b-c)
Second, you want to start getting A by its self so that means you have to multiply both sides by (b-c) to get (a-b) by its self. (underlined portion cancles out)
2d(b-c)=((a-b)/(b-c)) (b-c) ----> 2d(b-c)=a-b
Finally, you want to add b to both sides to get a completely by it's self. (underlined portion cancles out)
2d(b-c)+b=a-b+b -----> 2d(b-c)+b=a
Sal purchase b bowls fr $7.50 and paid $15 for shipping. The total cost of Sals purchase was $75. How many bowls did he buy?
Answer: 8
Step-by-step explanation:
Answer:
8
Step-by-step explanation:
L is between points O and P. OP is 25 and LP is 17. What is OL? (Write as a number only)
Answer:
8
Step-by-step explanation:
Salad restaurant served 6 1/2 cups of italian salad dressing if the restaurant serves 1/4 cup of dressing with each salad how many salads were ordered without dressing
Answer:
cc
Step-by-step explanation:
c
Inverse Function -5 + 5/2x
Answer:
y = (2/5)x + 2
Step-by-step explanation:
To find the inverse of a function, we simply exchange the variables x and y and solve for y.
For this function we will write it as such:
y = -5 + (5/2)x
So to find the inverse, we will swap the x and y and solve.
y = -5 + (5/2)x
x = -5 + (5/2)y
x + 5 = (5/2)y
(2/5) * (x + 5) = y
(2/5)x + (2/5)5 = y
(2/5)x + 2 = y
Thus the inverse of the function is:
y = (2/5)x + 2
Cheers.
Plsssss help me I’m finna die
Answer:
She is 90 feet above ground before she begins to descend.
She descends by a rate of 5 feet per second.
Step-by-step explanation:
She is 90 feet above ground before she begins to descend. You can see that by looking at the y value of the highest point of the line, which is just between 80 and 100, which is 90.
We can find the rate of her descending by finding the slope. Remember that the slope formula is (y1-y2)/(x1-x2)
We can find two points on the line and plug the x and y values in. Let's use the points (0, 90) and (16, 10).
We plug the values in:
(90-10)/(0-16)
(80)/-16
-5
The slope is negative, which makes sense, because Aretha is descending and not ascending.
So, she is descending by a rate of 5 feet per second.
I hope this helps you!
is the following a true statement? 4/8 < 5/16
Answer:
No, because 4/8*2= 8/16
And 8/16 is greater than 5/16
Answer:
The statement is false.
Step-by-step explanation:
The easiest way to answer this question is to make both fractions have the same common denominator. In this case, we should alter the first fraction to have a denominator of 16 so that it matches the second fraction. To do this, we should multiply both the numerator and the denominator of the fraction by 2 (this is the same as multiplying by 1, which does not change the value of the fraction). This is modeled below:
4/8 * 2/2 = 8/16
Now, we can plug this value back into our original statement.
8/16 < 5/16
From comparing the numerators, we know that 5 is NOT greater than 8, so the statement is false.
Hope this helps!
what is the largest number we counted to.
Answer: The biggest named number that we know is googolplex, ten to the googol power, or (10)^(10^100). That's written as a one followed by googol zeroes.
Explanation: The largest known prime number (as of August 2020) is 282,589,933 − 1, a number which has 24,862,048 digits when written in base 10. It was found via a computer volunteered by Patrick Laroche of the Great Internet Mersenne Prime Search (GIMPS) in 2018.
Hope this helps^^
I need help with this question
Answer:
x = (3√2)/2
Step-by-step explanation:
In the isosceles right triangle the side lengths have the ratio ...
1 : 1 : √2
This means the short leg (x) is 1/√2 times the length of the hypotenuse. You want the ratio with a rational denominator, so you need to multiply numerator and denominator by √2.
[tex]x=3\cdot\dfrac{1}{\sqrt{2}}=3\cdot\dfrac{\sqrt{2}}{(\sqrt{2})^2}\\\\\boxed{x=\dfrac{3}{2}\sqrt{2}}[/tex]
Please help asap!! Thank you
Answer:
The answer is #1
Step-by-step explanation:
If it orginially (30) (97) thats the answer you want, check out the other questions.
30(100-3) = (30) (97)30 ( 90 -3) = (30) (87)30( 97 - 97) = (30) (0)30 (90 - 7) = (30) (93)number one is the only one to the original therefore
30 (100-3) = (30) (97).
What is the factored form of 25b^2 -60b+36
Answer:
(5b-6)^2
Step-by-step explanation:
by using formula
(a-b)^2 = (a)^2 - 2(a)(b) + (b)^2
by putting values in the above formula
(5b)^2 - 2(5b)(6) + (6)
(5b-6)^2 answer
Answer:
(5b - 6)(5b - 6)
Step-by-step explanation;
25b^2 - 60b + 36
=> (5b)^2 - 2 × 5b × 6 + (6)^2 [Using (a + b)^2 = a^2 + b^2 + 2ab]
=> (5b - 6)^2
=> (5b - 6)(5b - 6)
6
In the proportion
21
k
the value of k is
10.
Answer:
I don't understand what you are asking, please ask the question with more info
Step-by-step explanation:
¼ (x-1) ≤ x+4/6 i'm stuck on this problem for math. could anyone help with steps
Answer:
x≥ -11/9
Step-by-step explanation:
HOPE THIS HELPS!!!!! :)
<3333333333
what ratios are equvailent to 2:9
Answer:
2/9 4/18 12/54
4/9 8/18 24/54
5/9 10/18 30/54
7/9 14/18 42/54
Step-by-step explanation:
Answer:
4 : 18 and 6 : 27
Step-by-step explanation:
To obtain equivalent ratios, multiply or divide both parts of the ratio by the same quantity.
Multiplying by 2
2 : 9 = 2(2) : 9(2) = 4 : 18
Multiplying by 3
2 : 9 = 2(3) : 9(3) = 6 : 27 , etc
The total cost to rent a row boat is $18 times the number of hours the boat is used. Write an equation to model this situation if c = total cost and h = number of hours.
Answer:
C = 18h
Step-by-step explanation:
y = mx + b
C (total cost) is equivalent to "Y"
18 is equivalent to "m"
h is equivalent to "x"
and there is no "b" in this situation.
I hope this helps!
-TheBusinessMan
The difference between a number and 22 is 57. what is the number
Answer:
79
Step-by-step explanation:
The difference between 79 and 22 is 57. 79 is THE number. All you have to do is add 22 and 57 because the answer you get would ALWAYS have one of the numbers added as the difference.
If a = 9 and b = 4, what is the value of 2a – b?
A
10
B
B
14
25
D
72
Answer:
Hey there!
2a-b
2(9)-4
18-4
14
Let me know if this helps :)
Answer: 14
Step-by-step explanation: It’s a good idea to get into the habit of
using parentheses when substituting numbers in for variables.
Since a = 9 and b = 4, 2a - b is 2(9) - (4).
Now think about your order of operations.
Multiplication comes before subtraction so first multiply 2(9) to get 18.
So we have (18) - (4) which is 14.
h(x) = 2^x
Solve the equation h^-1 (x) =0.5
Answer:
The answer is
[tex]\sqrt{2} \: \: or \: \: 1.414[/tex]Step-by-step explanation:
[tex]h(x) = {2}^{x} [/tex]To solve the equation we must first find h-¹(x)
To find h-¹(x) equate h(x) to y
That's
[tex]y = {2}^{x} [/tex]Next interchange the terms
x becomes y and y becomes x
That's
[tex] {2}^{y} = x[/tex]Make y the subject
Take logarithm to base 2 to both sides
That's
[tex] log_{2}( {2} )^{y} = log_{2}x \\ y log_{2}2 = log_{2}(x) [/tex]But
[tex] log_{2}(2) = 1[/tex][tex]y = log_{2}(x) [/tex]So we have
[tex] {h}^{ - 1} (x) = log_{2}(x) [/tex]Now we can solve the equation
We have
[tex] log_{2}(x) = 0.5[/tex]Convert the logarithm into exponential form using the fact that
[tex] log_{a}(x) = b \: \: \cong \: \: x = {a}^{b} [/tex]So we have
[tex]x = {2}^{0.5} [/tex]But
[tex] {2}^{0.5} = \sqrt{2} [/tex]So we have the final answer as
[tex] \sqrt{2} \: \: or \: \: 1.414[/tex]Hope this helps you
The sides of a triangle are (x+3), (x+4), and (x+7). Find the value of x if the perimeter of the triangle is 104
inches.
Answer:
x = 30
Step-by-step explanation:
The perimeter is the sum of all of the sides of a shape. Therefore, because the sum is equivalent to 104 inches and we are given the lengths of all three sides, we can add the three sides together and set them equal to 104 in order to solve for x.
(x + 3) + (x + 4) + (x + 7) = 104 Drop the parentheses.
x + 3 + x + 4 + x + 7 = 104 Combine like terms (variables first!).
3x + 3 + 4 + 7 = 104 Now, combine constant terms.
3x + 14 = 104 Subtract 14 from both sides.
3x = 90 Divide by 3 on both sides of the equation.
x = 30
The following table gives the result of a random sample of upper level students at Rocky Vista
University (the Fighting Prairie Dogs!), along with a mosaic plot.
100.0%
90.0%
80.0%
70.0%
Grade Level
Junior
14
22
15
Employment Status
Currently working
Not working but have had a job
Never had a job
60.0%
Senior
30
40
10
50.0%
40.0%
30.0%
Employment status
Never had a job
Not working but did in the past
. Currently working
20.0%
10.0%
0.0%
Junior
Senior
Grade Level
(a) Calculate the proportion of Juniors that are (1) currently working, (2) not working but have
had a job, and (3) never had a job.
Answer:
Juniors Currently Working: 14/51 = 0.27; Not Working but Have Had a Job: 22/51 = 0.43; Never Had a Job: 15/51 = 0.29.
Seniors Currently Working: 30/80 = 0.38; Not Working but Have Had a Job: 40/80 = 0.5; Never Had a Job: 10//80 = 0.13.
There is an association between employment status and grade level. Depending on whether the student is a senior or junior impact the likelihood of their employment status. For instance, more seniors are likely to be currently working than juniors.
triple a number less than 8
2 tripled is 6
2 x 3 = 6
Hope this helps! : )
Answer:
1x3=3
2x3=6
3x3=9
4x3=12
5x3=15
6x3=18
7x3=21
8x3=24
Consider the function f(x) = x^2 – 331. Chivonne claims a domain restriction x ≥ 0 produces the inverse function f–1(x) = √ x - 331 .
Which statement describes whether Chivonne is correct?
A) The expression for f–1(x) is correct, but the domain restriction is not.
B) The domain restriction is correct, but the expression for f–1(x) is not.
C) Both the expression for f–1(x) and the domain restriction are correct.
D) Neither the domain restriction nor the expression for f–1(x) is correct.
Answer:
The correct option is;
D) Neither the domain restriction nor the expression for f⁻¹(x) is correct
Step-by-step explanation:
The given function can be written as follows;
f(x) = x² - 331
The inverse of the function f(x), which is f⁻¹(x), can be found as follows;
Let f(x) = x² - 331 = y, we have;
f(x) + 331 = x²
x = √(f(x) + 331)
We replace x with f⁻¹(x) and f(x) with x, to get;
f⁻¹(x) = √(x + 331)
We note that the domain of the inverse function will include values from x ≥ -331, and the correct inverse function √(x + 331) ≠ √x - 331
Therefore, we have that neither the domain restriction nor the expression for f⁻¹(x) is correct.
Answer:
B) The domain restriction is correct, but the expression for f–1(x) is not.
The ANSWER IS NOT C as "oeerivona" stated
Step-by-step explanation:
The answer is B on Edge. (VERIFIED Edge Answer)
Make sure to click "thanks" and rate this answer to let others know this is the correct answer for this question.
Edge Tip: Answers do not mix or change.
carlos saw poster below at the mall advertising the opening day of the new video game arcade
Jojo's arcade grand opening first 3 games free 75 cents after three games if carlose saved up 9.00 dollars from his allowance how much games could he play
Answer:
Carlos could play a total of 15 games
Step-by-step explanation:
In the grand opening of JoJo's arcade:
First 3 games are free
75 cents after the first 3 free games
Carlos has $9 saved from his allowance
75 cents = $0.75
Number of games Carlos could play = Total saved allowance / cost per game after 3 free games
= $9 / $0.75
= 12 games
Total number of games Carlos could play = free games + games from his allowance
= 3 + 12
= 15 games
Carlos could play a total of 15 games
5. A giraffe is twice as tall as its baby. The baby's height and the mother's height total 4.5m. How tall is the baby? How tall is the mother?
Answer:
Step-by-step explanation:
call x the mother deer, y the baby deer, we have x = 2y
x + y = 4,5 ---> x = 3, y = 3/2
Answer:
2.25
Step-by-step explanation:
4.5 / 2
Solve for x:
2x +3=9
Answer:
x=3
Step-by-step explanation:
2(3)+3=9
6+3=9
9=9
Answer: [tex]x=3[/tex]
Subtract 3 from both sides
[tex]2x+3-3=9-3\\2x=6[/tex]
Divide both sides by 2
[tex]2x/2=6/2\\x=3[/tex]
PLS help :) Use complete sentences to describe the sum of CA and AB.
Answer:
CA+AB=CB
Step-by-step explanation:
CA + AB = CB
The lines CA and AB will sum up to CB.
What are collinear points?Collinear points are the points that lie on the same straight line or in a single line. If two or more than two points lie on a line close to or far from each other, then they are said to be collinear, in Euclidean geometry.
Given here: CA and AB along the same line CB also A,B,C are collinear also ∠DAB+∠CAD=180 as they are adjacent angles and thus are supplementary. Therefore CA+AB=CB
Hence, The lines CA and AB will sum up to CB.
Learn more about the lines here:
https://brainly.com/question/11806229
#SPJ2