Let [tex]r_A[/tex] and [tex]r_B[/tex] be the respective radii of balloons A and B. If the fixed total volume is V, then
[tex]V = \dfrac{4\pi}3\left({r_A}^3 + {r_B}^3\right)[/tex]
and knowing [tex]r_A=10\,\rm cm[/tex] and [tex]r_B=9\,\rm cm[/tex] at the start, we have V = 6916π/3 cm³. Then when [tex]r_A=12\,\rm cm[/tex], the radius of the other sphere is [tex]r_B=1\,\rm cm[/tex].
Differentiating both sides with respect to time t gives a relation between the rates of change of the radii:
[tex]0 = 4\pi \left({r_A}^2 \dfrac{dr_A}{dt} + {r_B}^2 \dfrac{dr_B}{dt}\right) \implies \dfrac{dr_B}{dt} = -\left(\dfrac{r_A}{r_B}\right)^2 \dfrac{dr_A}{dt}[/tex]
We're given [tex]\frac{dr_A}{dt} = 0.1\frac{\rm cm}{\rm s}[/tex] the whole time. At the moment [tex]r_A=12\,\rm cm[/tex], the radius of balloon B is changing at a rate of
[tex]\dfrac{dr_B}{dt} = -\left(\dfrac{12\,\rm cm}{1\,\rm cm}\right)^2 \left(0.1\dfrac{\rm cm}{\rm s}\right) = \boxed{-14.4 \dfrac{\rm cm}{\rm s}}[/tex]
If f(x)=2(3x-5) when f(x) =74,what is the value of x??
Answer:
x = 14
Step-by-step explanation:
given f(x) = 2(3x - 5) and f(x) = 74 , then equating gives
2(3x - 5) = 74 ( divide both sides by 2 )
3x - 5 = 37 ( add 5 to both sides )
3x = 42 ( divide both sides by 3 )
x = 14
4. At which point does the function y = -x² + 6x - 5 reach its maximum value?
Answer:
(3,4)
Step-by-step explanation:
Hello!
To find the maximum value, we can find the vertex of the graph.
Since the coefficient of x² is negative, the graph opens downwards, meaning that the vertex would be the highest point.
To solve for the vertex, we can convert it to vertex form.
Converty = -x² + 6x - 5y = -1(x² - 6x) - 5y = -1(x² - 6x + 9) - 5 + 9y = -1(x - 3)² + 4The vertex is (3,4)
Solve for for x:
3x - 2 > 5x + 10
a. X> 6
b. x < 6
c. x < -6
d. X > -6
Answer:
[tex]x < -6[/tex]
Step-by-step explanation:
[tex]~~~~~~3x-2 > 5x+10\\\\\implies 5x+10 < 3x-2\\\\\implies 5x < 3x-2-10\\\\\implies 5x < 3x-12\\\\\implies 5x-3x < -12\\\\\implies 2x < -12\\\\\implies x < -\dfrac{12}2\\\\\implies x < -6[/tex]
PLEASE HELP ME I'M GIVING 20PTS AND MARKING BRAINLIEST!!!!
If sinθ=1/3, what are the values of cosθ and tanθ?
Using a trigonometric identity, it is found that the values of the cosine and the tangent of the angle are given by:
[tex]\cos{\theta} = \pm \frac{2\sqrt{2}}{3}[/tex][tex]\tan{\theta} = \pm \frac{\sqrt{2}}{4}[/tex]What is the trigonometric identity using in this problem?The identity that relates the sine squared and the cosine squared of the angle, as follows:
[tex]\sin^{2}{\theta} + \cos^{2}{\theta} = 1[/tex]
In this problem, we have that the sine is given by:
[tex]\sin{\theta} = \frac{1}{3}[/tex]
Hence, applying the identity, the cosine is given as follows:
[tex]\cos^2{\theta} = 1 - \sin^2{\theta}[/tex]
[tex]\cos^2{\theta} = 1 - \left(\frac{1}{3}\right)^2[/tex]
[tex]\cos^2{\theta} = 1 - \frac{1}{9}[/tex]
[tex]\cos^2{\theta} = \frac{8}{9}[/tex]
[tex]\cos{\theta} = \pm \sqrt{\frac{8}{9}}[/tex]
[tex]\cos{\theta} = \pm \frac{2\sqrt{2}}{3}[/tex]
The tangent is given by the sine divided by the cosine, hence:
[tex]\tan{\theta} = \frac{\sin{\theta}}{\cos{\theta}}[/tex]
[tex]\tan{\theta} = \frac{\frac{1}{3}}{\pm \frac{2\sqrt{2}}{3}}[/tex]
[tex]\tan{\theta} = \pm \frac{1}{2\sqrt{2}} \times \frac{\sqrt{2}}{\sqrt{2}}[/tex]
[tex]\tan{\theta} = \pm \frac{\sqrt{2}}{4}[/tex]
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Fill in the missing number in this sequence:
{ } 216, 36, 6, 1
Answer:
1296
Step-by-step explanation:
times each number by 6
example: 1x6=6 6x6=36 36x6=216 216x6=1296
Hi student, let me help you out! :)
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
We are asked to fill in the missing number in the sequence
[tex]\star~\mathrm{(~~),216,36,6,1}[/tex]
[tex]\triangle~\fbox{\bf{KEY:}}[/tex]
Take a look at the common ratio.Since every number is divided by 6, we need to multiply 216 times the common ratio, 6:
[tex]\star~\mathrm{216\times6}[/tex]
Simplify!
[tex]\star~\mathrm{1296}[/tex]
Hope it helps you out! :D
Ask in comments if any queries arise.
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~Just a smiley person helping fellow students :)
1.How many more pupils go to school by tricycle than bicycle?
A.4
B.5
C.3
D.2
2.what is the total number of pupils in grade 6 Simplicity?
A.33
B.28
C.29
D.30
3.what fraction of the pupil in grade 6 Simplicity walk to school?
A.8/33
B.12/33
C.10/33
D.3/33
4.what percentage of the pupil goes to school by walking?
A.24%
B.33%
C.9%
D.36%
A caterer charges the same price for each wrap orderd.each bottle of water is also the same price. The cost of buying 50 wraps and 60 water bottles is $445. The cost of buying 60 wraps and 40 water bottles is $470 what is the price?
Answer:it’s in the explanation
Step-by-step explanation:
a. Each wrap costs $2.00, and each bottle of water costs $6.50.
b. Each wrap costs $4.70, and each bottle of water costs $4.70.
c.Each wrap costs $5.30, and each bottle of water costs $3.00.
d. Each wrap costs $6.50, and each bottle of water costs $2.00.
Answer:
The wraps are $6.50 and the water bottles are $2
Step-by-step explanation:
How to find x for −x/8 < 1.5
Answer:
x>-12
Step-by-step explanation:
We want to the equation so that x is the only thing on the left-hand side.
-x/8 < 1.5 (multiply both sides by 8)
-x < 12
Now, whenever you multiply or divide by a negative when dealing with an inequality, you have to switch the sign.
x > -12.
im wondering what is 4.3 x 2.9
Answer:
[tex]\frac{1247}{100}[/tex], or 12.47
Step-by-step explanation:
I looked this up on my scientific calculator. I hope this helps! :)
11-8(12+6)÷6²
pls answer right :)
Answer: The answer is 7
I did the math
Answer:
7
Step-by-step explanation:
11 - 8(12 + 6) / 6²
Rearrange using the order of operations.
11 - ((8 * (12 + 6)) / (6²))
((8 * (12 + 6)) = 144
(6²) = 36
(6²) / 144 = 4
(11 - 4)
= 7
Students in a math class recorded the number of text messages they received the previous day. how many students received at least 10 messages?
Answer:
14 students
Step-by-step explanation:
You didn't include a graph, so I looked up the question to find the graph you are likely talking about.
If this graph does not match, ignore my answer (although the question is exactly the same so I'm guessing it might be the same)
{even if different , conceptually, here is what you do: }
Receiving at least 10 messages includes those who receive 10 messages.
Each X represents 1 student. So, 3 students received exactly 10 messages.
3 (who received 10)
2 (who received 15)
4 (who received 20)
5 (who received 25)
+________
14 students
14 students received ≥ 10 messages
(≥ means greater than or equal to,
< is less than (less < more)
> is greater than (more > less)
the line under includes the value _ (same or more ≥ than this value ; same or less ≤ than this value)
hope this helps you !!
A ski resort claims that there is a 75% chance of snow on any given day in january and that snowfall happens independently from one day to the next. a family plans a four-day trip to this ski resort in january. let x represent the number of days it snows while the family is there. what are the mean and standard deviation of x? mu subscript x baseline = 1, sigma subscript x baseline = 1 mu subscript x baseline = 2, sigma subscript x baseline = 0.56 mu subscript x baseline = 3, sigma subscript x baseline = 0.75 mu subscript x baseline = 3, sigma subscript x baseline = 0.87
Using the binomial distribution, it is found that the mean and the standard deviation of variable x are given as follows:
[tex]\mu = 3, \sigma = 0.87[/tex]
What is the binomial probability distribution?It is the probability of exactly x successes on n repeated trials, with p probability of a success on each trial.
The expected value of the binomial distribution is:
E(X) = np
The standard deviation of the binomial distribution is:
[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]
In this problem, we have that the parameters are given as follows:
n = 4, p = 0.75.
Hence the mean and the standard deviation are given as follows:
E(X) = np = 4 x 0.75 = 3.[tex]\sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{4 \times 0.75 \times 0.25} = 0.87[/tex]More can be learned about the binomial distribution at https://brainly.com/question/24863377
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In ΔOPQ, o = 500 cm, p = 600 cm and q=380 cm. Find the measure of ∠P to the nearest 10th of a degree.
The measure of ∠P to the nearest 10th of a degree is 84.8°
Law of CosinesFrom the question, we are to determine the measure of ∠P
From the law of cosines, we can write that
[tex]cos \ P=\frac{o^{2}+q^{2}-p^{2} }{2oq}[/tex]
From the given information,
o = 500 cm
p = 600 cm
q = 380 cm
Putting the parameters into the formula, we get
[tex]cos \ P=\frac{500^{2}+380^{2}-600^{2} }{2\times 500 \times 380}[/tex]
[tex]cos \ P =\frac{34400}{380000}[/tex]
[tex]cos \ P =0.0905[/tex]
P = cos⁻¹(0.0905)
P = 84.8076
P ≅ 84.8°
Hence, the measure of ∠P to the nearest 10th of a degree is 84.8°
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helppppppppppppppppp pleaseeeeeeeeeeee
[100 POINTS] Find the values of x, y, and z.
[tex]\qquad\qquad\huge\underline{{\sf Answer}}[/tex]
Let's solve ~
x and y are values that represent the angle made by respective arcs on centre of the circle
that is :
x = 20°Here, Angle x + Angle z = 180°
[ because they form linear pair ]
z + x = 180z = 180 - xz = 180 - 20z = 160°Now, we can observe that angle made by Arc Y is equal to :
y = z + x = 160° + 20° = 180°Which equation has the solution x=4?
Answer: Option C is correct.
Part A
⇒ 4x = 20
⇒ x = 20/4
⇒ x = 5
Part B⇒ x/2 = 8
⇒ x = 8(2)
⇒ x = 16
Part C⇒ x + 8 = 3x
⇒ 3x - x = 8
⇒ 2x = 8
⇒ x = 4
Part D⇒ x = (x + 5)/2
⇒ 2x = x + 5
⇒ 2x - x = 5
⇒ x = 5
Graph the solution to your inequality on a number line or describe, in words, how to graph the inequality on a number line. 5x + 15< 60
The solution to the given inequality is x < 9
What are inequality
Inequality are expressions not separated by an equal sign, Given the inequality
5x + 15< 60
Subtract 15 from both sides
5x < 60 - 15
5x < 45
Divide both sides by 5
5x/5 < 45/5
x < 9
The number line that describes the solution is attached
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nth term of this quadratic sequence -1,2,7,14,23
Since we know it's quadratic, the n-th term will follow the pattern
[tex]x_n = an^2 + bn + c[/tex]
for some unknown coefficients a, b, and c.
Given that [tex]x_1=-1[/tex], [tex]x_2=2[/tex], and [tex]x_3=7[/tex], we have the following conditions on these coefficients:
[tex]\begin{cases} a + b + c = -1 \\ 4a + 2b + c = 2 \\ 9a + 3b + c = 7 \end{cases}[/tex]
Solve this system to get a = 1, b = 0, and c = -2. Then
[tex]\boxed{x_n = n^2 - 2}[/tex]
To solve the system, use elimination.
[tex](4a + 2b + c) - (a + b + c) = 2 - (-1) \implies 3a + b = 3[/tex]
[tex](9a + 3b + c) - (a + b + c) = 7 - (-1) \implies 8a + 2b = 8 \implies 4a + b = 4[/tex]
[tex](4a + b) - (3a + b) = 4 - 3 \implies a = 1 \implies b = 0 \implies c = -2[/tex]
A telephone company charges a $0.25
connection fee, then $0.10 per minute for
long distance calls. Which statement is
true regarding this situation?
The value of a dependent variable is dependent on the value of an independent variable. The correct option is C.
What are independent and dependent variables?Even though everything can be almost always related to its reason, when we talk about two related things, there might happen that one of those things is dependent on other.
If a variable is taking its values independently of any visible direct cause, then that variable is called independent variable.The variables who take their values based on some other variables' values are called dependent variables.The complete question is:
A telephone company charges a $0.25 connection fee, then $0.10 per minute for long distance calls. Which statement is true regarding this situation?
A. The rate of change is $0.25 and minutes are the independent variable.
B. The rate of change is $0.25 and minutes are the dependent variable.
C. The rate of change is $0.10 per minute and minutes are the independent variable
D. The rate of change is $0.10 per minute and minute are the dependent variable.
The cost of making a call is the sum of the cost of connection fee which is one time fee and cost $0.25, and the cost charged for a minute which depends on the number of minute for which the call is been established. Therefore, the total cost can be written for a x minute call is,
Total Cost = $0.25 + $0.10(x)
Since the total cost is dependent on x, therefore, x which is the minute is the independent variable. The rate of change is $0.10 per minute and minutes are the independent variable.
Hence, the correct option is C.
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A bedroom measures 9 feet long and 11 feet wide. A scale drawing is made using a scale factor of 112.
What is the length of the bedroom in the scale drawing?
Drag and drop a number to correctly complete the statement.
Given the previous length of the bedroom and the current scale factor, the length of the bedroom in the current scale drawing is 1008ft.
What is the length of the bedroom in the scale drawing?Scale factor is simply a measure for similar figures, who look the same but have different scales or measures.
To get new dimension;
New dimension = scale factor × current dimension
Given that;
Current length of the bedroom = 9ftCurrent width of the bedroom = 11ftScale factor = 112New length of the bedroom = ?New dimension = scale factor × current dimension
New length of the bedroom = 112 × 9ft
New length of the bedroom = 1008ft
Therefore, given the previous length of the bedroom and the current scale factor, the length of the bedroom in the current scale drawing is 1008ft.
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Hi, I'm in 7th grade and I'm about to fail Mathematics. Please help me...
x+7=5
Answer:
x=-2
Step-by-step explanation:
x+7=5
To find x, we subtract 7 from both sides, to get x+7-7=5-7
x=5-7
x=-2
Hope this helped!
Answer:
x = -2
Step-by-step explanation:
in order to find x u need to subtract 7 from 5 to get -2. therefore your answer is -2
What is the time in 24 hour clock for 03:50 pm?
a.0350 hrs
b.1350 hrs
c.1550 hrs
d.1650 hrs
Answer:
Option C
Step-by-step explanation:
Any evening time on a 24 hour clock will be that hour add 12 :
3:50 pm =
3:50 + 12:00 = 15:50
Option C must be the answer
Hope this helped and brainliest please
Answer:
c.1550 hrs
Step-by-step explanation:
It Is military time to it stays going for 12:00 to 13:00 14:00 15:00 and so on
Hope This Helped
Can anyone help me solve this?
Answer:9
Step-by-step explanation:
Use the pythagorean theorem. [tex]a^{2}+b^{2}=c^{2}[/tex]
We know both a and c, so it becomes
[tex]4^{2}+b^{2}=\sqrt{97}^{2}[/tex]=
16+b^2=97=
97-16=b^2=
81=b^2=
9=b
What is the base in the expression 4^5
4
5
9
20
PLS ANSWER FAST !!
Answer:
The answer is 4
Step-by-step explanation:
The base of 4^5 is 4. The exponent is 5 and 9 & 20 do not work as we are not multiplying 4 and 5 to get 20.
When Vince does 14 push-ups and 12 sit-ups, it takes a total of 52 seconds. In comparison, he needs 48 seconds to do 12 push-ups and 12 sit-ups. How long does it take Vince to do each kind of exercise?
Answer:
it takes 2 seconds to do one situp
it takes 2 seconds to do one pushup
to do 14 pushups, it takes 28 seconds.
to do 12 situps it takes 24 seconds
to do 12 pushups, it takes 24 seconds
BRAINLIEST PLEASE!
hope this helps :)
Step-by-step explanation:
14x + 12y = 52
12x + 12y = 48
^^^ this is an inequality that we can make.
x stands for pushups
y stands for situps
if we subtract the second equation from the first, we get
2x = 4
x = 2
now we can place x in one of the equations to solve for y
12(2)+12y=48
24 + 12y = 48
12y = 24
y = 2
Indigo needs to order some new supplies for the restaurant where she works. The restaurant needs at least 430 knives. There are currently 269 knives. If each set on sale contains 18 knives, what is the minimum number of sets of knives Indigo should buy? (Help please)
Inequalities help us to compare two unequal expressions. The minimum number of sets of knives Indigo should buy is 8.
What are inequalities?Inequalities help us to compare two unequal expressions. Also, it helps us to compare the non-equal expressions so that an equation can be formed.
It is mostly denoted by the symbol <, >, ≤, and ≥.
Let the number of sets of knives indigo should buy be represented by x.
Given Indigo needs to order some new supplies for the restaurant where she works and the restaurant needs at least 430 knives. Also, There are currently 269 knives. Now, If each set on sale contains 18 knives the inequality that can represent the minimum number of sets of knives Indigo should buy is,
269+18x≥430
18x≥430-289
18x≥141
x≥7.833
x≥8
Hence, the minimum number of sets of knives Indigo should buy is 8.
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Please someone help me with this
Answer:
Option c
Step-by-step explanation:
Since tangent = op/adj, in this case the tan37 would be x/1000.
Then, set it up as an algebra problem.
tan37 = x/1000
Multiply both sides by 1000, so 1000tan37=x
that simplifies to x = 753.6
To play a board game, a player spins the pointer of a spinner with four equal sections numbered 1–4, and then flips a fair coin. Use a tree diagram to represent the sample space. What is the probability of spinning either a 3 or a 4 AND flipping a head?
Answer:
2/8
Step-by-step explanation:
there is the 4 sections of a spinner and 2 sides on the coin when you lay it out that leaves 2 opportunities to spin a 3 or a 4 and flipping heads
The table below shows some inputs and outputs of the invertible function fff with domain all real numbers.
xxx 141414 -6−6minus, 6 -1−1minus, 1 101010 -10−10minus, 10 333
f(x)f(x)f, left parenthesis, x, right parenthesis 777 -10−10minus, 10 -15−15minus, 15 141414 -4−4minus, 4 -9−9minus, 9
Find the following values:
f^{-1}(f^{-1}(7))=f
−1
(f
−1
(7))=f, start superscript, minus, 1, end superscript, left parenthesis, f, start superscript, minus, 1, end superscript, left parenthesis, 7, right parenthesis, right parenthesis, equals
7
f^{-1}(-4)=f
−1
(−4)=f, start superscript, minus, 1, end superscript, left parenthesis, minus, 4, right parenthesis, equals
(thats for the people who copied and pasted it off Khan Academy.)
PS: I DONT KNOW IF IT IS CORRECT!!!!! please, someone check it.
The value of f⁻¹(f⁻¹(7)) is 10
How to determine the value of the expression?The expression is given as:
f⁻¹(f⁻¹(7))
We start by solving the inner expression f⁻¹(7).
The above means that we determine the x value when y = 7.
So, we have:
f⁻¹(7) = 14
Substitute f⁻¹(7) = 14 in f⁻¹(f⁻¹(7))
f⁻¹(14)
Next, we determine the x value when y = 14
f⁻¹(14) = 10
Hence, the value of f⁻¹(f⁻¹(7)) is 10
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Answer:
20
10
Step-by-step explanation:
Tanya and tim clean the house in 3 hours their 3 children at the same 6 hours
how long would it take to clean the whole house if they did it together?
It will take them exactly 4hours 48 minutes.
what is rate?Rate is a measure of a given quantity against a known or standard quantity.
Analysis:
If Tanya and Tim cleaned the house in 3 hours. Then either of them would clean the house in 2 x 3 = 6 hours.
If their 3 children cleaned the house in 6 hours, then each child would clean the house in = 3 x 6 = 18 hours
Total time for cleaning the house = 18 hours + 6 hours = 24 hours
If the five people were to do it at once then time taken to clean the house = 24/5 = 4.8 hours = 4 hours 48 minutes
In conclusion, the time for 5 people to clean the house is 4 hours 48 minutes
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