Answer:
[tex]\dfrac{dV}{dt}=502.65\ mm^3/s[/tex]
Step-by-step explanation:
The volume of a sphere is given by :
[tex]V=\dfrac{4}{3}\pi r^3[/tex]
The rate of change of volume means,
[tex]\dfrac{dV}{dt}=\dfrac{d}{dt}(\dfrac{4}{3}\pi r^3)\\\\\dfrac{dV}{dt}=\dfrac{4}{3}\pi \times 3r\times \dfrac{dr}{dt}[/tex]
We have, [tex]\dfrac{dr}{dt}=2\ mm/s\ and\ r=40\ mm[/tex]
So,
[tex]\dfrac{dV}{dt}=\dfrac{4}{3}\pi \times 3\times 20\times 2\\\\=502.65\ mm^3/s[/tex]
So, the volume is increasing at the rate of [tex]502.65\ mm^3/s[/tex].
complete the table by supplying the measure of inscribed angle and its intercepted arc
Answer/Step-by-step explanation:
Based on the inscribed angle theorem, any inscribed angle = ½ of its intercepted arc
Thus:
✔️Inscribed angle = 57°
Intercepted arc would be: 2*57 = 114°
✔️Intercepted arc would be: 123°
Inscribed angle = ½(123) = 61.5°
✔️Intercepted arc would be: 46°
Inscribed angle = ½(46) = 23°
✔️Inscribed angle = 69°
Intercepted arc would be: 2*69 = 138°
✔️Intercepted arc would be: 155°
Inscribed angle = ½(155) = 77.5°
2 3/4 yards of fabric for $22 express as unit rate. round to nearest cent if necessary
Answer:
7
Step-by-step explanation:
Answer:
13(rounded) cents per 1/4 yard and 50 cents per yard
Step-by-step explanation:
Step 1: Convert the mixed fraction into an improper fraction
[tex]2\frac{3}{4} = \frac{4}{4}+\frac{4}{4}+\frac{3}{4}[/tex]
[tex]2\frac{3}{4}=\frac{11}{4}[/tex]
Step 2: Find the unit price per 1/4 yard
[tex]\frac{11}{4}/22[/tex]
[tex]0.125 = 13 \ cents[/tex]
Step 3: Find the unit price per 1 yard
[tex]12.5\ cents\ per\ 1/4\ yard=50\ cents\ per\ 1\ yard[/tex]
Answer: 13(rounded) cents per 1/4 yard and 50 cents per yard
work out the value of angle x 62 degrees
Answer:
180- (62*2)= x( angles opposite to equal sides)
180-124= x
x= 56
Step-by-step explanation:
Help and show work please
Answer:
11111111 111 1 1 1 11
Step-by-step explanation:
Answer:
ok 1+1= 25 and add 3000 and you get 1
Step-by-step explanation:
Select all expressions that are equal to 3⋅3⋅3⋅3⋅3.
3^5
3^4 ⋅ 3
5 ⋅ 3
5^3
[tex]\huge\text{Hey there!}[/tex]
[tex]\mathsf{3\times3\times3\times3\times3}\\\\\mathsf{3\times3=\bf9}\\\\\mathsf{9\times9\times3}\\\\\mathsf{9\times9=\bf81}\\\\\mathsf{81\times3=\bf result}\\\\\mathsf{= \bf \underline{243}}\large\checkmark[/tex]
[tex]\text{Option A. }\downarrow\\\mathsf{3^5}\\\\\mathsf{3^5= 3\times3\times3\times3\times3}\\\\\mathsf{3\times3\times3\times3\times3}\\\\\mathsf{3\times3 = 9}\\\\\mathsf{9\times9\times3}\\\\\mathsf{9\times9 = 81}\\\\\mathsf{81\times3= 243}\\\\\large\text{\bold{Option A.} could possibly be your \bf ANSWER}\huge\checkmark[/tex]
[tex]\text{Option B. }\downarrow\\\mathsf{3^4\times5}\\\mathsf{3^4 = 3\times3\times3\times3}\\\\\mathsf{3\times3\times3\times3}\\\\\mathsf{3\times3=9}\\\\\mathsf{9\times9= 81}\\\\\mathsf{81\times3=243}\\\\\large\text{Option B. could possibly be your \bf ANSWER}\huge\checkmark[/tex]
[tex]\text{Option C. }\downarrow\\\mathsf{3\times5}\\\\\maths{3+3+3+3+3}\\\\\mathsf{3+3=6}\\\\\mathsf{6+6+3}\\\\\mathsf{6+6=12}\\\\\mathsf{12+3=15}\\\\\mathsf{15\neq243}\\\\\large\text{Option C is NOT your ANSWER}[/tex]
[tex]\text{Option D.}\downarrow\\\mathsf{5^3}\\\\\mathsf{5^3=5\times5\times5}\\\\\mathsf{5\times5\times5}\\\\\mathsf{5\times5=25}\\\\\mathsf{25\times5 = 125}\\\\\mathsf{125\neq243}\\\\\large\text{Option D. is NOT your ANSWER}[/tex]
[tex]\boxed{\boxed{\large\text{Answers: \boxed{\boxed{\mathsf{\bf{Option\ A.)\ 3^5 \ \& \ Option\ B.)\ 3^4 \times 3}}}}}}}}\huge\checkmark[/tex]
[tex]\text{Good luck on your assignment and enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
Answer:
A) 3^5 B) 3^4*3
Step-by-step explanation:
Ford provides an option of a sunroof and side air bag package for its Windstar model. This package costs$1400. Ford wants todetermine the percentage of Windstar buyers who would pay $1400 extra for the sunroof and side air bags. How many Windstar buyers must be surveyed if we want to be 95% confident that the sample percentage is within four percentage points of the true percentage for all Windstar buyers
Answer:
601 buyers must be surveyed.
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].
The margin of error is:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
95% confidence level
So [tex]\alpha = 0.05[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.05}{2} = 0.975[/tex], so [tex]Z = 1.96[/tex].
How many Windstar buyers must be surveyed if we want to be 95% confident that the sample percentage is within four percentage points of the true percentage for all Windstar buyers?
We need to survey n buyers. n is found when [tex]M = 0.04[/tex]. We dont have an estimate for the proportion, so we use [tex]\pi = 0.5[/tex], which is when the largest sample will be needed.
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
[tex]0.04 = 1.96\sqrt{\frac{0.5*0.5}{n}}[/tex]
[tex]0.04\sqrt{n} = 1.96*0.5[/tex]
[tex]\sqrt{n} = \frac{1.96*0.5}{0.04}[/tex]
[tex](\sqrt{n})^2 = (\frac{1.96*0.5}{0.04})^2[/tex]
[tex]n = 600.3[/tex]
Rounding up
601 buyers must be surveyed.
Evaluate the integral. (Use C for the constant of integration.)
cos(x) (8 + 7 sin^2(x)) dx
Answer: [tex]8 \sin x +7(\dfrac{\sin^3x}{3})+C[/tex]
Step-by-step explanation:
Consider [tex]\int \cos(x) (8+7 \sin^2(x)) \, dx[/tex]
Substitute t= sinx
then dt = cos x dx
[tex]\int \cos(x) (8+7 \sin^2(x)) \, dx = \int (8+7t^2)dt\\\\ =8t+7(\dfrac{t^3}{3})+C[/tex]
[tex][\int x^ndx=\dfrac{x^{n+1}}{n+1}+C][/tex]
[tex]=8 \sin x +7(\dfrac{\sin^3x}{3})+C[/tex]
Hence, [tex]\int \cos(x) (8+7 \sin^2(x)) \, dx=8 \sin x +7(\dfrac{\sin^3x}{3})+C[/tex]
Please help ..........
What is the value of k if (1, 1) is a solution of 2x + 7y=k?
Please help me I wanna go to sleep
What is true about this sequence?
8000, 4000, 2000, 1000, ...
Answer:
B
Step-by-step explanation:
each consecutive term is divided by 2
2х - 12 = 24
Зу - 15 = 60
Find the product of X and y.
450
325
120
260
144
I don’t know what to do or what the answer is
Answer:
x=18 y=25
Step-by-step explanation:
1)2x18=36-12=24
2)3x25=75-15-60
There are 12 counters. One third of the counters are yellow. How many counters are yellow?
Answer:
I think 4
Step-by-step explanation:
1/3 is how many are yellow. so if u do 12/3=4
Answer:
4
Step-by-step explanation:
1/3 is equivalent to 4×1 and 2/3 is equivalent to 4×2 and 3/3 is equivalent to 4×3 which equals 12 so there are 4 counters that are yellow.
How do you find the slope to (3,12),(3,-17)
Answer:
you plot them together
1. draw a t shape and then plot it like x then y
Answer:
trust your instincts
Step-by-step explanation:
decide on your own destiny i can not interfeir
Please help please please plewse
Answer:
-1 and -5
Step-by-step explanation:
Determine the slope of the line whose equation is 2x-3y=5
How many cups are in 16 gallons?
64
256
128
2,048
Answer:
256 cups
Each gallon has 16 cups so 16 gallons would have 16*16 cups. 16*16 = 256
Dalle note 3 green 1 we ame 7 vel maps on abier med up and make one of the
Answer:
I have no idea what this means
A rectangular city park is 6/8 mile long the park has an area of 1/4 Mile2. What is the width of the park?
I need an answer! Please!
Answer:
The answer is 1/3
Step-by-step explanation:
divide 6/8 and 1/4 and you will get 1/3
How do you simplify 32/48
Answer:
2/3
Step-by-step explanation:
divide numerator and denominator by 16
32÷16=2
48÷16=3
answer is 2/3
Thus, 2/3 is the simplified fraction for 32/48 by using the GCD or HCF method. Thus, 2/3 is the simplified fraction for 32/48 by using the prime factorization method.
The measures of two angles of a triangle are 22 and 85 degrees. Find the measure of the third angle.
Answer: [tex]73^{\circ}[/tex]
Step-by-step explanation:
Angles in a triangle add to 180 degrees.
If you were to calculate the average rate of change of a function over a variety of intervals and you found that they were all the same, what conclusion could you draw and why
The Property where if the order of addends changes, the sum stays the change
3/2 inches snow fell in 3/4 of an hour which two statements are true
Answer:
I don't see the two statements
Step-by-step explanation:
Answer:
A and E Usa test prep
Step-by-step explanation:
I know it might be late by now but this is for the people who are searching for the answer for the future
Please answer !!!! Due in 10 minutes
1-3=0kwgf8ebeuf iwbrjievtirvr8rvhe
Help me this math problem
Let f(x) be the trigonometric function f(x)=sin(x).
On the interval [0,2π), the maximum value(s) of f(x) occur(s) at what x-value(s)?
Answer:
im on a chalange
Step-by-step explanation:
please choose someone else i have 1 day to do this
(ab)(6a^5b)(-ab) simplified please
Answer:
25b3a+93b+60a=30a2+b2
Step-by-step explanation:
PLS HELP!!
Figure ABCD has vertices A(1, 1), B(1, 4), C(4,4), and D(4,1). What are the coordinates of the vertices of Figure
A'B'C'D' after a reflection across the line x = -2 and a translation 3 units up? Drag numbers to complete the coordinates.
Numbers may be used once, more than once, or not at all.
-
numbers are -8,-7,-6,-5,-4,4,5,6,7,8
Answer:
A’ (-5,4) B’ (-5,7), C’ (-8,7), D‘ (-8,4)
Step-by-step explanation:
Just had this test lol
hottest centralisation
Answer:
centralisation mean a direction explain that we often a high how well we cancan predict future actions of others.
Step-by-step explanation:
Nick went canoeing on the river he traveled 1 mile in 17 minutes.at this rate,how far will he travel in an hour and 25 minutes
9514 1404 393
Answer:
5 miles
Step-by-step explanation:
An hour and 25 minutes is 85 minutes. Using the given information we can find the distance d with the proportion ...
[tex]\dfrac{\text{distance}}{\text{time}}=\dfrac{d}{85\text{ min}}=\dfrac{1\text{ mi}}{17\text{ min}}\\\\d=\dfrac{85\text{ min}}{17\text{ min}}(1\text{ mi)}\qquad\text{multiply by $85$ min}\\\\d=5(1\text{ mi})\qquad\text{simplify}\\\\d=\boxed{5\text{ mi}}[/tex]
In 1 hour and 25 minutes, Nick will travel 5 miles.
What is the total interest paid on an $185,000 loan at 6.25% APR over 15 years (monthly payments)?
Answer:
Total Interest $100,522
Step-by-step explanation:
Answer:
$100,522
Step-by-step explanation: