Answer:
(a) 0.198 cm/s (b) 1 cm/s
Step-by-step explanation:
It is given that,
The rate of change of area of a cicle, [tex]\dfrac{dA}{dt}=5\ cm^2/s[/tex]
(a) The area of a circle is given by :
[tex]A=\pi r^2[/tex]
Differentiate both sides,
[tex]\dfrac{dA}{dt}=2\pi r\dfrac{dr}{dt}\\\\\text{Put the value of dA/dt and r = 4 cm}\\\\\dfrac{dr}{dt}=\dfrac{dA/dt}{2\pi r}\\\\\dfrac{dr}{dt}=\dfrac{5}{2\pi \times 4}\\\\\dfrac{dr}{dt}=0.198\ cm/s[/tex]
(b) Circumference, [tex]C=2\pi r[/tex] = 5 cm
[tex]\dfrac{dA}{dt}=2\pi r\dfrac{dr}{dt}\\\\\dfrac{dr}{dt}=\dfrac{dA/dt}{2\pi r}\\\\\dfrac{dr}{dt}=\dfrac{5}{5}\\\\\dfrac{dr}{dt}=1\ cm/s[/tex]
Hence,
(a) 0.198 cm/s (b) 1 cm/s
Wear a mask when spraying insecticides. right or not
Answer:
right. because if the insecticides gets in your mouth, it will infiltrate your lungs and you will suffocate.
Step-by-step explanation:
How much would 7 bottles of water cost
Answer:
$5.25
Step-by-step explanation:
You have saved $1500 to buy a TV you notice the store is offering one year same as cash deal you can take the TV home today and pay nothing until one year from now when you’re out of the store $1500 purchase price if your savings account earns 5% a year what is the NPV of this offer
Answer:
The net present value of 1,500 a year from now at 5% interest is $1,428.57.
Step-by-step explanation:
NPV = 1,500 / 1.05 = 1,428.57
A single card is drawn from a standard 52 card deck.
Work out the probability of choosing the "6 of hearts".
Give your answer in its simplest form.
Answer:
No. of 6 of hearts = 1
Total no. of cards = 52
Probability = 1/52
Hope it helps....... pls mark as brainliest
This is the likelihood or chance that an event will occur. The probability of choosing the "6 of hearts" is 1/52
What is probabiility?This is the likelihood or chance that an event will occur. Mathematically;
Probability =expected/total
Since a standard deck of card contains 52 cards, hence total outcome is 52 cards
No. of 6 of hearts is 1 from the deck of cards
Pr(choosing 6 of hearts) = 1/52
Hence the probability of choosing the "6 of hearts" is 1/52
Learn more on probability here: https://brainly.com/question/7965468
#SPJ2
Find the volume of the cylinder 9 cm and 23 cm 
A company sells 14 types of crackers that they label varieties 1 through 14, based on spice level. What is the probability that the purchase results in a selection of a cracker with an odd number, or a number greater than 11?
Answer:
The required probability is [tex]\mathit{\frac{9}{14}}[/tex]
Step-by-step explanation:
Probability: Rule of Addition
The probability that Event A or Event B occurs is equal to the probability that Event A occurs plus the probability that Event B occurs minus the probability that both Events A and B occur. It can be calculated as follows:
P(A ∪ B) = P(A) + P(B) - P(A ∩ B)
There are 14 types of crackers the company sells, numbered from 1 to 14. The sample space for purchasing one cracker is:
[tex]\Omega=\{1,2,3,4,5,6,7,8,9,10,11,12,13,14\}[/tex]
There are n=14 possible choices.
The favorable cases for a cracker with an odd number are:
A = {1,3,5,7,9,11,13}
There are 7 favorable cases.
The favorable cases for a cracker with a number greater than 11 are:
B = {12,13,14}
There are 3 favorable cases.
The cases which are common to both events are:
A ∩ B= {13}
There is 1 case.
The probability of each event is:
[tex]\displaystyle P(A)=\frac{7}{14}=\frac{1}{2}[/tex]
[tex]\displaystyle P(B)=\frac{3}{14}[/tex]
[tex]\displaystyle P(A\cap B)=\frac{1}{14}[/tex]
Therefore:
[tex]\displaystyle P(A\cup B)=\frac{1}{2}+\frac{3}{14}-\frac{1}{14}[/tex]
Adding the fractions:
[tex]\displaystyle P(A\cup B)=\frac{7+3-1}{14}=\frac{9}{14}[/tex]
The required probability is [tex]\mathbf{\frac{9}{14}}[/tex]
The graph of f(x) = x2 has been shifted into the form f(x) = (x − h)2 + k:
Answer:
3
Step-by-step explanation:
H is a horizontal shift to the right. The graph went over 2, so h=2. From there the graph went up 3 (vertical shift) so K=3
A baker bought a total of 12 pounds of apples and bananas for $10.20.
The system of equations {a+b=120.75a+1.05b=10.20 models this situation, where a is the number of pounds of apples, and b is the number of pounds of bananas.
How many pounds of each did the baker buy?
8 ÷ 10 =
R
wright the number and the remainder
Answer: 0.8
Step-by-step explanation:
Add a decimal point, and then add a zero to 8. Divide 8.0 ÷ 10. Your answer is 0.8 because 0.8 goes into 8 10 times. There is no remainder.
Hope it helps
lovelymoonlight
I need step by step help how to work this out
Answer:
31.73
Step-by-step explanation:
[tex]3x^{2} +5y[/tex]
x = 2.1
y = 3.7
Substitute;
[tex]3(2.1)^{2} +5(3.7)=3(4.41)+18.5=13.23+18.5=31.73[/tex]
Just answer number 1
M<7=30 ,m<2 ?
Answer:
Step-by-step explanation:
1). ∠7 ≅ ∠ 2 (alternate exterior)
m∠7 = m∠2 = 30°
2). ∠4 and ∠1 are supplementary angles
m∠1 = 180° - 72° = 108°
What are the solutions of 8x2 = 6 + 22x? Check all of the boxes that apply.
x = -3
x =
x = 3
x = 6
Answer:
x = 3 x = ‐1/4
Step-by-step explanation:
Was right on the quiz
Answer:
x = 3 x = ‐1/4
Step-by-step explanation:
the first one is also right!!
In the figure below, m angle a=3x+5;m angle b=5x-18 , and m angle c=7x-2 .
Answer:
∠a=44,∠b=47, ∠c=89
Step-by-step explanation:
we can note that
∠a+∠b+∠c=180
hence,
3x+5+5x-18+7x-2=180
therefore,
3x+5x+7x+5-18-2=180
15x-15=180
15x=180+15
15x=195
x=[tex]\frac{195}{15}[/tex]
then, x=13.
with this values we can find all the angles:
∠a=3x+5 ⇒∠a=3(13)+5⇒∠a=39+5⇒∠a=44
∠b=5x-18⇒∠b=5(13)-18⇒∠b=65-18⇒∠b=47
∠c=7x-2⇒∠c=7(13)-2⇒91-2⇒∠c=89
We can corroborate these result by adding them.
∠a+∠b+∠c=
44+47+89=180
Thats right !!
PLSSS HELP WILL MARK BRANLIEST!!
Which of the following expressions represents the area of the triangle above?
Select one:
A. ax2
B. x3
C. 2x3
D. 2a2x
Answer:
A
Step-by-step explanation:
the final answer after multiplying them all is 2ax^2, but since its a triangle you multiply that by 1/2 to get ax^2
Which system of linear inequalities has the point (2 ,3 ) in its solution set?
Answer:
Step-by-step explanation:
Given linear inequalities of the point (2,3)
So.
(X-2)(X-3)=0
x^2-2x-3x+6=0
x^2-5x+6=0
It's solutions is x^2-5x+6.
point y is between the points X and Z. if XY =3x- 4 , YZ = 2x +3, and XZ =24
Answer:
The numerical value of XY is 11
The numerical value of YZ is 13
Step-by-step explanation:
Given that
XY =3x- 4 , YZ = 2x +3, and XZ =24
As Y is between the points X and Z so the sum of length of XY and YZ will be equal to the length of XZ. Putting this in mathematical form
[tex]XY+YZ = XZ[/tex]
Putting the values
[tex](3x-4) + (2x+3) = 24\\3x-4+2x+3 = 24\\5x-1 = 24\\5x = 24+1 \\\frac{5x}{5} = \frac{25}{5}\\x = 5[/tex]
Now
[tex]XY = 3x-4 = 3(5)-4 = 15-4 = 11[/tex]
[tex]YZ = 2x+3 = 2(5)+3 = 10+3 = 13[/tex]
Hence,
The numerical value of XY is 11
The numerical value of YZ is 13
Write the slope-intercept form of the equation of each line. Identify the slopes y-intercept
Answer:
It is
X -6 -4 0 4 6
Y 8 6 2 -2 -4
If f(x) = 2x?- , what is f(- 6) ?
Answer:
Step-by-step explanation:
f(-6)= 2(-6)= -12
Answer:
Step-by-step explanation:
2x=2(-6)= -12
Lines x and y are parallel write an equation that represents the relationship between b and e. Explain how you know the equation is always true
Answer:
b+e= 180 degrees
Step-by-step explanation:
Because they are perpindicular
Answer:
Step-by-step explanation:
Race to get brainliest, need help!
The sum of digits in a two-digit number is 14. If you double the reversed number and add the result to the original number, the sum would be 222. Find the original number
Answer:
Original number is 86
Step-by-step explanation:
Original: 10x + y
Double reversed: 2(10y + x)
Constraints:
x + y = 14 ===> x = 14 - y
2(10y + x) + 10x + y = 222 ===> 21y + 12x = 222
Substitution to find y:
21y + 12x = 222
21y + 12(14 - y) = 222
21y + 168 - 12y = 222
9y + 168 = 222
9y = 54
y = 6
Substitution to find x:
x = 14 - y
x = 14 - 6
x = 8
Original: 10x + y
10(8) + (6)
80 + 6
86
Which algebraic expression represents this phrase? the product of 40 and the distance to the finish line A. 40•d B.
[tex] \frac{40}{d} [/tex]
C. 40 - d D. 40 + d
Answer:
A 40•d
Step-by-step explanation:
The product of 40 and the distance (d)
40•d
B is division
C is subtraction
D is addition
The product of two numbers is multiplication, so the answer must be A
You move up 2 units and down 7 units. You end at (1, -2). Where did you start?
(5,-2)
that's all. up and down basically means that the point is moving along the x axis.
Identify the range of the function shown in the graph. 10 B 0 4 2 -10 8 -10 O A. yis all numbers. O B. 4-1,1} C. -1sys 1 O D. y> -1
From the graph, the range of the sine function will be [-1, 1]. Then the correct option is C.
What is trigonometry?Trigonometric functions examine the interaction between the dimensions and angles of a triangular form.
It is a function that repeats itself in a particular time interval.
The domain means all the possible values of x and the range means all the possible values of y.
From the graph, the curve is a sinusoidal function. The domain of the sine function is all real numbers.
From the graph, the range of the sine function will be [-1, 1]. Then the correct option is C.
The diagram is given below.
More about the trigonometry link is given below.
https://brainly.com/question/22698523
#SPJ1
PBS News Hour reported in 2014 that 39.4% of Americans between the ages of 25 and 64 have at least a two-year college degree.† Assume that 55 Americans between the ages of 25 and 64 are selected randomly.
(a) What is the expected number of people with at least a two-year college-degree?
(b)What are the variance and standard deviation for the number of people with at least a two-year college degree? (Round your answers to four decimal places.)
Answer:
Mean = 22
Variance = 13.1320
Standard Deviation = 3.6238
Step-by-step explanation:
From the question, we can deduce that
n = 55 (sample)
p = 39.4% (proportion of those within the given range)
Solving (a): Expected Value, E(x)
This is calculated using the following formula.
E(x) = np
Substitute values for n and p
E(x) = 55 * 39.4%
E(x) = 55 * 0.394
E(x) = 21.67
E(x) = 22 ---- Approximated
Hence, the expected number of people is 22
Solving (b): Variance (σ²) and Standard Deviation (σ)
σ² is calculated as thus:
σ² = np(1 - p)
σ² = 55 * 39.4% * (1 - 39.4%)
σ² = 55 * 0.394 * (1 - 0.394)
σ² = 55 * 0.394 * 0.606
σ² = 13.13202
σ² = 13.1320 ---- Approximated
σ is calculated as follows:
σ = √σ²
Substitute value for σ²
σ = √13.13
σ = 3.6238 ----- Approximated
Write an equation in point-slope form and slope-intercept form for the line.
passes through (6, -6), slope = 5
Answer:
y = 5- 36
Step-by-step explanation:
6 is the x
-6 is the y
y=mx+b
so m times x, m is the slope
5 times 6 is 30
-6=30+b
so -36
y=5x-36
SORRY IF IM WRONG I TRIED
Please please help me get the anwser I just want the anwser I got a 33.3 on my last attempt and this is my last please :( I will literally give you 87 points I need help ASAP please I set it to 87 points please take Time and anwser correctly or I will report please :( I only have 11/6/2020
Answer: A
Step-by-step explanation:
Answer:
Its b
Step-by-step explanation:
Please help I’ll mark brainliest, also tell me why you got that answer please
Answer:
D
Step-by-step explanation:
I did the math on paper and I got d
What value should go in the empty boxes to complete the calculation for finding the product of 0.61 x 0.45? Both numbers are the same, however, only input the number one time in your answer.
Answer:
the empty boxes would both be 4
but it says only put the number one time in answer
so it would be 4
Step-by-step explanation:
An airplane travels 550 miles from North Carolina to Tennessee in 90 minutes. At this rate, how many minutes will it take the airplane to travel 6,600 miles?
Answer:
It will take 1,080 min or 18 hours
Step-by-step explanation:
Here is why, since 6600 miles is 12 times farther than 550 miles you'd multiply the time it took to go 550 miles by 12 too
I need help with Kumon math level I 187 B
Answer:
attached is the answer :)
Step-by-step explanation:
The length of the tangent AB is [tex]\sqrt{2a^{2}+2b^{2} }[/tex] if the radii of the largest circle is a and the radii of the smallest one is b.
What is the tangent?It is a line that touches a single point on the circle.
How to determine the length of that tangent?Firstly we have to draw a perpendicular from O to the radii of the smallest circle. In this way AOLB becomes a rectangle. We let the point where the bisector intersect the radii as L.
OA=a
Lb=a also
O'L=b-a
In triangle OLO' we use pythagoras to calculate the value of OL which wil then equal to AB so,
OL=[tex]\sqrt{(b-a)^{2}+(a+b)^{2} }[/tex]
=[tex]\sqrt{2a^{2}+2b^{2} }[/tex]
It will be the length of AB also.
Learn more about circles at https://brainly.com/question/24375372
#SPJ2
