Answer: It is 10
Step-by-step explanation:
If the radius r of a circle is decreasing at the rate of 5 cm per minute, find the rate of change of area when radius is 6 cm.
Answer:
-94.2 [tex]cm^2/min[/tex]
Step-by-step explanation:
Rate of change of radius = -5 cm per minute (as it is decreasing)
Radius of circle = 6 cm
Formula for area of Area:
[tex]A = \pi r^2[/tex]
Formula for differentiation of [tex]y = x^n[/tex]:
[tex]\dfrac{dy}{dt} = nx^{n-1}\dfrac{dx}{dt}[/tex]
Differentiating area w.r.to [tex]t[/tex]:
[tex]\dfrac{dA}{dt} = 2\pi r\dfrac{dr}{dt}[/tex]
Putting the values, [tex]r = 6, \frac{dr}{dt} = -5[/tex] cm per minute.
[tex]\dfrac{dA}{dt} = 6\pi \times (-5)\\\Rightarrow \dfrac{dA}{dt} = -30 \times 3.14\\\Rightarrow \dfrac{dA}{dt} = -94.2\ cm^2/min[/tex]
Negative sign indicates that area is decreasing.
Rate of change of area is -94.2 [tex]cm^2/min[/tex].
The area decreases at a rate of -188.4 square centimeter per minute
The area (A) of a circle of radius (r) is represented as:
[tex]A = \pi r^2[/tex]
Differentiate the area, with respect to r
[tex]A' = 2\pi r r'[/tex]
From the question, we have:
Radius (r) = 6cmRate of change of radius (r') = -5cm per minuteSo, the equation becomes
[tex]A' = 2\times 3.14 \times 6 \times (-5)[/tex]
[tex]A' =- 188.4[/tex]
Hence, the area decreases at a rate of -188.4 square centimeter per minute
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After writing a check mike had -$34.50 in his account, he deposited $20.00 how much did he have now?
Answer:
-$14.50
Step-by-step explanation:
This is easily solved on a calculator.
-34.50 + 20.00 = -14.50
This is soo hard can someone please help
-
18 The diagram shows triangle PQR.
Diagram NOT
accurately drawn
P
17.8 cm
360
R
26.3 cm
Calculate the length of PR.
Give your answer correct to 3 significant figures.
Answer:
The length of PR is 15.8 cm
Step-by-step explanation:
We will solve the question using the cosine rule
In ΔPQR
∵ (PR)² = (PQ)² + (RQ)² - 2(PQ)(RQ)(cos∠Q)
∵ PQ = 17.8 cm
∵ RQ = 26.3 cm
∵ m∠Q = 36°
→ Substitute them in the rule above
∵ (PR)² = (17.8)² + (26.3)² - 2(17.8)(26.3)(cos36)
∴ (PR)² = 316.84 + 691.69 - 936.28(cos36)
∴ (PR)² = 251.0635685
→ Take √ for both sides
∴ PR = 15.8449856
→ Correct it to 3 significant figures
∴ PR = 15.8 cm
∴ The length of PR is 15.8 cm
Mrs. Robert’s vegetable garden is 6 feet wide and 8 feet long. A drawing of the garden has a scale of 1 inch 2 feet. What is the area of the garden on the scale drawing? a. 192 in b. 12 in c. 7 in d. 28 in
Answer:
Step-by-step explanation:
It’s 24
Answer:
b.12 inch squared
Step-by-step explanation:
6 feet become 3 inches and 8 feet becomes 4 inches 3×4 = 12
The average lifetime of a light bulb is 3,000 hours with a standard deviation of 696 hours. A simple random sample of 36 bulbs is taken. a. What are the expected value, standard deviation, and shape of the sampling distribution of
Answer:
Answer and Explanation:
We have:
Population mean,
μ
=
3
,
000
hours
Population standard deviation,
σ
=
696
hours
Sample size,
n
=
36
1) The standard deviation of the sampling distribution:
σ
¯
x
=
σ
√
n
=
696
√
36
=
116
2) As per the central limit theorem, the expected value of the sampling distribution is equal to the population mean.
Therefore:
The expected value of the sampling distribution is equal to the population mean,
μ
¯
x
=
μ
=
3
,
000
The standard deviation of the sampling distribution,
σ
¯
x
=
116
The shape of the sampling distribution of
¯
x
is approximately normal. As the sample size is more than
30
.
3) The probability that the average life in the sample will be between
2670.56
and
2809.76
hours:
P
(
2670.56
<
x
<
2809.76
)
=
P
(
2670.56
−
3000
116
<
z
<
2809.76
−
3000
116
)
=
P
(
−
2.84
<
z
<
−
1.64
)
=
P
(
z
<
−
1.64
)
−
P
(
z
<
−
2.84
)
=
0.0482
Using Excel: =NORMSDIST(-1.64)-NORMSDIST(-2.84)
4) The probability that the average life in the sample will be greater than
3219.24
hours:
P
(
x
>
3219.24
)
=
P
(
z
>
3219.24
−
3000
116
)
=
P
(
z
>
1.89
)
=
0.0294
Using Excel: =NORMSDIST(-1.89)
5) The probability that the average life in the sample will be less than
3180.96
hours:
P
(
x
<
3180.96
)
=
P
(
z
<
3180.96
−
3000
116
)
=
P
(
z
<
1.56
)
=
0.9406
The expected value, standard deviation, and shape of the sampling distribution of will be 116.
What is Standard deviation?Standard deviation is the measure of dispersed the data is in relation to the mean. Low standard deviation means data are clustered around the mean, and high standard deviation indicates data are more spread out.
Given that;
The average lifetime of a light bulb is 3,000 hours with a standard deviation of 696 hours.
And, A simple random sample of 36 bulbs is taken.
Now,
Since, The average lifetime of a light bulb is 3,000 hours with a standard deviation of 696 hours.
And, A simple random sample of 36 bulbs is taken.
Hence, The expected value, standard deviation, and shape of the sampling distribution of is,
⇒ Standard error = 696 / √ 36
= 696 / 6
= 116
Thus, The expected value, standard deviation, and shape of the sampling distribution of = 116.
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An industrial factory makes / yards of chain every minute. The cost of each yard of chain is $2.00. What is the total cost for all chain produced in 10 minutes?
Answer:
Cost = $86.67
Step-by-step explanation:
Given
Yards = 4⅓ (missing part of the question)
Cost per yard = $2.00
Required
Determine cost of chains produced in 10 minutes
If 4⅓ yards is made in a minute, then
4⅓ * 10 yards are made in 10 minutes
Total = 4⅓ * 10
Total = 13/3 * 10
Total = 130/3 yards
Cost of a yard of chain is $2.00.
Cost of 130/3 yards would be:
Cost = $2.00 * 130/3
Cost = $260.00/3
Cost = $86.67 (approximated)
Hence, the required cost is approximately $86.67
Write the expression represented by the following:
The quotient of a number and 7, increased by 5
Answer:
x (divistion symbol) 7 + 5
Step-by-step explanation:
A rock is thrown upward with a velocity of 17 meters per second from the top of a 31 meter high cliff and it missies the cliff on the way back down when will the rock ve 8 meters from the ground level
Answer:
[tex]4.5\ \text{s}[/tex]
Step-by-step explanation:
t = Time taken
u = Initial velocity =17 m/s
v = Final velocity
s = Displacement
a = Acceleration
g = Acceleration due to gravity = 9.81 m/s² = a
[tex]v^2-u^2=2as\\\Rightarrow s=\dfrac{v^2-u^2}{2a}\\\Rightarrow s=\dfrac{0^2-17^2}{2\times -9.81}\\\Rightarrow s=14.73\ \text{m}[/tex]
Total height the rock is to fall when it is 8 meters from the ground is [tex]14.73+(31-8)=37.73\ \text{m}[/tex]
[tex]v=u+at\\\Rightarrow t=\dfrac{v-u}{a}\\\Rightarrow t=\dfrac{0-17}{-9.81}\\\Rightarrow t=1.73\ \text{s}[/tex]
Time taken to reach the maximum height is 1.73 s.
[tex]s=ut+\dfrac{1}{2}at^2\\\Rightarrow 37.73=0+\dfrac{1}{2}\times 9.81t^2\\\Rightarrow t=\sqrt{\dfrac{37.76\times 2}{9.81}}\\\Rightarrow t=2.77\ \text{s}[/tex]
Time taken from the maximum height to the point which is 8 m from the ground is 2.77 s.
So, time taken from the moment of the throw to the point 8 m from the ground is [tex]1.73+2.77=4.5\ \text{s}[/tex].
Evaluate the expression.
1.2 exponent 2
answer choices =
1.44
14.4
1.728
1.5
Answer:
1.44
Step-by-step explanation:
Answer:
the answer is 1.44
Step-by-step explanation:
Because the exponent of a number says how many times to use the number in a multiplication. In 1.2 exponent 2 the "2" says to use 1.2 twice in a multiplication, so 1.2'2 = 1.2 × 1.2 = 1.44 In words: 1.2'2 could be called "1.2 to the power 2" or "1.2 to the second power.
Your welcome
A box of 11 transistors has 4 defective ones.
A) If 2 transistors are drawn from the box together, what is the probability that both transistors are defective?
B) If 2 transistors are drawn from the box together, what is the probability that neither transistor is defective?
C) If 2 transistors are drawn from the box together, what is the probability that one transistor is defective?
Answer:
(a) 0.1325
(b) 0.4045
(c) 0.463
Step-by-step explanation:
Let X denote the number of defective transistors.
The proportion of defective transistors is, p = 4/11 = 0.364.
All the transistors are independent of the others.
The random variable X follows a binomial distribution.
(a)
Compute the probability that both transistors are defective, if 2 transistors are drawn from the box together as follows:
[tex]P(X=2)={2\choose 2}(0.364)^{2}(1-0.364)^{2-2}\\\\=1\times 0.132496\times 1\\\\=0.132496\\\\\approx 0.1325[/tex]
(b)
Compute the probability that neither transistors are defective, if 2 transistors are drawn from the box together as follows:
[tex]P(X=0)={2\choose 0}(0.364)^{0}(1-0.364)^{2-0}\\\\=1\times 1\times 0.404496\\\\=0.404496\\\\\approx 0.4045[/tex]
(c)
Compute the probability that one transistors are defective, if 2 transistors are drawn from the box together as follows:
[tex]P(X=1)={2\choose 1}(0.364)^{1}(1-0.364)^{2-1}\\\\=2\times 0.364\times 0.636\\\\=0.463008\\\\\approx 0.463[/tex]
what is the answer for 6.8×10²
Answer:
680
Step-by-step explanation:
Answer:
680
Step-by-step explanation:
10 to the 2nd power is 10 times 10 which is 100.
Now, 6.8 times 100 is 680.
Hope this helps you!!
Brainliest to RIGHT answer
Answer:
It's C
Step-by-step explanation:
Find n and r 10 pointsssss
Answer:
r = 11.623cm (aprox)
n = 6.153cm (aprox)
Step-by-step explanation:
Proportions:
9.8 ⇔ 4.3
n ⇔ 2.7
r ⇔ 5.1
n = 9.8*2.7/4.3 = 6.153 (aprox)
r = 9.8*5.1/4.3
r = 11.623 (aprox)
I need help with this question
Answer:
dfjkdhfhdsjfkldsjkljsdk;lv
Step-by-step explanation:
fjwdnjksnvl;snv;s
A professional language translator gets paid an average of $320 per hour with a standard deviation of $41.75 per hour. What proportion of professional language translators get paid less than $250 per hour? Assume the population is normally distributed. Round your answer to four decimal places
Answer:
0.0475 or 4% professional language translators get paid less than $250 per hour
Step-by-step explanation:
Mean = 320
Standard Deviation = 41.75
We need to find proportion of professional language translators get paid less than $250 per hour i.e P(x<250)
First we will find value of z
Using formula: [tex]z=\frac{x-\mu}{\sigma}[/tex]
We have x=250, finding z
[tex]z=\frac{x-\mu}{\sigma}\\z=\frac{250-320}{41.75}\\z=-1.67[/tex]
Now we will find P(z<-1.67) by looking into the normal distribution table
[tex]P(z<-1.67)=0.0475\\[/tex]
So,0.0475 or 4% professional language translators get paid less than $250 per hour
A Fahrenheit thermometer shows that the temperature is 13 degrees below zero. Enter the integer that represents the temperature in degrees Fahrenheit
Answer:
-13??? weird question... do you mean celcius themometer?
Step-by-step explanation:
Answer:
The integer that represents 13 degrees below 0 is -13°F.
Step-by-step explanation:
This is because the phrase "13 degrees below 0" is obviously not an integer meaning that the corresponding integer to this phrase would be -13.
P.S.
This question was asked by somebody else and I answered already so I am not copying the answer!
Hope this helps! :)
What is 56/15 as a decimal rounded to the nearest tenth
Answer:
3.73
Step-by-step explanation:
56/15
3 11/15
3.73
Find the value of θ from the following equation.(θ≤90°)
Answer: 10°
__________________________________________________________
We are given:
Sin(6θ) = Cos(3θ)
Solving for θ:
Simplifying Cos(3θ):
We know that:
Cos(θ) = Sin(90-θ)
So, we can say that:
Cos(3θ) = Sin(90 - 3θ)
Finding the value of θ:
Sin(6θ) = Cos(3θ)
Sin(6θ) = Sin(90 - 3θ) [Since Cos(3θ) = Sin(90 - 3θ)]
6θ = 90 - 3θ [If Sin(θ) = Sin(A) ; θ = A]
9θ = 90 [adding 3θ on both sides]
θ = 10° [dividing both sides by 9]
Please help with this as soon as you can. Really need help and no idea how to do it.
Answer:
DE, BC, BA, CA
Step-by-step explanation:
basically just find the ones that do not cross and those are parellel.
in need help wihe lateral asn and total surface area
what is the slope of the following line?
Answer:
-2
Hope this helps,
PumpkinSpice1
The slope of the line will be ( -1 / 2 ). The correct option is C.
Slope or the gradient is the number or the ratio which determines the direction or the steepness of the line.
An equation of the line is defined as a linear equation having a degree of one. The equation of the line contains two variables x and y. And the third parameter is the slope of the line which represents the elevation of the line.
The two points are (0,3) and ( 6,0). The slope of the line will be calculated by using the formula below;-
Slope = ( y₂ - y₁ ) / ( x₂ - x₁ )
Slope = ( 0 - 3 ) / ( 6 - 0 )
Slope = -3 / 6 = -1 / 2
Therefore, the slope of the line will be ( -1 / 2 ). The correct option is C.
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help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help
Answer:
41/200
This is solved and put in standard form
Please I need some answers
There are a total number of 38 possible equally likely outcomes on a roulette wheel. Out of the 38 outcomes, there are 18
odd-numbered outcomes. What's the probability of spinning an odd number?
• Express your answer as a fraction.
Answer:
9/19
Step-by-step explanation:
just put the total odd numbers, 18, over the total outcomes, 38, and divide them and simplify
Answer:
9/19
Step-by-step explanation:
PLEASE HELP FAST The Booster Club raised $30,000 for a sports fund. No more money will be placed into the fund. Each year the fund will decrease by 5%. Determine the amount of money, to the nearest dollar, that will be left in the sports fund after 4 years.
A.
$27,550
B.
$22,641
C.
$24,435
D.
$24,436
Answer:
c. $24,435
Step-by-step explanation:
[tex]30000(1 - .05)^{4} = 24,435.19[/tex]
The amount of money, to the nearest dollar, that will be left in the sports fund after 4 years is $24,435 option (C) is correct.
What is the percentage?It's the ratio of two integers stated as a fraction of a hundred parts. It is a metric for comparing two sets of data, and it is expressed as a percentage using the percent symbol.
It is given that:
The Booster Club raised $30,000 for a sports fund. No more money will be placed into the fund.
To find the amount of money, to the nearest dollar, that will be left in the sports fund after 4 years:
The money left after 4 years = 30000(1 - 0.05)⁴
After solving:
The money left after 4 years = $24,435
Thus, the amount of money, to the nearest dollar, that will be left in the sports fund after 4 years is $24,435 option (C) is correct.
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Sheila picks for 1 1/4 pounds of blueberries for $10 how many pounds can she pick for $1
Answer:
0.125 pounds of blueberries
Step-by-step explanation:
Trust me
Answer:
1/8
Step-by-step explanation:
1 1/4=1.25
1.25/10=0.125
0.125 in the simplest fraction form is 1/8
hope this helps :3
if it did pls mark brainliest
I NEED HELP WITH THIS PICTURE IS PROVIDED
At the start of the month, the value of an investment was $53.92. By the end of the month, the value of the investment changed by a loss of $17.40. What was the value, in dollars, of the investment at the end of the month
Answer:
$36.52
you're welcome :)
EAST MATH PLS HELP ASAP PLEASE PLEASE
If one side of a square is represented by x + 7, and the perimeter of the square is
represented by 8x - 20, what is the value of X?