SCALCET8 3.9.003. Each side of a square is increasing at a rate of 4 cm/s. At what rate is the area of the square increasing when the area of the square is 9 cm2
Answers
Answer: [tex]24\ cm^2/s[/tex]
Step-by-step explanation:
Given
Each side of square is increasing at a rate of 4 cm/s
Side of a square when area is [tex]9\ cm^2[/tex]
Suppose a is side of the square
[tex]\Rightarrow a=\sqrt{9}\\\Rightarrow a=3\ cm[/tex]
Area is given by
[tex]\Rightarrow A=a^2\\\text{Differentiate area w.r.t time}\\\\\Rightarrow \dfrac{dA}{dt}=2a\dfrac{da}{dt}\\\\\Rightarrow \dfrac{dA}{dt}=2\times 3\times 4\\\\\Rightarrow \dfrac{dA}{dt}=24\ cm^2/s[/tex]
Area is increasing at a rate of [tex]24\ cm^2/s[/tex]
Answer:
24cm^2/ s
Step-by-step explanation:
Related Questions
An initial deposit of $212 is placed in
a bank account and left to grow, with
interest compounded continuously.
what will it be after 6 years?
Round your answer to the nearest dollar.
Answers
Answer:
$224.932
Step-by-step explanation:
Note: The question is not complete
say the rate is 10%
Given data
Initial depostite= $212
TIme= 6years
rate= 10%
the expression for the compound interest is given as
A=P(1+r)^t
substitute
A=212(1+0.1)^6
A=212(1.01)^6
A=212*1.061
A= $224.932
Hence the final amount at the rate of 10% is $224.932
If the length, width, and height of a cube all change by a factor of 7, what happens to the volume of the cube?
The length is ___ times as large.
Answers
9514 1404 393
Answer:
The volume is 343 times as large.
The length is 7 times as large.
Step-by-step explanation:
If the original cube has side length s, its volume is given by ...
V = s³
When the side length is changed by a factor of 7, the new volume is ...
V = (7s)³ = 7³×s³ = 343s³
The volume of the cube changes by a factor of 7³ = 343.
__
The problem statement tells you the length is 7 times as large.
A film distribution manager calculates that 5% of the films released are flops. If the manager is right, what is the probability that the proportion of flops in a sample of 572 released films would be greater than 6%
Answers
Answer:
0.1357 = 13.57% probability that the proportion of flops in a sample of 572 released films would be greater than 6%
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal Probability Distribution
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]
A film distribution manager calculates that 5% of the films released are flops.
This means that [tex]p = 0.05[/tex]
Sample of 572
This means that [tex]n = 572[/tex]
Mean and standard deviation:
[tex]\mu = p = 0.05[/tex]
[tex]s = \sqrt{\frac{p(1-p)}{n}} = \sqrt{\frac{0.05*0.95}{572}} = 0.0091[/tex]
What is the probability that the proportion of flops in a sample of 572 released films would be greater than 6%?
1 subtracted by the p-value of Z when X = 0.06. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{0.06 - 0.05}{0.0091}[/tex]
[tex]Z = 1.1[/tex]
[tex]Z = 1.1[/tex] has a p-value of 0.8643
1 - 0.8643 = 0.1357
0.1357 = 13.57% probability that the proportion of flops in a sample of 572 released films would be greater than 6%
Amy has 2$, Jack has 3 times as much as Amy. Catherine has twice as much as Jack. How much does Catherine have?
Answers
2 times 3 is 6. 6 times 2 is 12. Final answer is 12.
Answer: 12 dollars
Step-by-step explanation:
2x3x2=12
Easy math
FIND THE EQUATION OF THE LINE.
I NEED ANSWER WITH STEP BY STEP PLEASE
Answers
Given:
The graph of a line.
To find:
The equation for the given line.
Solution:
From the given graph, it is clear that the line passes through the points (0,-5) and (5,0). So, the equation of the line is:
[tex]y-y_1=\dfrac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]
[tex]y-(-5)=\dfrac{0-(-5)}{5-0}(x-0)[/tex]
[tex]y+5=\dfrac{5}{5}(x)[/tex]
[tex]y+5=x[/tex]
Subtract 5 from both sides.
[tex]y+5-5=x-5[/tex]
[tex]y=x-5[/tex]
Therefore, the equation of the given line is [tex]y=x-5[/tex].
Choose the best graph that represents the linear equation:
y + 3 = 0
Graph A
On a coordinate plane, a line goes through (0, 3) and (1, 3).
Graph B
On a coordinate plane, a line goes through (negative 3, 0) and (negative 3, 1).
Graph C
On a coordinate plane, a line goes through (0, negative 3) and (1, negative 3).
Graph D
On a coordinate plane, a line goes through (0, 0) and (1, negative 3).
a.
Graph A
c.
Graph C
b.
Graph B
d.
Graph D
PLEASE HELP!!! Please select the best answer from the choices provided
A
B
C
D
Answers
Graph B is the best graph that represents the linear equation
Answer:
m=2b=1y=2x+1
just enter it
Which could be the function graphed below?
Answers
[tex]f(x)=\sqrt{x} -2[/tex] is the correct option
if 1 candian dollar is equivalent to 1.04 austrialian dollars what is the value if 4269 australian dollars in canadian currency?
Answers
Answer:
4104.807
Step-by-step explanation:
4269÷1.04
=4104.807
Answer:
4104.8
Step-by-step explanation:
To solve this problem, the easiest approach is to set up a proportion. Use the following general format;
[tex]\frac{currenncy_1}{currency_2}=\frac{balance_1}{balance_2}[/tex]
This will allow one to describe the relationship between the different currency values. Substitute in the given information and solve;
[tex]\frac{currenncy_1}{currency_2}=\frac{balance_1}{balance_2}[/tex]
[tex]\frac{canadian}{australian}=\frac{balance_1}{balance_2}[/tex]
[tex]\frac{1}{1.04}=\frac{x}{4269}[/tex]
Cross products,
[tex]\frac{1}{1.04}=\frac{x}{4269}[/tex]
[tex](1)(4269)=(1.04)(x)\\4269=1.04x[/tex]
Inverse operations,
[tex]4269=1.04x\\4104.8\approx x[/tex]
Simplify.
Rewrite the expression in the form 6^n6
n
6, start superscript, n, end superscript.
\dfrac{6^{4}}{6}=
6
6
4
Answers
Answer:
6^3
6 to the third power
or 3x3x3
Step-by-step explanation:
The solution of the expression 6⁻⁴.6⁶ will be 6².
What is an expression?Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.
Given that the expression is 6⁻⁴.6⁶. The expression will be solved as below:-
6⁻⁴.6⁶ = 6⁻⁴⁺⁶
Use the exponent property when the bases are the same then the powers will be added.
6⁻⁴.6⁶ = 6²
Therefore, the solution of the expression 6⁻⁴.6⁶ will be 6².
The complete question is to simplify the expression 6⁻⁴.6⁶.
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Ngân hàng rơi vào tình trạng vỡ nợ khi nào
Answers
Answer:
.
Step-by-step explanation:
.
please help please help
Answers
Answer:
1. 3
2. D
3. KE
4. B
5. A
Step-by-step explanation:
those should be your answers
Answer:
1. 3
2. D
3. E and K
4. B
5. A
negative integers lie on the negative side of the number line(usually having a minus sign in front of them)
positive ones lie on the positive side( usually have no signs in front of them)
if the area of a rectangle is 144cm and breadth is 6cm, find the perimeter of the rectangle
Answers
Find the length by dividing area by breadth:
144 /6 = 24 cm
Perimeter = 2breath + 2length
Perimeter = 2(6) + 2(24)
Perimeter = 12 + 48
Perimeter = 60 cm
Answer:
36
Step-by-step explanation:
Area = L*W
A = 144 cm^2
w = 6
L=?
144 = 6*L Divide by 6
144/6 = 6L/6
L = 24
P= 2w + 2L
P = 2*6 + 2*24
P = 12 + 25
P = 36 cm
On Monday, 27 adults visited an amusement park. On Tuesday, 23 adults visited the amusement park. The enterance fee for the adults is Rs. 100. How much amount is collected from the adults in these two days?
PLEASE TELL FULL SOLUTION.
Answers
Answer:
5000
Step-by-step explanation:
Add the number of adults first: 27+23=50
Then multiply the number of adults by 100 for the fee.
50*100 = 5000
Answer:
within the two days a total of 5000$ where collected in the two days
Solution:
R= 100 per adult
1 adult = 100
27(R)+ 23(R) = 27(100)+ 23(100)
27(100)+23(100) =5000
or add both 27 and 23 and multiple by 100
50•100 = 5000
Consignment Sale. Just Between Friends is the leading pop-up consignment sales event franchise in North America. The Des Moines event for Just Between Friends takes place each year at the Iowa State Fairgrounds for one week in the spring and one week in the fall. Families can earn money on gently used baby clothes, baby gear, maternity items, kids' clothes, shoes, toys, and books. Families sign-up as consignors and then price and tag their own items. At the end of the sale, consignors are given a check based on their item sales. Using historical records, the Des Moines event organizers advertise that their consignor check amounts follow a bell-shaped distribution (symmetric and unimodal) with a mean of $480 and a standard deviation of $110. Use the Empirical Rule: What percentage of consignors receive a check for more than $370
Answers
Answer:
Just Between Friends
The percentage of consignors who receive a check for more than $370 is:
= 16%.
Step-by-step explanation:
Mean of consignor check, μ = $480
Standard deviation, σ = $110
Value of check received, x > $370
Solution: find the z-score to determine the percentage of consignors who receive a check for more than $370:
z = (x-μ)/σ
z= ($370 - $480)/$110
z = -$110/$110
z = -1.00
Percentage of consignors who receive a check for more than $370
= 0.15866
= 0.16
= 16%
Which describes the transformation applied in the figure above?
1. Quadrilateral D’E’F’G’ was shifted down 6 units.
2. Quadrilateral DEFG was shifted up 6 units.
3. Quadrilateral D’E’F’G’ was reflected about the x-axis.
4. Quadrilateral DEFG was rotated counterclockwise 180 degrees about the point (-1,4).
Answers
Answer:
2 Quadrilateral DEFG was shifted up 6 units.
Step-by-step explanation:
trust me cuz when there is ' its not the orginal shape
How many voters should be sampled for a 95% confidence interval? Round up to the nearest whole number.
Answers
Answer:
467 voters
Step-by-step explanation:
Given
See attachment for complete question
Required
Sample size at 95% confidence interval
From the attachment, we have:
[tex]p = 65\% = 0.65[/tex]
[tex]E = 4.33\% = 0.0433[/tex]
[tex]CL = 0.95[/tex]
[tex]\alpha = 0.05[/tex] i.e. 1 - CL
First, we calculate the critical level
At [tex]CL = 0.95[/tex] and [tex]\frac{\alpha}{2}[/tex]
[tex]z^* = 1.96[/tex] --- the critical level
So, we have:
[tex]n = p * (1 - p) * (\frac{z^*}{E})^2[/tex]
[tex]n = 0.65 * (1 - 0.65) * (\frac{1.96}{0.0433})^2[/tex]
[tex]n = 0.65 * (1 - 0.65) * (45.3)^2[/tex]
[tex]n = 0.65 * 0.35 * 2052.1[/tex]
[tex]n = 466.9[/tex]
[tex]n = 467[/tex] --- approximated
What is the domain of the function f(x) = (-5/6)(3/5)superscript x
Answers
Answer:
[tex]-\infty < x < \infty[/tex]
Step-by-step explanation:
Given
[tex]f(x) = (-\frac{5}{6}) \cdot (\frac{3}{5})^x[/tex]
Required
The domain
There are no undefined points such as denominator of x or square roots.
Hence, the domain is:
[tex]-\infty < x < \infty[/tex]
Jonas builds a snow fort. He tells his friends it is 0.8 meters tall inside, but he rounded the height to the nearest tenth.
Which could be the height of the snow fort before Jonas rounded it?
2 answers
A. 0.85
B. 0.82
C. 077
Answers
Answer:
B. 0.82
C. 077
Step-by-step explanation:
Given
[tex]Number = 0.8[/tex] -- approximated
Required
The possible value of Number
Since [tex]Number = 0.8[/tex] is approximated, then the possible values of Number that can be gotten from the preparation
The approximated value 0.8 has the following range: 0.75 to 0.84
Options B and C are in this category.
HELP ASAP. I can’t miss anymore please help
Answers
[tex]4\pi[/tex]
Step-by-step explanation:
[tex]C = 2\pi r,\:\:\:\:r = 4[/tex]
The circumference of the circle of radius 4 is [tex]8\pi[/tex]. Since we are dealing with only half of the circle, the arc length is then half the circumference or [tex]4\pi[/tex].
If the nth term of a sequence is
28-3n what is the 7th term?
Answers
Answer:
7
Step-by-step explanation:
28-3(7)
The 7th term of the given sequence 28 - 3n is 7.
What is sequence?A sequence is an ordered list of elements with a specific pattern.
According to the given question.
We have a sequence 28 - 3n.
So, for finding the value 7th term of the sequence substitute n = 7 in
28 - 3n.
Therefore, the 7th term of the given sequence
= 28 - 3(7)
= 28 - 21
= 7
Hence, the 7th term of the given sequence 28 - 3n is 7.
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A quality control expert at Glotech computers wants to test their new monitors. The production manager claims they have a mean life of 82 months with a standard deviation of 7 months. If the claim is true, what is the probability that the mean monitor life would be greater than 83.8 months in a sample of 71 monitors
Answers
Answer:
0.015 = 1.5% probability that the mean monitor life would be greater than 83.8 months in a sample of 71 monitors
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
Mean life of 82 months with a standard deviation of 7 months.
This means that [tex]\mu = 82, \sigma = 7[/tex]
Sample of 71
This means that [tex]n = 71, s = \frac{7}{\sqrt{71}}[/tex]
What is the probability that the mean monitor life would be greater than 83.8 months?
1 subtracted by the p-value of Z when X = 83.8. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{83.8 - 82}{\frac{7}{\sqrt{71}}}[/tex]
[tex]Z = 2.17[/tex]
[tex]Z = 2.17[/tex] has a p-value of 0.985.
1 - 0.985 = 0.015
0.015 = 1.5% probability that the mean monitor life would be greater than 83.8 months in a sample of 71 monitors
it's tooooo easy who wants brain list
Answers
Answer:
1) Isosceles
2) Acute
3) Right angled
4( Obtuse
5) Equilateral
2)Acute
3) right angled
4)obtuse
5)Equilateral
DO THIS AND ILL MARK! PLEASE
Answers
Answer:
Sin = 7/25
Cos = 24/25
Tan = 7/24
Step-by-step explanation:
The ratio for sin is opposite/hypotenuse, cos is adjacent/ hypotenuse, and tan is opposite/ adjacent.
Find the distance between the points ( 4, 7) and (-1,2
Answers
Answer:
7.07 (3 significant figures)
Step-by-step explanation:
the distance between the two points on the x axis is 5 and the distance between the two point son the y axis is 5. thus by using pythagerous theorem you are able to get the hypotenuse which is the distance between the two points which in this case is 7.07 when rounded to 3 significant figures. not sure if im correct but i hope it helps
what is the formula for triangle
Answers
Answer:
BH/2
Step-by-step explanation:
For the area of the triangle, (BH)/2. B=base and H=height
Graph the solution set to this Inequality.
-2x + 9 < 51 12
Answers
Answer:
X<-2551.5
Step-by-step explanation:
-2x<5112-9
-2x/-2<5103/-2
x<-2551.5
F (x) = 1/3 x for x=4
Answers
Answer:
4/3
Step-by-step explanation:
Substitute in 4.
(1/3)4
Multiply
4/3
I hope this helps!
NO LINKS OR ANSWERING WHAT YOU DON'T KNOW!!!
9. Suppose y varies inversely with x, and y = 49 when x = 1/7. What is the value of x when y = 7?
a. 14
b. 2
c. 1
d. 7
10. Suppose y varies inversely with x, and y = 5 when x = 3. What is the inverse variation equation that relates x and y?
a. y = 3/x
b. y = 5/x
c. y = 15/x
d. y = 15x
Answers
9514 1404 393
Answer:
9. c. 1
10. c. y = 15/x
Step-by-step explanation:
The equation for inverse variation can be written as ...
y = k/x
The value of k can be determined from given values of x and y. Multiply by x to get ...
k = xy
Solving for x, you get ...
x = k/y
___
9. k = (1/7)(49) = 7
x = k/y = 7/7
x = 1
__
10. k = (3)(5) = 15
y = 15/x
Which is the graph of the function y = 2(4)^x
Answers
Answer:
the second graph is correct
Step-by-step explanation:
M H To determine the number of deer in a game preserve, a conservationist catches 412 deer, tags them and lets them loose. Later, 316 deer are caught, 158 of them are tagged. How many deer are in the preserve?
Answers
Answer:
There are 824 deer in the preserve.
Step-by-step explanation:
Since to determine the number of deer in a game preserve, a conservationist catches 412 deer, tags them and lets them loose, and later, 316 deer are caught, 158 of them are tagged, to determine how many deer are in the preserve you must perform the following calculation:
316 = 100
158 = X
158 x 100/316 = X
50 = X
50 = 412
100 = X
824 = X
Therefore, there are 824 deer in the preserve.