1. A restaurant supplier services the restaurants in a circular area in such way that the radius r is increasing at the rate of 2 miles per year at the moment when r = 5 miles. How fast is the area increasing?
Answer:
A= π*r²
dA/dt= π*r*dr/dt
dA/dt= π*5*2= 10π km/yr
Using implicit differentiation, it is found that the area is increasing at a rate of 62.8 miles squared per year.
The area of a circle of radius r is given by:
[tex]A = \pi r^2[/tex]
Applying implicit differentiation, the rate of change is given by:
[tex]A = 2r\pi \frac{dr}{dt}[/tex]
In this problem:
Radius increasing at a rate of 2 miles per year, hence [tex]\frac{dr}{dt} = 2[/tex].Moment of a radius of 5 miles, hence [tex]r = 5[/tex].Then:
[tex]A = 2r\pi \frac{dr}{dt}[/tex]
[tex]A = 2(5)\pi(2)[/tex]
[tex]A = 62.8[/tex]
The area is increasing at a rate of 62.8 miles squared per year.
A similar problem is given at https://brainly.com/question/9543179
Please help me out. The topic is angles. Anything helps.
The ______ identity is 1.
Answer:
I believe its ,multiplication
Step-by-step explanation:
because any number you multiply be one is one
mark brainliest if correct please
Answer:
multiplication
Step-by-step explanation:
Cause of Peter griffen
suppose we have function defined by :
f(x)= -3x+7
what values of x give f(x) =-17?
Answer:
x = 8
Step-by-step explanation:
if f(x) = -17
then we can type:
- 3 x + 7 = -17
solving for "x", subtract 7 from both sides
- 3 x = - 17 - 7
- 3 x = - 24
divide both sides by -3 to isolate "x"
x = -24 / (-3)
x = 8
tells diere expression
2x + 4y - 3
es
-3
B)
2
3
D)
4
Answer:
sorry I don't understand the way its written
A checking account is overdrawn if it has a
negative balance. Marc's account is overdrawn by
$45. What will the balance be after he deposits
$170 and writes a check for $59?
Answer:
64.
Step-by-step explanation:
170 - 59 = 109
109 - 45 = 64
or do
59 + 45 = 104
104 - 170 = 64
Answer: it’s 66
Step-by-step explanation:
What can you determine from the tape diagram
Gary leaves school to go home. He walks 8 blocks north and then 14 blocks east. If Gary could walk in a straight line to the school, what is the exact distance between Gary and the school?
Answer:
16.12 blocks
Step-by-step explanation:
Given that,
Gary walks 8 blocks north and then 14 blocks east.
We need to find the exact distance between Gary and the school. We can find it by using Pythagoras theorem as follows :
[tex]d=\sqrt{8^2+14^2} \\\\=16.12\ \text{blocks}[/tex]
So, the exact distance between Gary and the school is 16.12 blocks.
PLEASE HELP! Determine the slope & the y-intercept of the following graphs.
Hey girl! It's me again to explain this to you :)
Number 21.) If we start from our y-intercept -2 and move up 2 on our y-axis we get to point (0,0). If we move over 1 space to the right, we are on (1,0), which is the x-intercept.
Slope: 2/1 or just 2
Y-intercept: -2
You didn't ask for this but i'm gonna write it anyways. The equation for this line is y=2x-2
Number 22.) If we start from our y-intercept 2 and move down 2 on your y-axis we get to point (0,0). If we move over 1 space to the right, we are on (1,0), which is the x-intercept.
Slope: -2/1 or just -2
Y-intercept: 2
Again you didn't ask for this but the equation for this line is y=-2x+2
Hope this helped you understand and again make this brainliest and reply if you need more help or have any more questions :)
Step-by-step explanation:
Determine the slope of the line passing through the points (-10, -2) and (-12, 2).
1. 4
2. -4
3. 2
4. -2
Answer:
-2
Step-by-step explanation:
you do change in y over change in x which is 2-(-2) over -12-(-10)
when you do the caluclations you get 4 over -2 so then you get -2
rationalise the denominator 1/√20
Answer:
1/10
Step-by-step explanation:
uf no me dij hi g go be h in go i
Step-by-step explanation:
Given:1/√20
The denominator = 20
We know that
The rationalising factor of √a is √a. To rationalise the denominator of 1/√20, we multiply this by √20/√20.
1/√20
→ (1/√20) * (√20/√20)
→ [1(√20)]/[(√20)(√20)]
→ (√20)/√(20×20)
→ √20/20 Ans.
Find the slope of the line passing through each pair of points. (9,4) and (5,-3).
Answer:
[tex]m=\frac{7}{4}[/tex]
General Formulas and Concepts:
Order of Operations: BPEMDASSlope Formula: [tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Step-by-step explanation:
Step 1: Define
(9, 4)
(5, -3)
Step 2: Find slope m
Substitute: [tex]m=\frac{-3-4}{5-9}[/tex]Subtract: [tex]m=\frac{-7}{-4}[/tex]Simplify: [tex]m=\frac{7}{4}[/tex]please helppp! and thank you
Answer:53
Step-by-step explanation:
Identify which of these terms do not belong with the other three: square,circle , hexagon or triangle and explain your reasoning
Answer:
Circle
Step-by-step explanation:
It dosen't have sides
1. If 15% of adults in a certain country work from home, what is the probability that fewer than 42 out of a random sample of 350 adults will work from home? (Round your answer to 3 decimal places)
2. Suppose we want to estimate the proportion of teenagers (aged 13-18) who are lactose intolerant. If we want to estimate this proportion to within 4% at the 95% confidence level, how many randomly selected teenagers must we survey?
Answer:
(1) 0.058
(2) 601
Step-by-step explanation:
(1)
According to the Central limit theorem, if from an unknown population large samples of sizes n > 30, are selected and the sample proportion for each sample is computed then the sampling distribution of sample proportion follows a Normal distribution.
The mean of this sampling distribution of sample proportion is:
[tex]\mu_{\hat p}=p\\[/tex]
The standard deviation of this sampling distribution of sample proportion is:
[tex]\sigma_{\hat p}=\sqrt{\frac{p(1-p)}{n}}[/tex]
As the sample size is large, i.e. n = 350 > 30, the Central limit theorem can be used to approximate the sampling distribution of sample proportion of adults in a certain country work from home.
Compute the probability that fewer than 42 out of a random sample of 350 adults will work from home:
Sample proportion: [tex]\hat p=\frac{42}{350}=0.12[/tex]
[tex]P(\hat p < 0.12)=P(\frac{\hat p-\mu_{\hat p}}{\sigma_{\hat p}}<\frac{0.12-0.15}{\sqrt{\frac{0.15(1-0.15)}{350}}})\\\\=P(Z<-1.57)\\\\=0.05821\\\\\approx 0.058[/tex]
Thus, the probability that fewer than 42 out of a random sample of 350 adults will work from home is 0.058.
(2)
The (1 - α)% confidence interval for population proportion is:
[tex]CI=\hat p\pm z_{\alpha/2}\cdot\sqrt{\frac{\hat p(1-\hat p)}{n}}[/tex]
The margin of error for this interval is:
[tex]MOE= z_{\alpha/2}\cdot\sqrt{\frac{\hat p(1-\hat p)}{n}}[/tex]
Given:
MOE = 0.04
Confidence level = 95%
Assume that the sample proportion is 50%.
The critical z-value for 95% confidence level is 1.96.
Compute the required sample size as follows:
[tex]MOE= z_{\alpha/2}\cdot\sqrt{\frac{\hat p(1-\hat p)}{n}}[/tex]
[tex]n=[\frac{z_{\alpha/2}\cdot\sqrt{\hat p(1-\hat p)}}{MOE}]^{2}\\\\=[\frac{1.96\times \sqrt{0.50(1-0.50)}}{0.04}]^{2}\\\\=600.25\\\\\approx 601[/tex]
Thus, the required sample size is 601.
1. Using the normal approximation to the binomial, it is found that there is a 0.05 = 5% probability that fewer than 42 out of a random sample of 350 adults will work from home.
2. Solving the equation for the margin of error of a confidence interval of proportions, it is found that we must survey 601 randomly selected teenagers.
Question 1:
Normal Probability Distribution
In a normal distribution 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]
It 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, which is the percentile of X.The binomial distribution is the probability of x successes on n trials, with p probability of a success on each trial. It can be approximated to the normal distribution with [tex]\mu = np, \sigma = \sqrt{np(1-p)}[/tex].In this problem:
15% work from home, thus [tex]p = 0.15[/tex].Sample of 350 adults, thus [tex]n = 350[/tex]Then, for the approximation:
[tex]\mu = np = 350(0.15) = 52.5[/tex]
[tex]\sigma = \sqrt{np(1-p)} = \sqrt{350(0.15)(0.85)} = 6.68[/tex]
Using continuity correction, the probability is [tex]P(X < 42 - 0.5) = P(X < 41.5)[/tex], which is the p-value of Z when X = 41.5. So:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{41.5 - 52.5}{6.68}[/tex]
[tex]Z = -1.65[/tex]
[tex]Z = -1.65[/tex] has a p-value of 0.05.
0.05 = 5% probability that fewer than 42 out of a random sample of 350 adults will work from home.
Question 2:
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]\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
z is the z-score that has a p-value of [tex]\frac{1+\alpha}{2}[/tex].The margin of error is:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In this problem:
Within 4%, thus [tex]M = 0.04[/tex].We do not have an estimate for the true proportion, thus [tex]\pi = 0.5[/tex].95% confidence level, thus z has a p-value of [tex]\frac{1 + 0.95}{2} = 0.975[/tex], thus z = 1.96.We have to solve for n, then:
[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 = 600.25[/tex]
Rounding up:
We must survey 601 randomly selected teenagers.
A similar problem is given at https://brainly.com/question/24261244
Gavin has a box of crayons. There are four purple crayons, three black crayons, three blue crayons, and two red crayons. What is the probability Gavin will draw a purple crayon put it on the table and then draw another purple
Answer:
4/12
Step-by-step explanation:
HELP PLS Describe two real-life situations that could be represented by the graph below
the amount you walk by the hour?
x axis- distance
y axis- hours
:))
when you get in your car and you start driving, you start at a speed of 0 and then your speed can be anything from 0 to the maximum speed of your car. If you graphed your speed during a trip, you would end up with one continuous curve for your graph. You won't have any breaks in the graph.
Thomas got a haircut from the barber. If the
haircut costs $32 and he wants to leave a
18% tip, how much will he pay in total?
What is 34 and -7 as a fraction
34 as a fraction is 17/50
-7 as a fraction is 8/20
Answer:
34/1
-7/1
Step-by-step explanation:
Viktor purchases a car for $10,608. He makes monthly payments for 48 months in order to pay off the car. He does not pay interest. How much are his payments each month?
rewrite the function f(x)=-3(x+3)^2-13
in the form f(x)=ax^2+bx+c
Answer:
-3x^2-18x-40
Step-by-step explanation:
(x+3)^2: x^2+6x+9
= -3(x^2+6x+9)-13
Expand:
-3(x^2+6x+9): -3x^2-18x-27
= -3x^2-18x-27-13
Final Answer: -3x^2-18x-40
Answer:
-3x^2-18x-40
Step-by-step explanation:
-3(x+3)^2-13
-3(x^2+6x+9)-13
-3x^2-18x-27-13
-3x^2-18x-40
PICTURE PLEASEEEEEEEEEEE
Answer: C
Step-by-step explanation: Because none of the triangles are the same.
What is the distance in units between 16 and -25?
Answer:
41
Step-by-step explanation:
a teacher wants to arrange 16 chairs
Answer:
Okay, anything else along with that or was it just a statement?
Step-by-step explanation:
Which statements are always true regarding the diagram? Select three options.
m∠5 + m∠3 = m∠4
m∠3 + m∠4 + m∠5 = 180°
m∠5 + m∠6 =180°
m∠2 + m∠3 = m∠6
m∠2 + m∠3 + m∠5 = 180°
TIMED PLS HURRY
Evaluate 4p+q/p when p= -2 and q= -3
a) -11/2
b) 9/2
c) -9/2
d) 11/2
Answer:
D
Step-by-step explanation:
Answer:
d. 11/2
Step-by-step explanation:
(4p + q)/p
(4(-2) + (-3))/(-2) = (-8-3)/(-2)
11/2
Basketball shoes are on sale for 22% off. What is the regular price if the sale price is $42?
Answer:
x =53.85
Step-by-step explanation:
Let x be the original price
If the price is 22% of, you will pay 100% -22% = 78%
x * 78% = 42
Change to decimal form
.78x = 42
Divide each side by .78
.78x/.78 = 42/.78
Rounding to the nearest cent
x =53.85
Five years ago, John’s age was half of the age he will be in 8 years. How old is he now? Show your steps.
Answer:
John is 18 years old at this point in time.
Step-by-step explanation:
This question is basic algebra. The equation you will need to write to solve it is (x-5) = (x+8)/2. When you solve this equation, the answer comes out to 18.
Simonne, Marco, and Evon were partners in
business. Simonne and Marco each received
twice as much of the profit as Evon received. If
the total profit was $1,800, how much did Evon
receive?
PICTURE PLEASE TYSMMM
Answer:
(B).
Step-by-step explanation:
Statement B is not correct. PR and ST are not corresponding segments.
