Answer: Biased sample
Step-by-step explanation:
This is a biased sample because only students with strong opinions are likely going to volunteer or show interest in representing the school at the board meeting. This sample is a voluntary type sample, and at such the conclusion is not valid. This sample is biased because a group or population of students have a higher or lower sampling probability.
The length of a rectangle is increasing at a rate of 8 cmys and its width is increasing at a rate of 3 cmys. When the length is 20 cm and the width is 10 cm, how fast is the area of the rectangle increasing?
Answer:
The area of the rectangle increasing at the rate of 140 cm²/s
Step-by-step explanation:
Rectangle area:
A rectangle has two dimensions, length l and width w.
It's area is:
A = l*w.
When the length is 20 cm and the width is 10 cm, how fast is the area of the rectangle increasing?
We apply implicit differentiation to solve this question:
[tex]A = l*w[/tex]
So
[tex]\frac{dA}{dt} = l\frac{dw}{dt} + w\frac{dl}{dt}[/tex]
Length is 20, so [tex]l = 20[/tex].
Width is 10, so [tex]w = 10[/tex]
The length of a rectangle is increasing at a rate of 8 cm/s and its width is increasing at a rate of 3 cm/s.
This means that [tex]\frac{dl}{dt} = 8, \frac{dw}{dt} = 3[/tex]
So
[tex]\frac{dA}{dt} = l\frac{dw}{dt} + w\frac{dl}{dt}[/tex]
[tex]\frac{dA}{dt} = 20*3 + 10*8 = 140[/tex]
Area in cm².
So
The area of the rectangle increasing at the rate of 140 cm²/s
Some shrubs have the useful ability to resprout from their roots after their tops are destroyed. Fire is a particular threat to shrubs in dry climates, as it can injure the roots as well as destroy the aboveground material. One study of resprouting took place in a dry area of Mexico. The investigation clipped the tops of samples of several species of shrubs. In some cases, they also applied a propane torch to the stumps to simulate a fire. Of 18 specimens of a particular species, 5 resprouted after fire. Estimate with 99.5% confidence the proportion of all shrubs of this species that will resprout after fire.
Answer:
The 99.5% confidence interval for the proportion of all shrubs of this species that will resprout after fire is (0, 0.5745).
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].
For this problem, we have that:
[tex]n = 18, \pi = \frac{5}{18} = 0.2778[/tex]
99.5% confidence level
So [tex]\alpha = 0.005[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.005}{2} = 0.9975[/tex], so [tex]Z = 2.81[/tex].
The lower limit of this interval is:
[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.2778 - 2.81\sqrt{\frac{0.2778*0.7222}{18}} = -0.01 = 0[/tex]
We cannot have a negative proportion, so we use 0.
The upper limit of this interval is:
[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.2778 + 2.81\sqrt{\frac{0.2778*0.7222}{18}} = 0.5745[/tex]
The 99.5% confidence interval for the proportion of all shrubs of this species that will resprout after fire is (0, 0.5745).
Fractions - Addition : 3/7 + 1/56
Explanation needed
[tex]answer = \frac{25}{56} \\ solution \\ \frac{3}{7} + \frac{1}{56} \\ = \frac{3 \times 8 + 1}{56} \\ = \frac{24 + 1}{56} \\ = \frac{25}{56} \\ hope \: it \: helps \: \\ good \: luck \: on \: your \: assignment[/tex]
Answer:
25/56
Step-by-step explanation:
3/7 + 1/56
We have to find the L.C.M of 7 and 56
The L.C.M of 7 and 56 is 56
Now, we have to change the denominators to 56
we dont need to change the denominator of 1/56 to 56 as it is already 56
[tex]\frac{3}{7}[/tex] * [tex]\frac{8}{8}[/tex] = [tex]\frac{24}{56}[/tex]
Now we can add the fractions
[tex]\frac{24}{56} + \frac{1}{56}[/tex] [tex]= \frac{25}{56}[/tex]
Hope it helped :>
A bottle maker believes that 14% of his bottles are defective. If the bottle maker is accurate, what is the probability that the proportion of defective bottles in a sample of 622 bottles would be less than 11%
Answer:
[tex] z = \frac{0.11-0.14}{0.0139} = -2.156[/tex]
And we can use the normal standard distribution table and we got:
[tex] P(Z<-2.156) =0.0155[/tex]
Step-by-step explanation:
For this case we know the following info given:
[tex] p =0.14[/tex] represent the population proportion
[tex] n = 622[/tex] represent the sample size selected
We want to find the following proportion:
[tex] P(\hat p <0.11)[/tex]
For this case we can use the normal approximation since we have the following conditions:
i) np = 622*0.14 = 87.08>10
ii) n(1-p) = 622*(1-0.14) =534.92>10
The distribution for the sample proportion would be given by:
[tex] \hat p \sim N (p ,\sqrt{\frac{p(1-p)}{n}}) [/tex]
The mean is given by:
[tex] \mu_{\hat p}= 0.14[/tex]
And the deviation:
[tex]\sigma_{\hat p}= \sqrt{\frac{0.14*(1-0.14)}{622}}= 0.0139[/tex]
We can use the z score formula given by:
[tex] z=\frac{\hat p -\mu_{\hat p}}{\sigma_{\hat p}}[/tex]
And replacing we got:
[tex] z = \frac{0.11-0.14}{0.0139} = -2.156[/tex]
And we can use the normal standard distribution table and we got:
[tex] P(Z<-2.156) =0.0155[/tex]
How can you use mathematics to help scientists explore Martian Craters ?
Answer:
Mathematics could make scientists to have a preliminary understanding of the dimensions, perimeters, areas and volumes of different craters on Mars.
Step-by-step explanation:
Martian Craters are series of craters formed on the surface of Mars. The study of a planets crater gives an understanding of the properties of matter that lies under the crater.
Mathematics can be applied to determine the dimensions, perimeter, area and volume of the features of a crater using appropriate conversions and theorems.
The Pi in the sky theorem can be applied to determine the area and perimeter, even volume of different craters on the Mars surface. Also, eingenfunction expansion theorem gives a preliminary knowledge of the craters.
By measurements and conversions processes, the features of Martian crater could be studied from images.
what is the solution set for the equation (x+3)(x-8)=0
Answer:
x= -3 x=8
Step-by-step explanation:
(x+3)(x-8)=0
We can use the zero product property to solve
x+3 =0 x-8 =0
x= -3 x=8
Answer:
x=8
Step-by-step explanation:
Inflation causes things to cost more, and for our money to buy less (hence your grandparents saying "In my day, you could buy a cup of coffee for a nickel"). Suppose inflation decreases the value of money by 4% each year. In other words, if you have $1 this year, next year it will only buy you $0.96 worth of stuff. How much will $100 buy you in 25 years?
Answer:
Step-by-step explanation:
[tex]100 (0.96)^{25} =[/tex] around 36.04
What is the average rate of change for this function for the interval from x= 1
to x = 3?
Answer:
The average rate of change is 12x=12.0x.
Description:
Function: x= 1x = 3 convert to short form: x 1x 3
Interval: x= 1 , x 3
Steps:
Input: Find the average rate of change of f(x)=3x2 on the interval [x,3x].
We have that a=x, b=3x, f(x)=3x2
Thus, f(b)−f(a)b−a=3((3x))2−(3(x)2)3x−(x)=12x.
Answer: the average rate of change is 12x=12.0x.
Please mark brainliest
Hope this helps.
Answer:
3
Step-by-step explanation:
A P E X
Arlene sleeps for 7hr20min each night. How many hours does she sleep in a week? Write your answer as a mixed number,
Answer:
51 1/3 hours
Step-by-step explanation:
Multiply the amount of sleep per day (7 1/3) by the number of days in a week (7), to get the total amount of sleep (51 1/3 hours)
One angle of a right triangle measures 51 degrees. What is the measure of the other small angle?
Answer:
a rigt angle is a total of 90 degrees so subtratct 51 from 90 and you get 39 degrees.
6q+4-q+5 please right now
Answer:
5q + 9
Step-by-step explanation:
Combine like terms to simplify the expression.
Have a blessed day!
Answer:
7q+9
Step-by-step explanation:
6q+4+q+5
6q+q+4+5
=7q+9
1.
On hand: Magnesium sulfate 30 grams is mixed in 500 ml Lactated Ringers. Order: infuse a
maintenance dose of magnesium sulfate at 4 grams/hour. At what rate should the nurse set the
pump:
Answer:
The IV will run [tex]66.67 \ ml /hr[/tex]
Step-by-step explanation:
From the question we are told that
The mass of Magnesium sulfate is [tex]m_g = 30 \ g[/tex]
The volume of the Magnesium sulfate [tex]V_R = 500ml[/tex]
The rate at which the dose of the solution (Magnesium sulfate + Lactated Ringers. ) is infused is [tex]R = 4g/hr[/tex]
The concentration of Magnesium sulfate in Lactated Ringers is mathematically evaluated as
[tex]C_m = \frac{m_g}{V_R}[/tex]
substituting values
[tex]C_m = \frac{30}{500}[/tex]
[tex]C_m = 0.06\ g/ ml[/tex]
This implies that
0.06 g of Magnesium sulfate is in every 1 ml of Lactated Ringers
So 4 g of Magnesium sulfate is in x ml of Lactated Ringers
So
[tex]x = \frac{4}{0.06}[/tex]
[tex]x = 66.67 \ ml[/tex]
So the amount of the solution in ml that is been infused in 1 hour is
[tex]66.67 \ ml /hr[/tex]
Find the surface area of this triangular prism. Be sure to include the correct unit in your answer.
15 m
12 m
0
9 m
11 m
Thanks for anyone that answers
Which is the equation of a line that has a slope of 1 and passes through point (5, 3)?
y = -2
y = x + 2
y = x + 3
y=x-5
Answer:
y = x - 2
Step-by-step explanation:
y = x + b
3 = 5 + b
y = x - 2
We can use the slope intercept form of a line.
y = mx+b where m is the slope and b is the y intercept
y = 1x +b
Substitute the point into the equation
3 = 1*5+b
3 = 5+b
Subtract 5 from each side
3-5 = 5+b-5
-2 =b
y = x-2
Solve the system if possible by using Cramer's rule. If Cramer's rule does not apply, solve the system by using another method. Write all numbers as integers or simplified fractions.
7x + 6y + 4z = 10
3x + 3y + 3z - 1
4x + 4y + 4z = 2
Part: 0/2
Part 1 of 2
Evaluate the determinants D, Dx Dy and Dz.
D=
Dx=
Dy=
Dz=
Answer:
D = 0 , Dx = 4 , Dy = -6 , Dz = 2
Step-by-step explanation:
As per cramer's rule,
D = | 7 6 4 | = 0
| 3 3 3 |
| 4 4 4 |
Dx = | 10 6 4 | = 4
| 1 3 3 |
| 2 4 4 |
Dy = | 7 10 4 | = -6
| 3 1 3 |
| 4 2 4 |
Dz = | 7 6 10 | = 2
| 3 3 1 |
| 4 4 2 |
PLEASE HELP. if f(x)=x and g(x)=2, what is (f*g)(x)
Answer:
Step-by-step explanation:
hey
(f*g)(x) = f(g(x)) = f(2) = 2
second answer is correct
thanks
An online shopping website collected data regarding its operations and obtained the following linear regression model for the estimated revenue in millions, Y-hat, based on the click-through rate in thousands, x. Y-hat = 1.2+0.2x
What is the best interpretation of the value of the estimated slope of 0.2?
Answer:
There is an estimated increase in revenue of $0.2 million for each 1,000 additional clicks
Step-by-step explanation:
The slope (0.2) is the rate of change in Y-hat for each unit change in x.
In this specific case, since Y-hat is the revenue, in millions, and x is the number of clicks, in thousands, the best interpretation is that there is an estimated increase in revenue of $0.2 million for each 1,000 additional clicks
The probability that a freshman at a certain college takes an introductory statistics class is 0.21. What is the probability that a randomly selected freshman from this college does not take an introductory statistics class
Answer:
[tex] P(A) = 0.21[/tex]
We want to find the probability that a randomly selected freshman from this college does not take an introductory statistics class, so then we can use the complement rule given by:
[tex] P(A') = 1-P(A)[/tex]
Where A is the event of interest (a freshman at a certain college takes an introductory statistics class) and A' the complement (a freshman at a certain college NOT takes an introductory statistics class) and then replacing we got:
[tex] P(A')=1-0.21= 0.79[/tex]
Step-by-step explanation:
For this problem we know that the probability that a freshman at a certain college takes an introductory statistics class is 0.21, let's define of interest as A and we can set the probability like this:
[tex] P(A) = 0.21[/tex]
We want to find the probability that a randomly selected freshman from this college does not take an introductory statistics class, so then we can use the complement rule given by:
[tex] P(A') = 1-P(A)[/tex]
Where A is the event of interest (a freshman at a certain college takes an introductory statistics class) and A' the complement (a freshman at a certain college NOT takes an introductory statistics class) and then replacing we got:
[tex] P(A')=1-0.21= 0.79[/tex]
What is the additive inverse of the complex number 9-4i?
Answer:
[tex] \frac{1}{9 - 4i} [/tex]
I'm not sure
A fair die is rolled twice, with outcomes X for the first roll and Y for the second roll. Find the moment generating function MX`Y ptq of X ` Y . Note that your answer should be a function of t and can contain unsimplified finite sums.
Answer:
[tex]\mathbf{\dfrac{e^{2t}}{36} + \dfrac{e^{3t}}{18} + \dfrac{e^{4t}}{12} +\dfrac{e^{5t}}{9} + \dfrac{5e^{6t}}{36} + \dfrac{7e^{7t}}{6} + \dfrac{5e^{8t}}{36} + \dfrac{e^{9t}}{9} + \dfrac{e^{10t}}{12} + \dfrac{e^{11t}}{18} + \dfrac{e^{12t}}{36} }[/tex]
Step-by-step explanation:
The objective is to find the moment generating function of [tex]M_{X+Y}(t) \ of \ X+Y[/tex].
We are being informed that the fair die is rolled twice;
So; X to be the value for the first roll
Y to be the value of the second roll
The outcomes of X are: X = {1,2,3,4,5,6}
Where ;
[tex]P (X=x) = \dfrac{1}{6}[/tex]
The outcomes of Y are: y = {1,2,3,4,5,6}
Where ;
[tex]P (Y=y) = \dfrac{1}{6}[/tex]
The outcome of Z = X+Y
[tex]= \left[\begin{array}{cccccc}(1,1)&(1,2)&(1,3)&(1,4)&(1,5)&(1,6)\\ (2,1)&(2,2)&(2,3)&(2,4)&(2,5)&(2,6)\\ (3,1)&(3,2)&(3,3)&(3,4)&(3,5)&(3,6) \\ (4,1)&(4,2)&(4,3)&(4,4)&(4,5)&(4,6) \\ (5,1)&(5,2)&(5,3)&(5,4)&(5,5)&(5,6) \\ (6,1)&(6,2)&(6,3)&(6,4)&(6,5)&(6,6) \end{array}\right][/tex]
= [2,3,4,5,6,7,8,9,10,11,12]
Here;
[tex]P (Z=z) = \dfrac{1}{36}[/tex]
∴ the moment generating function [tex]M_{X+Y}(t) \ of \ X+Y[/tex]is as follows:
[tex]M_{X+Y}(t) \ of \ X+Y[/tex] = [tex]E(e^{t(X+Y)}) = E(e^{tz})[/tex]
⇒ [tex]\sum \limits^{12}_ {z=2 } et ^z \ P(Z=z)[/tex]
= [tex]\mathbf{\dfrac{e^{2t}}{36} + \dfrac{e^{3t}}{18} + \dfrac{e^{4t}}{12} +\dfrac{e^{5t}}{9} + \dfrac{5e^{6t}}{36} + \dfrac{7e^{7t}}{6} + \dfrac{5e^{8t}}{36} + \dfrac{e^{9t}}{9} + \dfrac{e^{10t}}{12} + \dfrac{e^{11t}}{18} + \dfrac{e^{12t}}{36} }[/tex]
Classify the following triangle .check all that apply
Answer:
Its right and scalene.
It has a right angle and all the sides are diferent.
The equation 9(u – 2) + 1.5u = 8.25 models the total miles Michael traveled one afternoon while sledding, where u equals the number of hours walking up a hill and (u – 2) equals the number of hours sledding down the hill. Which is the value of u?
Answer:
2.5
Step-by-step explanation:
[tex]9(u-2)+1.5u=8.25 \\\\9u-18+1.5u=8.25\\\\10.5u-18=8.25\\\\10.5u=26.25\\\\u=2.5[/tex]
Hope this helps!
f(x)=x^3-3x^2-9x+4 find the intervals on which f is increasing or decreasing b. find the local maximum and minimum values of f. c. find the intervals of concavity and inflection points
Answer:
Please read the complete answer below!
Step-by-step explanation:
You have the following function:
[tex]f(x)=x^3-3x^2-9x+4[/tex] (1)
a) To find the interval on which f is increasing or decreasing, you first calculate the critical points of f(x).
You calculate the derivative f(x) respect to x:
[tex]\frac{df}{dx}=3x^2-6x-9[/tex] (2)
Next, you equal the derivative to zero, and then you find the roots of the polynomial by using the quadratic formula:
[tex]3x^2-6x-9=0\\\\x_{1,2}=\frac{-(-6)\pm\sqrt{(-6)^2-4(3)(-9)}}{2(3)}\\\\x_{1,2}=\frac{6\pm12}{6}\\\\x_1=-1\\\\x_2=3[/tex]
Then, the critical points are x=-1 and x=3
Next, you calculate df/dx for a values of x to the left and to the right of the critical points x1 and x2. If df/dx < 0 the function is decreasing, if df/dx > 0 the function is increasing.
for x = -1.01
[tex]\frac{df(-1.01)}{dx}=3(-1.01)^2-6(-1.01)-9=0.12[/tex]
Then, in the interval (-∞,-1), the function is increasing
for x = -0.99
[tex]\frac{df(-0.99)}{dx}=3(-0.99)^2-6(-0.99)-9=-0.11[/tex]
In the interval (-1,3) the function is decreasing
for x = 3.01
[tex]\frac{df(3.01)}{dx}=3(3.01)^2-6(3.01)-9=0.12[/tex]
In the interval (3,+∞) the function is increasing
b) To find the local minimum and maximum you use the second derivative of the function:
[tex]\frac{d^2f}{dx^2}=6x-6[/tex] (3)
you evaluate the second derivative for the critical points x1 and x2, if the second derivative is positive, you have a local minimum. If the second derivative is negative, you have a local maximum:
for x1 = -1
[tex]6(-1)-6=-12<0[/tex]
x=-1 is a local maximum
for x2 = 3
[tex]6(3)-6=12>0[/tex]
x=3 is a local minimum
c) upward concavity: (-1,3)
downward concavity: (-∞,-1)U(3,+∞)
The inflection points are calculated with the second derivative equal to zero:
[tex]6x-6=0\\\\x=1[/tex]
For x = 1 you have an inflection point
If a man takes 30 minutes to drive at work and it is 44 miles into work what is the average speed?
Answer:
1.46666 miles / minutes
88 miles per hour
Step-by-step explanation:
The speed is distance over time
44 miles / 30 minutes
1.46666 miles / minutes
or if we want in miles per hour
44 miles / .5 hours
88 miles per hour
Answer:
1.467 mile/minute
Step-by-step explanation:
you should divide the distance on the time i.e. 44/30
build the greatest and the smallest number using the digit 7,2,6
greatest _____ and smallest ____
SOMEONE PLEASE HELP ME ASAP PLEASE!!!
Answer:
7.1
Step-by-step explanation:
d = sqrt(7^2 + -1^2)= sqrt(50)=7.1
Answer:
by using distance formula
putting values
d=√(-1-6)²+(-4--5)²
d=√(-7)²+(1)²
d=√49+1
d=√50
d=5√2=7.1
(a) Use the power series expansions for ex, sin x, cos x, and geometric series to find the first three nonzero terms in the power series expansion of the given function.
(b) Based on the information given in the section on algebraic properties of power series, for which values of x can you guarantee that the new series converges.
(If you have a CAS, you can easily find several more nonzero terms in the power series expansions of the functions.)
(e^x)/(cos(x))
Answer:
a) [tex]\mathbf{4 + \dfrac{x}{1!}- \dfrac{2x^2}{2!} ...}[/tex]
b) See Below for proper explanation
Step-by-step explanation:
a) The objective here is to Use the power series expansions for ex, sin x, cos x, and geometric series to find the first three nonzero terms in the power series expansion of the given function.
The function is [tex]e^x + 3 \ cos \ x[/tex]
The expansion is of [tex]e^x[/tex] is [tex]e^x = 1 + \dfrac{x}{1!}+ \dfrac{x^2}{2!}+ \dfrac{x^3}{3!} + ...[/tex]
The expansion of cos x is [tex]cos \ x = 1 - \dfrac{x^2}{2!}+ \dfrac{x^4}{4!}- \dfrac{x^6}{6!}+ ...[/tex]
Therefore; [tex]e^x + 3 \ cos \ x = 1 + \dfrac{x}{1!}+ \dfrac{x^2}{2!}+ \dfrac{x^3}{3!} + ... 3[1 - \dfrac{x^2}{2!}+ \dfrac{x^4}{4!}- \dfrac{x^6}{6!}+ ...][/tex]
[tex]e^x + 3 \ cos \ x = 4 + \dfrac{x}{1!}- \dfrac{2x^2}{2!} + \dfrac{x^3}{3!}+ ...[/tex]
Thus, the first three terms of the above series are:
[tex]\mathbf{4 + \dfrac{x}{1!}- \dfrac{2x^2}{2!} ...}[/tex]
b)
The series for [tex]e^x + 3 \ cos \ x[/tex] is [tex]\sum \limits^{\infty}_{x=0} \dfrac{x^x}{n!} + 3 \sum \limits^{\infty}_{x=0} ( -1 )^x \dfrac{x^{2x}}{(2n)!}[/tex]
let consider the series; [tex]\sum \limits^{\infty}_{x=0} \dfrac{x^x}{n!}[/tex]
[tex]|\frac{a_x+1}{a_x}| = | \frac{x^{n+1}}{(n+1)!} * \frac{n!}{x^x}| = |\frac{x}{(n+1)}| \to 0 \ as \ n \to \infty[/tex]
Thus it converges for all value of x
Let also consider the series [tex]\sum \limits^{\infty}_{x=0}(-1)^x\dfrac{x^{2n}}{(2n)!}[/tex]
It also converges for all values of x
Which decimal is closest in value to 9/20
Answer:
0.45
Step-by-step explanation:
9/20 is the same as 0.45
Answer:
0.45
Step-by-step explanation:
9/20= 9*5/20*5= 45/100= 0.45
Here's a graph of a linear function. Write the
equation that describes that function.
Express it in slope-intercept form.
HELP PLEASE
Answer:
y=2/3x+1
Step-by-step explanation:
The slope is 2/3 and the y-intercept is 1.
Sarah wants to refurbish her shop.
She is quoted £2500 for the refurbishment, with a 20% discount to be taken off.
What is the final cost of the refurbishment after the discount?
Answer:
2000
Step-by-step explanation:
2500 / 100 = 25 (1%)
25 X 20 =500 (20%)
2500 - 500 =2000
