Answer:
[tex]\text{The implicit solution:} \frac{1}{81} e^{9x}(9x - 1) + \frac{3}{e^t} = C[/tex]
Step-by-step explanation:
It is given that there is arbitrary constant C and we have to find the implicit solution. Therefore, first separate the variable that is given in equation and then use integration to find the implicit solution. Here, below is the calculation.
The given equation is:
[tex]\frac{dx}{dt} = \frac{3}{xe^{t-9x}}[/tex]
Now, if we use separation of variable.
[tex]\frac{dx}{dt} = \frac{3}{xe^{t-9x}} \\\frac{dx}{dt} = \frac{3}{xe^{9x}e^{t}} \\xe^{9x}dx = \frac{3}{e^{t}}dt \\[/tex]
Now integrate both side:
[tex]\int xe^{9x} dx = \int \frac{3}{e^{t}} dt \\\frac{e^{9x}}{9}(x) - \int \left [ \frac{e^{9x}}{9} \right]dx = -3e^{-t} + C \\[/tex]
[tex]\frac{xe^{9x}}{9} - \frac{e^{9x}}{81} = -3e^{-t} + C \\\frac{1}{81} e^{9x}(9x - 1) + \frac{3}{e^t} = C \\[/tex]
Thus, the implicit solution is:
[tex]\frac{1}{81} e^{9x}(9x - 1) + \frac{3}{e^t} = C[/tex]
If you can get an answer to any question, what would you ask? You toss a fair coin 4 times. What is the probability that (round to 4 decimal places) a) you get all Heads? b) you get at least one Tail?
Answers:
a) 0.0625
b) 0.9375
==================================================
Work Shown:
The probability of landing on heads is 1/2 = 0.5 since both sides are equally likely to land on. Getting 4 heads in a row is (1/2)^4 = (0.5)^4 = 0.0625
The event of getting at least one tail is the complement of getting all four heads. This is because you either get all four heads or you get at least one tail. One or the other must happen. We subtract the result we got from 1 to get 1-0.0625 = 0.9375
You can think of it like this
P(getting all four heads) + P(getting at least one tail) = 1
The phrasing "at least one tail" means "one tail or more".
Sameer chose 12 different toppings for his frozen yogurt sundae, which was Three-fourths of the total number of different toppings available at the make-your-own sundae shop. To determine the number of different toppings available at the shop, Sameer set up and solved the equation as shown below.
Three-fourths = StartFraction x over 12 EndFraction. Three-fourths (12) = StartFraction x over 12 EndFraction (12). 9 = x.
Which best describes the error that Sameer made?
Sameer did not use the correct equation to model the given information.
Sameer should have multiplied both sides of the equation by Four-thirds instead of by 12.
The product of Three-fourths(12) is not equal to 9.
The product of Four-thirds and StartFraction 1 over 12 EndFraction should have been the value of x.
Answer: B. Sameer did not use the correct equation
Step-by-step explanation:
12 IS three-fourths OF x
IS: equals
OF: multiplication
[tex]12=\dfrac{3}{4}x[/tex]
48 = 3x
16 = x
Answer:
it's b in Edg
Step-by-step explanation:
A superintendent of a school district conducted a survey to find out the level of job satisfaction among teachers. Out of 53 teachers who replied to the survey, 13 claim they are satisfied with their job.
z equals fraction numerator p with hat on top minus p over denominator square root of begin display style fraction numerator p q over denominator n end fraction end style end root end fraction
The superintendent wishes to construct a significance test for her data. She find that the proportion of satisfied teachers nationally is 18.4%.
What is the z-statistic for this data? Answer choices are rounded to the hundredths place.
a. 2.90
b. 1.15
c. 1.24
d. 0.61
Answer:
b. 1.15
Step-by-step explanation:
The z statistics is given by:
[tex]Z = \frac{X - p}{s}[/tex]
In which X is the found proportion, p is the expected proportion, and s, which is the standard error is [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]
Out of 53 teachers who replied to the survey, 13 claim they are satisfied with their job.
This means that [tex]X = \frac{13}{53} = 0.2453[/tex]
She find that the proportion of satisfied teachers nationally is 18.4%.
This means that [tex]p = 0.184[/tex]
Standard error:
p = 0.184, n = 53.
So
[tex]s = \sqrt{\frac{0.184*0.816}{53}} = 0.0532[/tex]
Z-statistic:
[tex]Z = \frac{X - p}{s}[/tex]
[tex]Z = \frac{0.2453 - 0.184}{0.0532}[/tex]
[tex]Z = 1.15[/tex]
The correct answer is:
b. 1.15
If 16 student drove to school out of a class of 21, what percentage drove to school
Your answer would be 76.2% to the nearest tenth.
We can find this by first dividing 16 by 21 to get 0.7619. which is the proportion as a decimal. To convert this into a percentage, we need to multiply it by 100 to get 76.19% = 76.2% to the nearest tenth.
I hope this helps! Let me know if you have any questions :)
F =9/5 C + 32 A) constants B) units C) variables D) numbers
Answer:
a) 32
b) none?
c) C & F
D) 9/5, 32?
Step-by-step explanation:
A 30% cranberry juice drink is mixed with a 100% cranberry juice drink. The function f(x)=(6)(1.0)+x(0.3)6+x models the concentration of cranberry juice in the drink after x gallons of the 30% drink are added to 6 gallons of pure juice. What will be the concentration of cranberry juice in the drink if 2 gallons of 30% drink are added? Give the answer as a percent.
Answer:
82.5%
Step-by-step explanation:
It helps to start with the correct formula:
f(x) = ((6)(1.0) +x(0.3))/(6 +x) . . . . parentheses are required
Then f(2) is ...
f(2) = (6 +.3(2))/(6+2) = 6.6/8
f(2) = 82.5%
ANSWER ASAP! PLEASE HELP!
Which angles are pairs of alternate exterior angles
Answer:
when a straight line cuts two or more parallel lines then the angles forming on the side of transversal line exteriorly opposite to eachother is called exterior alternative angle.
for eg if AB //CD and EF is a transversal line meeting the parallel lines at G abd H then the exterior alternative angle are angle EGB = angle CHF and angle AGE=angle DHF are two pairs of exterior alternative angle .
hope its helpful to uh !!!!!!
The amount of pollutants that are found in waterways near large cities is normally distributed with mean 8.6 ppm and standard deviation 1.3 ppm. 38 randomly selected large cities are studied. Round all answers to 4 decimal places where possible
a. What is the distribution of X?
b. What is the distribution of a?
c. What is the probability that one randomly selected city's waterway will have more than 8.5 ppm pollutants?
d. For the 38 cities, find the probability that the average amount of pollutants is more than 8.5 ppm.
e. For part d), is the assumption that the distribution is normal necessary?
f. Find the IQR for the average of 38 cities.
Q1=__________ ppm
Q3 =_________ ppm
IQR=_________ ppm
We assume that question b is asking for the distribution of [tex] \\ \overline{x}[/tex], that is, the distribution for the average amount of pollutants.
Answer:
a. The distribution of X is a normal distribution [tex] \\ X \sim N(8.6, 1.3)[/tex].
b. The distribution for the average amount of pollutants is [tex] \\ \overline{X} \sim N(8.6, \frac{1.3}{\sqrt{38}})[/tex].
c. [tex] \\ P(z>-0.08) = 0.5319[/tex].
d. [tex] \\ P(z>-0.47) = 0.6808[/tex].
e. We do not need to assume that the distribution from we take the sample is normal. We already know that the distribution for X is normally distributed. Moreover, the distribution for [tex] \\ \overline{X}[/tex] is also normal because the sample was taken from a normal distribution.
f. [tex] \\ IQR = 0.2868[/tex] ppm. [tex] \\ Q1 = 8.4566[/tex] ppm and [tex] \\ Q3 = 8.7434[/tex] ppm.
Step-by-step explanation:
First, we have all this information from the question:
The random variable here, X, is the number of pollutants that are found in waterways near large cities.This variable is normally distributed, with parameters:[tex] \\ \mu = 8.6[/tex] ppm.[tex] \\ \sigma = 1.3[/tex] ppm.There is a sample of size, [tex] \\ n = 38[/tex] taken from this normal distribution.a. What is the distribution of X?
The distribution of X is the normal (or Gaussian) distribution. X (uppercase) is the random variable, and follows a normal distribution with [tex] \\ \mu = 8.6[/tex] ppm and [tex] \\ \sigma =1.3[/tex] ppm or [tex] \\ X \sim N(8.6, 1.3)[/tex].
b. What is the distribution of [tex] \\ \overline{x}[/tex]?
The distribution for [tex] \\ \overline{x}[/tex] is [tex] \\ N(\mu, \frac{\sigma}{\sqrt{n}})[/tex], i.e., the distribution for the sampling distribution of the means follows a normal distribution:
[tex] \\ \overline{X} \sim N(8.6, \frac{1.3}{\sqrt{38}})[/tex].
c. What is the probability that one randomly selected city's waterway will have more than 8.5 ppm pollutants?
Notice that the question is asking for the random variable X (and not [tex] \\ \overline{x}[/tex]). Then, we can use a standardized value or z-score so that we can consult the standard normal table.
[tex] \\ z = \frac{x - \mu}{\sigma}[/tex] [1]
x = 8.5 ppm and the question is about [tex] \\ P(x>8.5)[/tex]=?
Using [1]
[tex] \\ z = \frac{8.5 - 8.6}{1.3}[/tex]
[tex] \\ z = \frac{-0.1}{1.3}[/tex]
[tex] \\ z = -0.07692 \approx -0.08[/tex] (standard normal table has entries for two decimals places for z).
For [tex] \\ z = -0.08[/tex], is [tex] \\ P(z<-0.08) = 0.46812 \approx 0.4681[/tex].
But, we are asked for [tex] \\ P(z>-0.08) \approx P(x>8.5)[/tex].
[tex] \\ P(z<-0.08) + P(z>-0.08) = 1[/tex]
[tex] \\ P(z>-0.08) = 1 - P(z<-0.08)[/tex]
[tex] \\ P(z>-0.08) = 0.5319[/tex]
Thus, "the probability that one randomly selected city's waterway will have more than 8.5 ppm pollutants" is [tex] \\ P(z>-0.08) = 0.5319[/tex].
d. For the 38 cities, find the probability that the average amount of pollutants is more than 8.5 ppm.
Or [tex] \\ P(\overline{x} > 8.5)[/tex]ppm?
This random variable follows a standardized random variable normally distributed, i.e. [tex] \\ Z \sim N(0, 1)[/tex]:
[tex] \\ Z = \frac{\overline{X} - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex] [2]
[tex] \\ z = \frac{\overline{8.5} - 8.6}{\frac{1.3}{\sqrt{38}}}[/tex]
[tex] \\ z = \frac{-0.1}{0.21088}[/tex]
[tex] \\ z = \frac{-0.1}{0.21088} \approx -0.47420 \approx -0.47[/tex]
[tex] \\ P(z<-0.47) = 0.31918 \approx 0.3192[/tex]
Again, we are asked for [tex] \\ P(z>-0.47)[/tex], then
[tex] \\ P(z>-0.47) = 1 - P(z<-0.47)[/tex]
[tex] \\ P(z>-0.47) = 1 - 0.3192[/tex]
[tex] \\ P(z>-0.47) = 0.6808[/tex]
Then, the probability that the average amount of pollutants is more than 8.5 ppm for the 38 cities is [tex] \\ P(z>-0.47) = 0.6808[/tex].
e. For part d), is the assumption that the distribution is normal necessary?
For this question, we do not need to assume that the distribution from we take the sample is normal. We already know that the distribution for X is normally distributed. Moreover, the distribution for [tex] \\ \overline{X}[/tex] is also normal because the sample was taken from a normal distribution. Additionally, the sample size is large enough to show a bell-shaped distribution.
f. Find the IQR for the average of 38 cities.
We must find the first quartile (25th percentile), and the third quartile (75th percentile). For [tex]\\ P(z<0.25)[/tex], [tex] \\ z \approx -0.68[/tex], then, using [2]:
[tex] \\ -0.68 = \frac{\overline{X} - 8.6}{\frac{1.3}{\sqrt{38}}}[/tex]
[tex] \\ (-0.68 *0.21088) + 8.6 = \overline{X}[/tex]
[tex] \\ \overline{x} =8.4566[/tex]
[tex] \\ Q1 = 8.4566[/tex] ppm.
For Q3
[tex] \\ 0.68 = \frac{\overline{X} - 8.6}{\frac{1.3}{\sqrt{38}}}[/tex]
[tex] \\ (0.68 *0.21088) + 8.6 = \overline{X}[/tex]
[tex] \\ \overline{x} =8.7434[/tex]
[tex] \\ Q3 = 8.7434[/tex] ppm.
[tex] \\ IQR = Q3-Q1 = 8.7434 - 8.4566 = 0.2868[/tex] ppm
Therefore, the IQR for the average of 38 cities is [tex] \\ IQR = 0.2868[/tex] ppm. [tex] \\ Q1 = 8.4566[/tex] ppm and [tex] \\ Q3 = 8.7434[/tex] ppm.
A small regional carrier accepted 19 reservations for a particular flight with 17 seats. 14 reservations went to regular customers who will arrive for the flight. Each of the remaining passengers will arrive for the flight with a 52% chance, independently of each other. (Report answers accurate to 4 decimal places.)
1. Find the probability that overbooking occurs.
2. Find the probability that the flight has empty seats.
Answer:
(a) The probability of overbooking is 0.2135.
(b) The probability that the flight has empty seats is 0.4625.
Step-by-step explanation:
Let the random variable X represent the number of passengers showing up for the flight.
It is provided that a small regional carrier accepted 19 reservations for a particular flight with 17 seats.
Of the 17 seats, 14 reservations went to regular customers who will arrive for the flight.
Number of reservations = 19
Regular customers = 14
Seats available = 17 - 14 = 3
Remaining reservations, n = 19 - 14 = 5
P (A remaining passenger will arrive), p = 0.52
The random variable X thus follows a Binomial distribution with parameters n = 5 and p = 0.52.
(1)
Compute the probability of overbooking as follows:
P (Overbooking occurs) = P(More than 3 shows up for the flight)
[tex]=P(X>3)\\\\={5\choose 4}(0.52)^{4}(1-0.52)^{5-4}+{5\choose 5}(0.52)^{5}(1-0.52)^{5-5}\\\\=0.175478784+0.0380204032\\\\=0.2134991872\\\\\approx 0.2135[/tex]
Thus, the probability of overbooking is 0.2135.
(2)
Compute the probability that the flight has empty seats as follows:
P (The flight has empty seats) = P (Less than 3 shows up for the flight)
[tex]=P(X<3)\\\\1-P(X\geq 3)\\\\=1-[{5\choose 3}(0.52)^{3}(1-0.52)^{5-3}+{5\choose 4}(0.52)^{4}(1-0.52)^{5-4}+{5\choose 5}(0.52)^{5}(1-0.52)^{5-5}]\\\\=1-[0.323960832+0.175478784+0.0380204032]\\\\=0.4625399808\\\\\approx 0.4625[/tex]
Thus, the probability that the flight has empty seats is 0.4625.
What is the solution to the system of equations x+y=10 and x+2y=4 using the linear combination method?
Answer:
The solution:
X = 16 and Y = -6
Step-by-step explanation:
The equations to be solved are:
x+y = 10 ------- equation 1
x+2y = 4 ----------- equation 2
we can multiply equation 1 by -1 to make the value of x and y negative.
This will give us
-x- y = - 10 ------- equation 3
x+2y = 4 ----------- equation 2
We will now add equations 3 and 2 together so that x will cancel itself out.
this will give us
y = -10 +4 = -6
hence, we have the value of y as -6.
To get the value of x, we can put this value of y into any of the equations above. (I will use equation 1)
x - 6 = 10
from this, we have that x = 4
Therefore, we have our answer as
X = 16 and Y = -6
If a baseball player has a batting average of 0.375, what is the probability that the player will get the following number of hits in the next four times at bat?
A. Exactly 2 hits(Round to 3 decimal places as needed)
B. At least 2 hits (Round to 3 decimal places as needed)
Answer:
a) [tex]P(X=2)=(4C2)(0.375)^2 (1-0.375)^{4-2}=0.330[/tex]
b) [tex]P(X\geq 2)=1-P(X< 2)=1-[P(X=0)+P(X=1)][/tex]
[tex]P(X=0)=(4C0)(0.375)^0 (1-0.375)^{4-0}=0.153[/tex]
[tex]P(X=1)=(4C1)(0.375)^1 (1-0.375)^{4-1}=0.366[/tex]
And replacing we got:
[tex]P(X\geq 2)=1-P(X< 2)=1-[0.153+0.366]=0.481[/tex]
Step-by-step explanation:
Let X the random variable of interest, on this case we now that:
[tex]X \sim Binom(n=4, p=0.375)[/tex]
The probability mass function for the Binomial distribution is given as:
[tex]P(X)=(nCx)(p)^x (1-p)^{n-x}[/tex]
Where (nCx) means combinatory and it's given by this formula:
[tex]nCx=\frac{n!}{(n-x)! x!}[/tex]
Part a
[tex]P(X=2)=(4C2)(0.375)^2 (1-0.375)^{4-2}=0.330[/tex]
Part b
[tex]P(X\geq 2)=1-P(X< 2)=1-[P(X=0)+P(X=1)][/tex]
[tex]P(X=0)=(4C0)(0.375)^0 (1-0.375)^{4-0}=0.153[/tex]
[tex]P(X=1)=(4C1)(0.375)^1 (1-0.375)^{4-1}=0.366[/tex]
And replacing we got:
[tex]P(X\geq 2)=1-P(X< 2)=1-[0.153+0.366]=0.481[/tex]
34% of U.S. adults have very little confidence in newspapers. You randomly select eight U.S. adults. Find the probability that the number of U.S. adults who have very little confidence in newspapers is (a) exactly six, (b) at least four, and (c) less than five.
What is the volume of a cubed shaped box with edges 6 cm. in length?
Answer:
216 cm³
Step-by-step explanation:
The volume of a cube is denoted by V = s³, where s is the side length.
Here, the side length is 6 centimetres, so plug this into the formula to find V:
V = s³
V = 6³ = 6 * 6 * 6 = 216
The answer is thus 216 cm³.
~ an aesthetics lover
Answer:
216
Step-by-step explanation:
6³ = 216
Find the critical numbers of the function. (Enter your answers as a comma-separated list. Use n to denote any arbitrary integer values. If an answer does not exist, enter DNE.) f(θ)=6cosθ+3sin2θ g
Answer:
The critical value of [tex]f(\theta) = 6\cdot \cos \theta + 3\cdot \sin 2\theta[/tex] are given by [tex]\theta \approx 0.091\pi \pm 2\pi\cdot n[/tex] or [tex]\theta \approx 0.909\pi \pm 2\pi \cdot n[/tex], [tex]\forall \,n \in \mathbb{N}[/tex]
Step-by-step explanation:
The function to be evaluated is [tex]f(\theta) = 6\cdot \cos \theta + 3\cdot \sin 2\theta[/tex], the first derivative of the function must be taken in order to determine the set of critical numbers. Each derivative are found by using the differentiation rule for a sum of functions and rule of chain and subsequently simplified by trigonometric and algebraic means:
First derivative
[tex]f'(\theta) = - 6 \cdot \sin \theta +6\cdot \cos 2\theta[/tex]
[tex]f'(\theta) = -6\cdot \sin \theta + 2\cdot (\cos^{2}\theta-\sin^{2}\theta)[/tex]
[tex]f'(\theta) = -6\cdot \sin \theta + 2\cdot [(1-\sin^{2}\theta-\sin^{2}\theta)][/tex]
[tex]f'(\theta) = -6\cdot \sin \theta + 2\cdot (1-2\cdot \sin^{2}\theta)[/tex]
[tex]f'(\theta) = -6\cdot \sin \theta + 2 - 4\cdot \sin^{2}\theta[/tex]
[tex]f'(\theta) = -4\cdot \sin^{2}\theta - 6\cdot \sin \theta +2[/tex]
The procedure to determine the critical number of the given function are described briefly:
1) First derivative is equalised to zero.
2) The resultant equation is solved.
Then,
[tex]-4\cdot \sin^{2}\theta - 6\cdot \sin \theta +2 = 0[/tex]
Whose roots are:
[tex]\sin \theta_{1} \approx 0.281[/tex] and [tex]\sin \theta_{2} \approx -1.781[/tex]
The sine function is a continuous function with a range between 1 and -1, so, only the first root offers a realistic solution. In addition, such function is positive at first and second quadrants and has a periodicity of [tex]2\pi[/tex] radians, the family of critical values are determined by the unse of inverse trigonometric functions:
[tex]\theta \approx \sin^{-1} 0.281[/tex]
There are two subsets of solutions:
[tex]\theta \approx 0.091\pi \pm 2\pi\cdot n[/tex] or [tex]\theta \approx 0.909\pi \pm 2\pi \cdot n[/tex], [tex]\forall \,n \in \mathbb{N}[/tex]
which point is a solution to the inequality shown in the graph? (3,2) (-3,-6)
The point that is a solution to the inequality shown in the graph is:
A. (0,5).
Which points are solutions to the inequality?The points that are on the region shaded in blue are solutions to the inequality.
(3,2) and (-3,-6) are on the dashed line, hence they are not solutions. Point (5,0) is to the right of the line, hence it is not a solution, and point (0,5) is a solution, meaning that option A is correct.
More can be learned about inequalities at https://brainly.com/question/25235995
#SPJ1
You buy six pens for $2.99 each, and sales tax is 10%. How much change should you receive from a clerk if you give her a $20 bill?
Answer:
$2.06
Step-by-step explanation:
$2.99 x 6 = $17.94
$20.00 - $17.94 = $2.06
Hope this helps
Answer: $0.26
Step-by-step explanation:
Cost of 6 pens
= 2.99 x 6
= 17.94
Add sales tax at 10%,
= 17.94 x 1.1
= 19.74
Change due to me
= 20 - 19.74
= 0.26
What is the difference in milligrams between a powdered headache medicine at 12 mg and a headache tablet at 0.018 g?
Answer:
6 mg
Step-by-step explanation:
12 mg
0.018 g * 1000 mg/g = 18 mg
18 mg - 12 mg = 6 mg
Which expression is equivalent to 2−35,? Choose 1 answer:
Answer:
The answer is option A.
Step-by-step explanation:
2 - 35 can be written as 2 + (-35) since in 2+( -35) when the bracket is removed it becomes 2 - 35.
Hope this helps
Answer:
Your correct answer is option a. 2 + (-35)
Step-by-step explanation:
When you are finding which equation is equivalent to the one you have, the best thing to find is what your equation's answer is.
Solve the equation 3x-13y = 2 for y.
Answer:
y= 3/13x + 2/13
Step-by-step explanation:
3x-13y=2
Subtract 3x from both side
-13y=-3x-2
Divide by -13
y= 3/13x + 2/13
Answer:
[tex]y = \frac{2-3x}{-13}[/tex]
Step-by-step explanation:
=> 3x-13y = 2
Subtract 3x to both sides
=> -13y = 2-3x
Dividing both sides by -13
=> [tex]y = \frac{2-3x}{-13}[/tex]
Suppose IQ scores were obtained for 20 randomly selected sets of siblings . The 20 pairs of measurements yield x overbar equals98.26, y overbar equals99, requals 0.911, P-valueequals 0.000, and ModifyingAbove y with caret equals negative 5.9 plus 1.07 x , where x represents the IQ score of the older child . Find the best predicted value of ModifyingAbove y with caret given that the older child has an IQ of 102 ? Use a significance level of 0.05 g
Answer:
The answer to the best prediction is 115.04
Step-by-step explanation:
We have to:
x = 102
They also tell us that:
y = 5.9 + 1.07 * x
If we replace we have:
y = 5.9 + 1.07 * (102)
y = 115.04
Therefore, the best predicted value of ModifyingAbove and with caret given that the older child has an IQ of 102 is 115.04
Which is the graph of x - y = 1?
Answer:
This question is very simple,
Ok first you will need to find the x and y intercepts by letting y=0 and x=0
First let x=0
so, 0-y=1
y=-1
let y=0
x-0=1
x=1
now we know
x-intercept=(1,0)
y-intercept=(0-1)
Hence, find the graph that has the two corresponding points and that would be the graph you are looking for.
Step-by-step explanation:
Select the correct answer. The function h(x) = 31x2 + 77x + 41 can also be written as which of the following? A. h(x) + 41 = 31x2 + 77x B. y + 41 = 31x2 + 77x C. y = 31x2 + 77x + 41 D. y = 31x2 + 77x − 41
Answer:
[tex]y=31x^2+77x+41[/tex]
which agrees with option C in your list of possible answers.
Step-by-step explanation:
Since normally functions are represented on the x-y plane, it is common to replace h(x) with the "y" variable of the vertical axis where its values will be represented (plotted). Then the expression can be also written as follows:
[tex]h(x)=31x^2+77x+41\\y=31x^2+77x+41[/tex]
NEED HELP ASAP!!! PLEASE
Answer:
1144cm²
Approx. 1100cm²
Step-by-step explanation:
Area of rectangle=
L×B
34×20 = 680cm²
Area of semi-circle=
πr²
3.14 × (10)² = 314cm²
Area of triangle=
½b×h
b = 49 - 34 = 15
20 × 15 = 150cm²
2
Area of shape =
680 + 314 + 150 = 1144cm²
approx. 1100cm²
Please mark my answer as brainliest <3
What are the two shapes of cross sections we could create by slicing the pyramid
PLEASE HELP. FINAL TEST QUESTION!!!!
Devon is having difficulty determining if the relation given in an input-output table is a function. Explain why he is correct or incorrect.
Step-by-step explanation:
input x , output y
if x= x1 then y=y1 and y1 is the only value then it is a function
if we get multiple values of y then it is not a function
According to the Vivino website, suppose the mean price for a bottle of red wine that scores 4.0 or higher on the Vivino Rating System is $32.48. A New England-based lifestyle magazine wants to determine if red wines of the same quality are less expensive in Providence, and it has collected prices for 65 randomly selected red wines of similar quality from wine stores throughout Providence. The mean and standard deviation for this sample are $30.15 and $12, respectively.
(a) Develop appropriate hypotheses for a test to determine whether the sample data support the conclusion that the mean price in Providence for a bottle of red wine that scores 4.0 or higher on the Vivino Rating System is less than the population mean of $32.48. (Enter != for ≠ as needed.)
H0:
Ha:
(b) Using the sample from the 60 bottles, what is the test statistic? (Round your answer to three decimal places.)
Using the sample from the 60 bottles, what is the p-value? (Round your answer to four decimal places.)
p-value =
(c) At α = 0.05, what is your conclusion?
Do not reject H0. We can conclude that the price in Providence for a bottle of red wine that scores 4.0 or higher on the Vivino Rating System is less than the population mean of $32.48.
Reject H0. We can conclude that the price in Providence for a bottle of red wine that scores 4.0 or higher on the Vivino Rating System is less than the population mean of $32.48.
Do not reject H0. We cannot conclude that the price in Providence for a bottle of red wine that scores 4.0 or higher on the Vivino Rating System is less than the population mean of $32.48.
Reject H0. We cannot conclude that the price in Providence for a bottle of red wine that scores 4.0 or higher on the Vivino Rating System is less than the population mean of $32.48.
(d) Repeat the preceding hypothesis test using the critical value approach.
State the null and alternative hypotheses. (Enter != for ≠ as needed.)
H0:
Ha:
Find the value of the test statistic. (Round your answer to three decimal places.)
State the critical values for the rejection rule. Use
α = 0.05.
(Round your answers to three decimal places. If the test is one-tailed, enter NONE for the unused tail.)
test statistic ≤
test statistic ≥
State your conclusion.
Do not reject H0. We can conclude that the price in Providence for a bottle of red wine that scores 4.0 or higher on the Vivino Rating System is less than the population mean of $32.48.
Reject H0. We can conclude that the price in Providence for a bottle of red wine that scores 4.0 or higher on the Vivino Rating System is less than the population mean of $32.48.
Do not reject H0. We cannot conclude that the price in Providence for a bottle of red wine that scores 4.0 or higher on the Vivino Rating System is less than the population mean of $32.48.
Reject H0. We cannot conclude that the price in Providence for a bottle of red wine that scores 4.0 or higher on the Vivino Rating System is less than the population mean of $32.48.
Answer:
a) Null and alternative hypothesis
[tex]H_0: \mu=32.48\\\\H_a:\mu< 32.48[/tex]
b) Test statistic t=-1.565
P-value = 0.0612
NOTE: the sample size is n=65.
c) Do not reject H0. We cannot conclude that the price in Providence for a bottle of red wine that scores 4.0 or higher on the Vivino Rating System is less than the population mean of $32.48.
d) Null and alternative hypothesis
[tex]H_0: \mu=32.48\\\\H_a:\mu< 32.48[/tex]
Test statistic t=-1.565
Critical value tc=-1.669
t>tc --> Do not reject H0
Do not reject H0. We cannot conclude that the price in Providence for a bottle of red wine that scores 4.0 or higher on the Vivino Rating System is less than the population mean of $32.48.
Step-by-step explanation:
This is a hypothesis test for the population mean.
The claim is that the mean price in Providence for a bottle of red wine that scores 4.0 or higher on the Vivino Rating System is less than the population mean of $32.48.
Then, the null and alternative hypothesis are:
[tex]H_0: \mu=32.48\\\\H_a:\mu< 32.48[/tex]
The significance level is 0.05.
The sample has a size n=65.
The sample mean is M=30.15.
As the standard deviation of the population is not known, we estimate it with the sample standard deviation, that has a value of s=12.
The estimated standard error of the mean is computed using the formula:
[tex]s_M=\dfrac{s}{\sqrt{n}}=\dfrac{12}{\sqrt{65}}=1.4884[/tex]
Then, we can calculate the t-statistic as:
[tex]t=\dfrac{M-\mu}{s/\sqrt{n}}=\dfrac{30.15-32.48}{1.4884}=\dfrac{-2.33}{1.4884}=-1.565[/tex]
The degrees of freedom for this sample size are:
[tex]df=n-1=65-1=64[/tex]
This test is a left-tailed test, with 64 degrees of freedom and t=-1.565, so the P-value for this test is calculated as (using a t-table):
[tex]\text{P-value}=P(t<-1.565)=0.0612[/tex]
As the P-value (0.0612) is bigger than the significance level (0.05), the effect is not significant.
The null hypothesis failed to be rejected.
At a significance level of 0.05, there is not enough evidence to support the claim that the mean price in Providence for a bottle of red wine that scores 4.0 or higher on the Vivino Rating System is less than the population mean of $32.48.
Critical value approach
At a significance level of 0.05, for a left-tailed test, with 64 degrees of freedom, the critical value is t=-1.669.
As the test statistic is greater than the critical value, it falls in the acceptance region.
The null hypothesis failed to be rejected.
2{ 3[9 + 4(7 -5) - 4]}
Answer:
2{3[9+4(7-5)-4]}
2{3[9+4(2)-4]}
2{3[13(2)-4]}
2{3[26-4]}
2{3[22]}
2{66}
132
Step-by-step explanation:
Yvette exercises 14 days out of 30 in one month. What is the ratio of the number of days she exercises to the number of days in the month? Simplify the ratio.
Answer:
7 to 15, 7:15, 7/15
Step-by-step explanation:
Ratios can be written as:
a to b
a:b
a/b
We want to find the ratio of exercise days to days in the month. She exercises 14 days out of 30 days in the month. Therefore,
a= 14
b= 30
14 to 30
14:30
14/30
The ratios can be simplified. Both numbers can be evenly divided by 2.
(14/2) to (30/2)
7 to 15
(14/2) : (30/2)
7:15
(14/2) / (30/2)
7/15
Answer:
divide both numbers by 14.. the ans is 1: 2
A committee has ten members. There are two members that currently serve as the board's chairman and vice chairman. Each member is equally likely to serve in any of the positions. Two members are randomly selected and assigned to be the new chairman and vice chairman. What is the probability of randomly selecting the two members who currently hold the positions of chairman and vice chairman and reassigning them to their current positions?
Answer:
1/90 = 1.11%
Step-by-step explanation:
We have that the number of ways of total selections and assignments possible is a permutation.
We know that permutations are defined like this:
nPr = n! / (n-r)!
In our case n = 10 and r = 2, replacing:
10P2 = 10! / (10 - 2)! = 10! / 8!
10P2 = 90
In addition to this, there will only be one way to randomly select the two members currently holding the positions of President and Vice President and reassign them to their current positions. Thus,
Probability would come being the following:
P = 1/90 = 1.11%