Answer:
3 1/2 gallons or 56 cups
Step-by-step explanation:
1. Analyze the questions.
We have 3 gallons, and we add another 1/2 gallon. This means that our equation must be 3 + 1/2.
2. Solve.
3 + 1/2 = 3 1/2 gallons
3. Convert.
1 gallon = 16 cups
1 * 3 1/2 gallons = 16 * 3 1/2 cups
3 1/2 gallons = 56 cups
Answer: 3 1/2
Hope this helped! :D
A statistics professor receives an average of five e-mail messages per day from students. Assume the number of messages approximates a Poisson distribution. What is the probability that on a randomly selected day she will have five messages
Answer:
The probability that on a randomly selected day the statistics professor will have five messages is 0.1755.
Step-by-step explanation:
Let the random variable X represent the number of e-mail messages per day a statistics professor receives from students.
The random variable is approximated by the Poisson Distribution with parameter λ = 5.
The probability mass function of X is as follows:
[tex]P(X=x)=\frac{e^{-5}\cdot 5^{x}}{x!};\ x=0,1,2,3...[/tex]
Compute the probability that on a randomly selected day she will have five messages as follows:
[tex]P(X=5)=\frac{e^{-5}\cdot 5^{5}}{5!}[/tex]
[tex]=\frac{0.006738\times 3125}{120}\\\\=0.17546875\\\\\approx 0.1755[/tex]
Thus, the probability that on a randomly selected day the statistics professor will have five messages is 0.1755.
Suppose cattle in a large herd have a mean weight of 3181lbs and a standard deviation of 119lbs. What is the probability that the mean weight of the sample of cows would differ from the population mean by greater than 11lbs if 49 cows are sampled at random from the herd
Answer:
51.56% probability that the mean weight of the sample of cows would differ from the population mean by greater than 11lbs if 49 cows are sampled at random from the herd
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal probability distribution
When the distribution is normal, we use the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore 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 pvalue, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem estabilishes 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.
In this question, we have that:
[tex]\mu = 3181, \sigma = 119, n = 49, s = \frac{119}{\sqrt{49}} = 17[/tex]
What is the probability that the mean weight of the sample of cows would differ from the population mean by greater than 11lbs if 49 cows are sampled at random from the herd
Lower than 3181 - 11 = 3170 lbs or greater than 3181 + 11 = 3192 lbs. Since the normal distribution is symmetric, these probabilities are equal. So i will find one of them, and multiply by 2.
Probability of mean weight lower than 3170 lbs:
This is 1 subtracted by the pvalue of Z when X = 3170. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{3170 - 3181}{17}[/tex]
[tex]Z = -0.65[/tex]
[tex]Z = -0.65[/tex] has a pvalue of 0.2578
2*0.2578 = 0.5156
51.56% probability that the mean weight of the sample of cows would differ from the population mean by greater than 11lbs if 49 cows are sampled at random from the herd
What is the center of the circle?
Answer:The point from which circle is drawn is called center of circle.
Step-by-step explanation:I don't say u must have to mark my ans as brainliest but if it has really helped u plz don't forget to thnk me...
If (x + k) is a factor of f(x), which of the following must be true?
f(K) = 0
fl-k)=0
A root of f(x) is x = k.
A y intercept of f(x) is x = -k.
Answer:
f(-k)=0Step-by-step explanation:
(x + k) is a factor of f(x)
x+k=0 => x= -k; -k is a root of f(x)
=> f(-k)=0
[tex](x + k) is a factor of f(x)x+k=0 = > x= -k; -k is a root of f(x)= > f(-k)=0[/tex]
So the correct option is B.fl-k)=0.
What is a root function example?
The cube root function is f(x)=3√x f ( x ) = x 3 . A radical function is a function that is defined by a radical expression. The following are examples of rational functions: f(x)=√2x4−5 f ( x ) = 2 x 4 − 5 ; g(x)=3√4x−7 g ( x ) = 4 x − 7 3 ; h(x)=7√−8x2+4 h ( x ) = − 8 x 2 + 4 7 .
What is the root function?
The root function is used to find a single solution to a single function with a single unknown. In later sections, we will discuss finding all the solutions to a polynomial function. We will also discuss solving multiple equations with multiple unknowns. For now, we will focus on using the root function.
Learn more about root function here: https://brainly.com/question/13136492
#SPJ2
The sum of two fractions can always be written as a
Answer: decimal
Step-by-step explanation:
because i did this quiz
A student takes a multiple-choice test that has 11 questions. Each question has five choices. The student guesses randomly at each answer. Let X be the number of questions answered correctly. (a) Find P (6). (b) Find P (More than 3). Round the answers to at least four decimal places.
Answer:
a) P(6) = 0.0097
b) P(More than 3) = 0.1611
Step-by-step explanation:
For each question, there are only two possible outcomes. Either it is guessed correctly, or it is not. Questions are independent of each other. So we use the binomial probability distribution to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
A student takes a multiple-choice test that has 11 questions.
This means that [tex]n = 11[/tex]
Each question has five choices.
This means that [tex]p = \frac{1}{5} = 0.2[/tex]
(a) Find P (6)
This is P(X = 6).
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 6) = C_{11,6}.(0.2)^{6}.(0.8)^{5} = 0.0097[/tex]
P(6) = 0.0097
(b) Find P (More than 3).
Either P is 3 or less, or it is more than three. The sum of the probabilities of these outcomes is 1. So
[tex]P(X \leq 3) + P(X > 3) = 1[/tex]
We want P(X > 3). So
[tex]P(X > 3) = 1 - P(X \leq 3)[/tex]
In which
[tex]P(X \leq 3) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)[/tex]
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{11,0}.(0.2)^{0}.(0.8)^{11} = 0.0859[/tex]
[tex]P(X = 1) = C_{11,1}.(0.2)^{1}.(0.8)^{10} = 0.2362[/tex]
[tex]P(X = 2) = C_{11,2}.(0.2)^{2}.(0.8)^{9} = 0.2953[/tex]
[tex]P(X = 3) = C_{11,3}.(0.2)^{3}.(0.8)^{8} = 0.2215[/tex]
[tex]P(X \leq 3) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) = 0.0859 + 0.2362 + 0.2953 + 0.2215 = 0.8389[/tex]
Then
[tex]P(X > 3) = 1 - P(X \leq 3) = 1 - 0.8389 = 0.1611[/tex]
P(More than 3) = 0.1611
what is the common ratio of the geometric sequence below ?
-96,48,-24,12,-6...
Answer:
r = - [tex]\frac{1}{2}[/tex]
Step-by-step explanation:
The common ratio r is the ratio between consecutive terms in the sequence.
r = [tex]\frac{48}{-96}[/tex] = [tex]\frac{-24}{48}[/tex] = [tex]\frac{12}{-24}[/tex] = [tex]\frac{-6}{12}[/tex] = - [tex]\frac{1}{2}[/tex]
Answer:
-1/2 or b on edge
Step-by-step explanation:
Find an Equation of a line with the given slope that passes through the point. Write the equation in the form Ax + By=C
M=3/2, (7,-2) -problem
Bridge math sails
Module 4B2
Answer:
c = 24 can i get brainliest
Step-by-step explanation:
HELP! Let f(x) = x + 1 and g(x)=1/x The graph of (fg)(x) is shown below.
Answer:
Step-by-step explanation:
all numbers except y = 1
because (f*g)(x) = 1+1/x
and 1/x cannot be equal to 0
One number is 4 plus one half of another number. Their sum is 31. Find the numbers.
Answer:
18, 13
Step-by-step explanation:
x=4+1/2y
x+y=31
4+1/y+y=31
3/2y=27
y=18
x=31-18=13
Answer:
13 & 18
Step-by-step explanation:
Create the formulas:
0.5x+4=y
x+y=31
0.5x+4=y
Multiply both sides by 2
x+8=2y
x+y=31
Subtract 31 from both sides
x+y-31=0
Subtract y from both sides
x-31= -y
Multiply both sides by -1
-x+31=y
Multiply both sides by 2
-2x+62=2y
Combine equations:
-2x+62=x+8
Add 2x to both sides
62=3x+8
Subtract 8 from both sides
3x=54
Divide both sides by 3
x=18
0.5x+4=y
Subtract y from both sides
0.5x-y+4=0
Subtract 0.5x from both sides
-y+4= -0.5x
Multiply both sides by -1
y-4=0.5x
Multiply both sides by 2
2y-8=x
x+y=31
Subtract y from both sides
x= -y+31
Combine equations:
2y-8= -y+31
Add y to both sides
3y-8=31
Add 8 to both sides
3y=39
Divide both sides by 3
y=13
Graph the line with slope -1/3 and y -intercept 6 .
Answer:
plot a point at 6 up from (0,0) and then go down one and over three places then plot another point- and so on - and so on
Step-by-step explanation:
To graph the line using the slope and intercept, first understand what the slope and intercept mean:
Slope is how steep or flat the line appears on the graph.
A very high or low slope (100 or -100) will be very steep on the graph.A slope very close to zero (0.0001 or -0.0001) will be very flat on the graph.A positive slope will travel northeast and southwest (for linear equations).A negative slope will travel northwest and southeast (for linear equations).The y-intercept is the point at which the line hits the y-axis. In this equation, the line hits the y-axis at positive 6, which means that the point is (0, 6).
You can use a method called "rise over run" to graph. The slope is negative one over three, so the line will "rise" negative one units after "running" three units.
So, for every one unit down, the line will travel three units to the right.
Graph this from the point (0, 6), your y-intercept, and plot the points according to the slope:
Simplify the following expression:
-5[(x^3 + 1)(x + 4)]
Answer:
[tex]-5x^{4} -20x^{3} -5x-20[/tex]
Step-by-step explanation:
[tex]-5[(x^{3} +1)(x+4)][/tex]
Use the FOIL method for the last two groups.
[tex]-5(x^{4} +4x^{3} +x+4)[/tex]
Now, distribute the -5 into each term.
[tex]-5x^{4} -20x^{3} -5x-20[/tex]
11+11=4
22+22=16
33+33=
What’s the answer
Answer:
what method exactly r u using ????
Find the general solution to y′′+6y′+13y=0. Give your answer as y=.... In your answer, use c1 and c2 to denote arbitrary constants and x the independent variable. Enter c1 as c1 and c2 as c2.
Answer:
[tex]y(x)=c_1e^{-3x} cos(2x)+c_2e^{-3x} sin(2x)[/tex]
Step-by-step explanation:
In order to find the general solution of a homogeneous second order differential equation, we need to solve the characteristic equation. This is basically as easy as solving a quadratic.
For a second order differential equation of type:
[tex]ay''+by'+cy=0[/tex]
Has characteristic equation:
[tex]a r^{2} +br+c=0[/tex]
Whose solutions [tex]r_1 , r_2 ,.., r_n[/tex] are the roots from which the general solution can be formed. There are three cases:
Real roots:
[tex]y(x)=c_1e^{r_1 x} +c_2e^{r_2 x}[/tex]
Repeated roots:
[tex]y(x)=c_1e^{r x} +c_1 xe^{r x}[/tex]
Complex roots:
[tex]y(x)=c_1e^{\lambda x}cos(\mu x) +c_2e^{\lambda x}sin(\mu x)\\\\Where:\\\\r_1_,_2=\lambda \pm \mu i[/tex]
Therefore:
The characteristic equation for:
[tex]y''+6y'+13y=0[/tex]
Is:
[tex]r^{2} +6r+13=0[/tex]
Solving for [tex]r[/tex] :
[tex]r_1_,_2= -3 \pm 2i[/tex]
So:
[tex]\mu = 2\\\\and\\\\\lambda=-3[/tex]
Hence, the general solution of the differential equation will be given by:
[tex]y(x)=c_1e^{-3x} cos(2x)+c_2e^{-3x} sin(2x)[/tex]
Find the area of a circle with radius, r = 5.7m.
Give your answer rounded to 2 DP.
The diagram is not drawn to scale.
(I attached the diagram below!)
Answer:
the area of the circle is 102.11 square metres
1. In an arithmetic sequence, the first term is -2, the fourth term is 16, and the n-th term is 11,998
(a) Find the common difference d
(b) Find the value of n.
pls help...
Answer:
see explanation
Step-by-step explanation:
The n th term of an arithmetic sequence is
[tex]a_{n}[/tex] = a₁ + (n - 1)d
(a)
Given a₁ = - 2 and a₄ = 16, then
a₁ + 3d = 16 , that is
- 2 + 3d = 16 ( add 2 to both sides )
3d = 18 ( divide both sides by 3 )
d = 6
--------------
(b)
Given
[tex]a_{n}[/tex] = 11998 , then
a₁ + (n - 1)d = 11998 , that is
- 2 + 6(n - 1) = 11998 ( add 2 to both sides )
6(n - 1) = 12000 ( divide both sides by 6 )
n - 1 = 2000 ( add 1 to both sides )
n = 2001
------------------
Write the number that is ten thousand more than
1,853,604,297:
Answer:
The answer would be 1,853,614,297
Write an
explicit formula for
ans
the nth
term of the sequence 20, -10,5, ....
Answer:an=20(-1/2)^n-1
Step-by-step explanation:
m is directly proportional to r squared when r=2 m=14 work out the value of r when m = 224
Answer:
32
Step-by-step explanation:
r:m
2:14
1:7
m=224
r=224 divided by 7
224/7=32
Edit: unless it is proportional to r^2 in which case it is a different answer
Answer:
m=504
Step-by-step explanation:
Find the constant of variation for the relation and use it to write and solve the equation.
if y varies directly as x and as the square of z, and y=25/9 when x=5 and z=1, find y when x=1 and z=4
Answer:
When x = 1 and z = 4, [tex]y=\frac{80}{9}[/tex]
Step-by-step explanation:
The variation described in the problem can be written using a constant of proportionality "b" as:
[tex]y=b\,\,x\,\,z^2[/tex]
The other piece of information is that when x = 5 and z = 1, then y gives 25/9. So we use this info to find the constant "b":
[tex]y=b\,\,x\,\,z^2\\\frac{25}{9} =b\,\,(5)\,\,(1)^2\\\frac{25}{9} =b\,\,(5)\\b=\frac{5}{9}[/tex]
Knowing this constant, we can find the value of y when x=1 and z=4 as:
[tex]y=b\,\,x\,\,z^2\\y=\frac{5}{9} \,\,x\,\,z^2\\y=\frac{5}{9} \,\,(1)\,\,(4)^2\\y=\frac{5*16}{9}\\y=\frac{80}{9}[/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.
Find the measure of a positive angle and a negative angles that are coterminal with each given angle 400°
Answer: see below
Step-by-step explanation:
To find a coterminal angle, add or subtract 360° to the given angle as many times as needed to get a positive or negative angle.
I should mention that there are an infinite number of answers!
4) 400°
I can subtract 360° to get a positive angle of 40°
I can subtract another 360° to get a negative angle of -320°
5) -360°
I can subtract 360° to get a negative angle of -720°
I can add 360° twice to get a positive angle of 360°
6) -1010°
I can add 360° to get a negative angle of -650°
I can add 360° another 3 times to get a positive angle of 720°
7) 567°
I can subtract 360° to get a positive angle of 207°
I can subtract another 360° to get a negative angle of -153°
8) -164°
I can subtract 360° to get a negative angle of -524°
I can add 360° to get a positive angle of 194°
9) 358°
I can subtract 360° to get a negative angle of -2°
I can add 360° to get a positive angle of 718°
In a completely randomized design involving three treatments, the following information is provided: Treatment 1 Treatment 2 Treatment 3 Sample Size 5 10 5 Sample Mean 4 8 9 The overall mean for all the treatments is a. 7.00 b. 6.67 c. 7.25 d. 4.89
Answer:
c. 7.25
Step-by-step explanation:
Given the following information from an experiment:
[tex]\left\begin{array}{ccc}&$Sample Size&$Sample Mean \\$Treatment 1&5&4\\$Treatment 2&10&8\\$Treatment 3&5&9\end{array}\right[/tex]
Total Sample Size =5+10+5=20
Therefore, the overall mean
[tex]=\dfrac{(5 \times 4)+ (10 \times 8) + (5 \times 9)}{20} \\=\dfrac{145}{20}\\\\=7.25[/tex]
Evaluate 1/2 + 1/2 ÷ 18
Answer:
1/18
Step-by-step explanation:
First you would add 1/2 and 1/2 to get 1 then you would divide it by 18 to get 1/18
Answer:
1/18
Step-by-step explanation:
plz mark me brainliest.
A city has just added 100 new female recruits to its police force. The city will provide a pension to each new hire who remains with the force until retirement. In addition, if the new hire is married at the time of her retirement, a second pension will be provided for her husband. A consulting actuary makes the following assumptions: (i) Each new recruit has a 0.4 probability of remaining with the police force until retirement. (ii) Given that a new recruit reaches retirement with the police force, the probability that she is not married at the time of retirement is 0.25. (iii) The events of different new hires reaching retirement and the events of different new hires being married at retirement are all mutually independent events. Calculate the probability that the city will provide at most 90 pensions to the 100 new hires and their husbands. (A) 0.60 (B) 0.67 (C) 0.75 (D) 0.93 (E) 0.99
Answer:
E) 0.99
Step-by-step explanation:
100 recruits x 0.4 chance of retiring as police officer = 40 officers
probability of being married at time of retirement = (1 - 0.25) x 40 = 30 officers
each new recruit will result in either 0, 1 or 2 new pensions
0 pensions when the recruit leaves the police force (0.6 prob.)1 pension when the recruit stays until retirement but doesn't marry (0.1 prob.)2 pensions when the recruit stays until retirement and marries (0.3 prob.)mean = µ = E(Xi) = (0 x 0.6) + (1 x 0.1) + (2 x 0.3) = 0.7
σ² = (0² x 0.6) + (1² x 0.1) + (2² x 0.3) - µ² = 0 + 0.1 + 1.2 - 0.49 = 0.81
in order for the total number of pensions (X) that the city has to provide:
the normal distribution of the pension funds = 100 new recruits x 0.7 = 70 pension funds
the standard deviation = σ = √100 x √σ² = √100 x √0.81 = 10 x 0.9 = 9
P(X ≤ 90) = P [(X - 70)/9] ≤ [(90 - 70)/9] = P [(X - 70)/9] ≤ 2.22
z value for 2.22 = 0.9868 ≈ 0.99
Please answer this correctly
Answer:
Bailey: 16%
Coco: 28%
Ginger: 32%
Ruby: 24%
I hope this helps!
Which number is irrational
Answer:
Can you give the question. Can you post the picture. I can help solve. I will edit this answer once you have given the question/picture.
I need help with this one
Answer:
2 2/3
Step-by-step explanation:
Isabella averages 152 points per bowling game with a standard deviation of 14.5 points. Suppose Isabella's points per bowling game are normally distributed. Let X= the number of points per bowling game. Then X∼N(152,14.5)______.
If necessary, round to three decimal places.
Suppose Isabella scores 187 points in the game on Sunday. The z-score when x=187 is ___ The mean is _________
This z-score tells you that x = 187 is _________ standard deviations.
Answer:
The z-score when x=187 is 2.41. The mean is 187. This z-score tells you that x = 187 is 2.41 standard deviations above the mean.
Step-by-step explanation:
Problems of normally distributed samples are solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore 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 pvalue, we get the probability that the value of the measure is greater than X.
In this question:
[tex]\mu = 152, \sigma = 14.5[/tex]
The z-score when x=187 is ...
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{187 - 152}{14.5}[/tex]
[tex]Z = 2.41[/tex]
The z-score when x=187 is 2.41. The mean is 187. This z-score tells you that x = 187 is 2.41 standard deviations above the mean.
arl rides his bicycle 120 feet in 10 seconds. How many feet does he ride in 1 minute? 2 feet 12 feet 720 feet 7,200 feet
Answer: 720 ft
Step-by-step explanation: He rides 720 feet.
if 120 feet are in 10 seconds then;
60 seconds are 60/10*120=720 feet
Answer:
720
Step-by-step explanation:
120/10 to find his feet per second which is 12 feet per second
12*60
since there are 60 seconds in a minute
= 720
