Answer:
the variance of the refund payment to the couple = 9463.394
Step-by-step explanation:
Given that :
A couple book a cruise to Alaska that promises to refund 100 per day of rain on the seven day cruise up to a maximum of 300.
It is possible that the couple won't be able to refund up 100 per day or more than 100 per day.
SO; let assume that the refund payment happens to be 0, 100,200, 300
Let X be the total refund payment on the seven day cruise.
We can say X = 0, if there is no rain on all 7 days.
[tex]P(X = 0) = _nC_x * P^x * (1 - P)n-x[/tex]
[tex]P(X = 0) = _7C_o * 0.2^0 * (1-0.2)^{7-0[/tex]
[tex]P(X = 0) =1 * 1* (1-0.2)^{7[/tex]
[tex]P(X = 0) =(0.8)^{7[/tex]
[tex]P(X = 0) =0.2097152[/tex]
If it rains on any one day; then X = 100
[tex]P(X = 100) = _nC_x * P^x * (1 - P)n-x[/tex]
[tex]P(X = 100) = _7C_1 * 0.2^1 * (1-0.2)^{7-1[/tex]
[tex]P(X = 0) =7 * 0.2* (1-0.2)^{6[/tex]
[tex]P(X = 100) =7* 0.2* (0.8)^{6[/tex]
[tex]P(X = 100) =0.3670016[/tex]
if it rains on any two day ; then X = 200
[tex]P(X = 200) = _nC_x * P^x * (1 - P)n-x[/tex]
[tex]P(X = 200) = _7C_2 * 0.2^2 * (1-0.2)^{7-2[/tex]
[tex]P(X = 200) = 21 * 0.2^2 * (0.8)^{5[/tex]
[tex]P(X = 200) = 0.2752512[/tex]
if it rains on any three day or more than that ; then X = 300
[tex]P(X \ge 300) = 1 - P(X < 300) \\ \\ P(X \ge 300) = 1 - [P(X = 0) + P(X = 100) + P(X = 200)] \\ \\ P(X \ge 300) = 1 - [0.2097152 + 0.3670016 + 0.2752512] \\ \\ P(X \ge 300) = 0.148032[/tex]
Now; we have our probability distribution function as:
P(X = 0) = 0.2097152
P(X = 100) = 0.3670016
P(X = 200) = 0.2752512
P(X = 300) = 0.148032
In order to determine the variance of the refund payment to the couple; we use the formula:
variance of the refund payment to the couple[tex][Var X] =E [X^2] - (E [X])^2[/tex]
where;
[tex]E[X^2] = \sum x^2 \times p \\ \\ E[X^2] = 0^2 * 0.2097152 + 100^2 * 0.3670016 + 200^2 * 0.2752512 + 300^2 * 0.148032 \\ \\ E[X^2] = 0 + 3670.016 + 11010.048+ 13322.88 \\ \\ E[X^2] =28002.944[/tex]
[tex](E [X]) = \sum x * p\\ \\ (E [X]) = 0 * 0.2097152 + 100 * 0.3670016 + 200 * 0.2752512 + 300 * 0.148032 \\ \\ (E [X]) = 0 + 36.70016 + 55.05024 + 44.4096\\ \\ (E [X]) = 136.16 \\ \\ (E [X])^2 = 136.16^2 \\ \\ (E [X])^2 = 18539.55[/tex]
NOW;
the variance of the refund payment to the couple = 28002.944 - 18539.55
the variance of the refund payment to the couple = 9463.394
According to an airline, flights on a certain route are on time 80% of the time. Suppose 17 flights are randomly selected and the number of on-time flights is recorded.
Required:
a. Explain why this is a binomial experiment.
b. Find and interpret the probability that exactly 11 flights are on time.
c. Find and interpret the probability that fewer than 11 flights are on time
d. Find and interpret the probability that at least 11 flights are on time.
e. Find and interpret the probability that between 9 and 11 flights, inclusive, are on time.
Answer:
a) Check Explanation
b) Probability that 11 out of the 17 randomly selected flights are on time = P(X = 11) = 0.0680
c) Probability that fewer than 11 out of the 17 randomly selected flights are on time
= P(X < 11) = 0.0377
d) Probability that at least 11 out of the 17 randomly selected flights are on time
= P(X ≥ 11) = 0.9623
e) Probability that between 9 and 11 flights, inclusive, out of the randomly selected 17 are on time = P(9 ≤ X ≤ 11) = 0.1031
Step-by-step explanation:
a) How to know a binomial experiment
1) A binomial experiment is one in which the probability of success doesn't change with every run or number of trials. (Probability of each flight being on time is 80%)
2) It usually consists of a number of runs/trials with only two possible outcomes, a success or a failure. (It's either the flights are on time or not).
3) The outcome of each trial/run of a binomial experiment is independent of one another.
All true for this experiment.
b) Probability that exactly 11 flights are on time.
Let X be the random variable that represents the number of flights that are on time out of the randomly selected 17.
Binomial distribution function is represented by
P(X = x) = ⁿCₓ pˣ qⁿ⁻ˣ
n = total number of sample spaces = 17 randomly selected flights
x = Number of successes required = number of flights required to be on time
p = probability of success = Probability of a flight being on time = 80% = 0.80
q = probability of failure = Probability of a flight NOT being on time = 1 - p = 1 - 0.80 = 0.20
P(X = 11) = ¹⁷C₁₁ (0.80)¹¹ (0.20)¹⁷⁻¹¹ = 0.06803777953 = 0.0680
c) Probability that fewer than 11 flights are on time
This is also computed using binomial formula
It is the probability that the number of flights on time are less than 11
P(X < 11) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) + P(X = 6) + P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10) = 0.0376634429 = 0.0377
d) Probability that at least 11 out of the 17 randomly selected flights are on time
This is the probability of the number of flights on time being 11 or more.
P(X ≥ 11) = P(X = 11) + P(X = 12) + P(X = 13) + P(X = 14) + P(X = 15) + P(X = 16) + P(X = 17)
= 1 - P(X < 11)
= 1 - 0.0376634429
= 0.9623365571 = 0.9623
e) Probability that between 9 and 11 flights, inclusive, are on time = P(9 ≤ X ≤ 11)
This is the probability that exactly 9, 10 or 11 flights are on time.
P(9 ≤ X ≤ 11) = P(X = 9) + P(X = 10) + P(X = 11)
= 0.0083528524 + 0.02672912767 + 0.06803777953
= 0.1031197592 = 0.1031
Hope this Helps!!!
. Suppose X ∼ Unif(−1, 3). Find the probabilities of the following events, both by hand calculation and with R’s punif function. (a) (X ≤ 2) (b) (X ≥ 1) (c) (−0.5 < X < 1.5) (d) (X = 0)
Answer:
a) [tex] P(X \leq 2) = \frac{2+1}{3+1}= 0.75[/tex]
b) [tex] P(X \geq 1) = 1- P(X <1) =1-\frac{1+1}{3+1}= 1-0.5=0.5[/tex]
c) [tex]P(-0.5 <X <1.5)= P(X<1.5)- P(X<-0.5)= \frac{1.5+1}{4} -\frac{-0.5+1}{4}=0.625-0.125= 0.5[/tex]
d) [tex] f(x) = \frac{1}{3+1}= 0.25[/tex]
Step-by-step explanation:
Let X the random variable of interest and we know that the distribution is given by:
[tex]X \sim Unif (a= -1, b=3)[/tex]
And for this problem we can use the cumulative distribution function in order to solve the items:
[tex] F(x) =\frac{x-a}{b-a}, a\leq x \leq b[/tex]
Part a
We want to find this probability:
[tex] P(X \leq 2) = \frac{2+1}{3+1}= 0.75[/tex]
Part b
[tex] P(X \geq 1) = 1- P(X <1) =1-\frac{1+1}{3+1}= 1-0.5=0.5[/tex]
Part c
[tex]P(-0.5 <X <1.5)[/tex]
And we can calculate the probability with this difference:
[tex]P(-0.5 <X <1.5)= P(X<1.5)- P(X<-0.5)= \frac{1.5+1}{4} -\frac{-0.5+1}{4}=0.625-0.125= 0.5[/tex]
Part d
Since we have a continuous distribution the the probability for an unique value would be:
[tex] f(x) = \frac{1}{3+1}= 0.25[/tex]
A cone-shaped paper drinking cup is to be made to hold 33 cm3 of water. Find the height and radius of the cup that will use the smallest amount of paper. (Round your answers to two decimal places.) height cm radius cm
Answer:
The height and the radius of the cylinder are 3.67 centimeters and 5.19 centimeters, respectively.
Step-by-step explanation:
The volume ([tex]V[/tex]) and the surface area ([tex]A_{s}[/tex]) of the cone, measured in cubic centimeters and square centimeters, respectively, are modelled after these formulas:
Volume
[tex]V = \frac{h\cdot r^{2}}{3}[/tex]
Surface area
[tex]A_{s} = \pi\cdot r \cdot \sqrt{r^{2}+h^{2}}[/tex]
Where:
[tex]h[/tex] - Height of the cylinder, measured in centimeters.
[tex]r[/tex] - Radius of the base of the cylinder, measured in centimeters.
The volume of the paper drinking cup is known and first and second derivatives of the surface area functions must be found to determine the critical values such that surface area is an absolute minimum. The height as a function of volume and radius of the cylinder is:
[tex]r = \sqrt{\frac{3\cdot V}{h} }[/tex]
Now, the surface area function is expanded and simplified:
[tex]A_{s} = \pi\cdot \sqrt{\frac{3\cdot V}{h} }\cdot \sqrt{\frac{3\cdot V}{h}+ h^{2}}[/tex]
[tex]A_{s} = \pi\cdot \sqrt{\frac{9\cdot V^{2}}{h^{2}} + 3\cdot V\cdot h }[/tex]
[tex]A_{s} = \pi\cdot \sqrt{3\cdot V} \cdot\sqrt{\frac{3\cdot V+ h^{3}}{h^{2}} }[/tex]
[tex]A_{s} = \pi\cdot \sqrt{3\cdot V}\cdot \left(\frac{\sqrt{3\cdot V + h^{3}}}{h}\right)[/tex]
If [tex]V = 33\,cm^{3}[/tex], then:
[tex]A_{s} = 31.258\cdot \left(\frac{\sqrt{99+h^{3}}}{h} \right)[/tex]
The first and second derivatives of this function are require to determine the critical values that follow to a minimum amount of paper:
First derivative
[tex]A'_{s} = 31.258\cdot \left[\frac{\left(\frac{3\cdot h^{2}}{\sqrt{99+h^{2}}}\right)\cdot h - \sqrt{99+h^{3}} }{h^{2}}\right][/tex]
[tex]A'_{s} = 31.258\cdot \left(\frac{3\cdot h^{3}-99-h^{3}}{h^{2}\cdot \sqrt{99+h^{2}}} \right)[/tex]
[tex]A'_{s} = 31.258\cdot \left(\frac{2\cdot h^{3}-99}{h^{2}\cdot \sqrt{99+h^{2}}} \right)[/tex]
[tex]A'_{s} = 31.258\cdot \left[2\cdot h\cdot (99+h^{2}})^{-0.5} -99\cdot h^{-2}\cdot (99+h^{2})^{-0.5}\right][/tex]
[tex]A'_{s} = 31.258\cdot (2\cdot h - 99\cdot h^{-2})\cdot (99+h)^{-0.5}[/tex]
Second derivative
[tex]A''_{s} = 31.258\cdot \left[(2+198\cdot h^{-3})\cdot (99+h)^{-0.5}-0.5\cdot (2\cdot h - 99\cdot h^{-2})\cdot (99+h)^{-1.5}\right][/tex]
Let equalize the first derivative to zero and solve the resultant expression:
[tex]31.258\cdot (2\cdot h - 99\cdot h^{-2})\cdot (99+h)^{-0.5} = 0[/tex]
[tex]2\cdot h - 99 \cdot h^{-2} = 0[/tex]
[tex]2\cdot h^{3} - 99 = 0[/tex]
[tex]h= \sqrt[3]{\frac{99}{2} }[/tex]
[tex]h \approx 3.672\,cm[/tex]
Now, the second derivative is evaluated at the critical point:
[tex]A''_{s} = 31.258\cdot \{[2+198\cdot (3.672)^{-3}]\cdot (99+3.672)^{-0.5}-0.5\cdot [2\cdot (3.672) - 99\cdot (3.672)^{-2}]\cdot (99+3.672)^{-1.5}\}[/tex]
[tex]A''_{s} = 18.506[/tex]
According to the Second Derivative Test, this critical value leads to an absolute since its second derivative is positive.
The radius of the cylinder is: ([tex]V = 33\,cm^{3}[/tex] and [tex]h \approx 3.672\,cm[/tex])
[tex]r = \sqrt{\frac{3\cdot V}{h} }[/tex]
[tex]r = \sqrt{\frac{3\cdot (33\,cm^{3})}{3.672\,cm} }[/tex]
[tex]r \approx 5.192\,cm[/tex]
The height and the radius of the cylinder are 3.672 centimeters and 5.192 centimeters, respectively.
250 balls are numbered from 1 to 250 and placed in a box. A ball is picked random. What is a probabilty of picking ball with three- digit number?
Answer:
150/250 or 3/5 or a 60% chance
Step-by-step explanation:
Why?
because you need to calculate the number of balls that are a three-digit number and they will not be a three-digit number up until you get to 100 so what is 250-100? its 150 so your fraction is 150/250 or 3/5 if you need it simplified. To get a percent you need to divide 150 by 250 to get 0.6 and then you multiply by 100.
what is the answer to 263·24−164·24+24
Answer:
2400
Step-by-step explanation:
You have to follow PEMDAS (Parentheses, Exponent, Multiplication, Division, Addition, Subtraction). Based off of this, you have to do the multiplication first, and then add.
263 × 24 - 164 × 24 + 24
6312 - 3936 + 24
2376 + 24
2400
The value of the expression 263 · 24 − 164 · 24 + 24 will be 2400.
What is the value of the expression?When the relevant components and basic processes of a numerical method are given values, the expression's result is the result of the computation it depicts.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This rule is used to answer the problem correctly and precisely.
The expression is given below.
⇒ 263 · 24 − 164 · 24 + 24
Simplify the expression, then the value of the expression is given as,
⇒ 263 · 24 − 164 · 24 + 24
⇒ 6312 − 3936 + 24
⇒ 6336 − 3936
⇒ 2400
The value of the expression 263 · 24 − 164 · 24 + 24 will be 2400.
More about the value of the expression link is given below.
https://brainly.com/question/23671908
#SPJ2
Read the passage.
(1) I think that schools should switch from using paper textbooks to using computer tablets. (2)
Textbooks were effective in the pre-digital age, but now we live in a technology-based society, so
schools need to get with the program and adopt a modern approach to learning. (3) In fact, the chair
of the Federal Communications Commission said that "it's time for the next stage" of learning with
tablets and pointed out how textbooks are often out of date. (4) Opponents argue that tablets aren't
a good choice because initially they're very expensive. (5) The secretary of education pointed out
that tablets can be updated regularly, which saves money in the long run. (6) Not to mention the
pluses of having the latest and greatest info! (7) Many experts agree that switching to tablets is
important for the future of education.
To improve the logical flow of the paragraph, the bestplace to move sentence 7 is before
This question is incomplete because the options are missing; here is the question statement and options:
To improve the logical flow of the paragraph, the best place to move sentence 7 is before
A. Sentence 1.
B. Sentence 3.
C. Sentence 5.
D. Sentence 6.
The correct answer is B. Sentence 3
Explanation:
The paragraph develops an argument through different sections. This includes the thesis statement "schools should switch from using paper textbooks to using computer tablets", reasons and evidence that support this thesis, the explanation of one counterclaim, and finally, reasons to disprove the counterclaim and confirm the claim.
In the case of sentence 7 "Many experts agree that switching to tablets is important for the future of education" this provides a reason that supports the argument and due to this, it is more appropriate this sentence is placed after the thesis and before the counterclaim "Opponents argue that tablets ...".
In this context, this sentence should be placed before sentence 3 that belongs to the evidence provided to support the claim. Moreover, sentence 7 would appropriately introduce sentence 3 as they are both related to the opinion of experts about this issue.
The 7th sentence can be placed before the first, third, and fifth.
Decision makingThe process of making an important decision is known as decision making.
Given
7 statement is there.
To find the position of the 7th sentence.
How to place 7th sentences?7th sentence can be placed before the first because it seems that the conversation is starting.
7th sentence can be placed before the third because you can say as an update will be done by Federal Communications Commission.
7th sentence can be placed before the fifth because the secretary wants to implement it in his system due to its regular update.
Thus, the 7th sentence can be placed before the first, third, and fifth.
More about the decision-making link is given below.
https://brainly.com/question/3369578
Please answer this correctly
Answer:
75%
Step-by-step explanation:
There are 3 numbers that fit this rule, 3, 5, and 6. There is a 3/4 chance spinning one or a 75% chance.
Answer:
75%
Step-by-step explanation:
The numbers 6 or odd are 3, 5, and 6.
3 numbers out of a total of 4 numbers.
3/4 = 0.75
Convert to percentage.
0.75 × 100 = 75
P(6 or odd) = 75%
Help me! (Snog, Ujalakhan01, Pragya5, whoever else) 2(x-1)=
Answer:
2x-2
Step-by-step explanation:
2(x-1)=
Distribute
2x* -2*1
2x-2
Answer:
[tex]2x - 2[/tex]
Solution,
[tex]2(x - 1) \\ = 2 \times x - 2 \times 1 \\ = 2x - 2[/tex]
hope this helps..
Use the substitution x = 2 − cos θ to evaluate the integral ∫ 2 3/2 ( x − 1 3 − x )1 2 dx. Show that, for a < b, ∫ q p ( x − a b − x )1 2 dx = (b − a)(π + 3√ 3 − 6) 12 , where p = ???????????????????????????
If the integral as written in my comment is accurate, then we have
[tex]I=\displaystyle\int_{3/2}^2\sqrt{(x-1)(3-x)}\,\mathrm dx[/tex]
Expand the polynomial, then complete the square within the square root:
[tex](x-1)(3-x)=-x^2+4x-3=1-(x-2)^2[/tex]
[tex]I=\displaystyle\int_{3/2}^2\sqrt{1-(x-2)^2}\,\mathrm dx[/tex]
Let [tex]x=2-\cos\theta[/tex] and [tex]\mathrm dx=\sin\theta\,\mathrm d\theta[/tex]:
[tex]I=\displaystyle\int_{\pi/3}^{\pi/2}\sqrt{1-(2-\cos\theta-2)^2}\sin\theta\,\mathrm d\theta[/tex]
[tex]I=\displaystyle\int_{\pi/3}^{\pi/2}\sqrt{1-\cos^2\theta}\sin\theta\,\mathrm d\theta[/tex]
[tex]I=\displaystyle\int_{\pi/3}^{\pi/2}\sqrt{\sin^2\theta}\sin\theta\,\mathrm d\theta[/tex]
Recall that [tex]\sqrt{x^2}=|x|[/tex] for all [tex]x[/tex], but for all [tex]\theta[/tex] in the integration interval we have [tex]\sin\theta>0[/tex]. So [tex]\sqrt{\sin^2\theta}=\sin\theta[/tex]:
[tex]I=\displaystyle\int_{\pi/3}^{\pi/2}\sin^2\theta\,\mathrm d\theta[/tex]
Recall the double angle identity,
[tex]\sin^2\theta=\dfrac{1-\cos(2\theta)}2[/tex]
[tex]I=\displaystyle\frac12\int_{\pi/3}^{\pi/2}(1-\cos(2\theta))\,\mathrm d\theta[/tex]
[tex]I=\dfrac\theta2-\dfrac{\sin(2\theta)}4\bigg|_{\pi/3}^{\pi/2}[/tex]
[tex]I=\dfrac\pi4-\left(\dfrac\pi6-\dfrac{\sqrt3}8\right)=\boxed{\dfrac\pi{12}+\dfrac{\sqrt3}8}[/tex]
You can determine the more general result in the same way.
[tex]I=\displaystyle\int_p^q\sqrt{(x-a)(b-x)}\,\mathrm dx[/tex]
Complete the square to get
[tex](x-a)(b-x)=-(x-a)(x-b)=-x^2+(a+b)x-ab=\dfrac{(a+b)^2}4-ab-\left(x-\dfrac{a+b}2\right)^2[/tex]
and let [tex]c=\frac{(a+b)^2}4-ab[/tex] for brevity. Note that
[tex]c=\dfrac{(a+b)^2}4-ab=\dfrac{a^2-2ab+b^2}4=\dfrac{(a-b)^2}4[/tex]
[tex]I=\displaystyle\int_p^q\sqrt{c-\left(x-\dfrac{a+b}2\right)^2}\,\mathrm dx[/tex]
Make the following substitution,
[tex]x=\dfrac{a+b}2-\sqrt c\,\cos\theta[/tex]
[tex]\mathrm dx=\sqrt c\,\sin\theta\,\mathrm d\theta[/tex]
and the integral reduces like before to
[tex]I=\displaystyle\int_P^Q\sqrt{c-c\cos^2\theta}\,\sin\theta\,\mathrm d\theta[/tex]
where
[tex]p=\dfrac{a+b}2-\sqrt c\,\cos P\implies P=\cos^{-1}\dfrac{\frac{a+b}2-p}{\sqrt c}[/tex]
[tex]q=\dfrac{a+b}2-\sqrt c\,\cos Q\implies Q=\cos^{-1}\dfrac{\frac{a+b}2-q}{\sqrt c}[/tex]
[tex]I=\displaystyle\frac{\sqrt c}2\int_P^Q(1-\cos(2\theta))\,\mathrm d\theta[/tex]
(Depending on the interval [p, q] and thus [P, Q], the square root of cosine squared may not always reduce to sine.)
Resolving the integral and replacing c, with
[tex]c=\dfrac{(a-b)^2}4\implies\sqrt c=\dfrac{|a-b|}2=\dfrac{b-a}2[/tex]
because [tex]a<b[/tex], gives
[tex]I=\dfrac{b-a}2(\cos(2P)-\cos(2Q)-(P-Q))[/tex]
Without knowing p and q explicitly, there's not much more to say.
2) Which two statements are not true?
The product of two irrational numbers is always rational
1. The sum of a rational and an irrational number is always irrational
c. The product of two rational numbers is always rational.
d. The product of a rational number (other than zero) and an irrational number is always irrational
e. A repeating decimal is not a rational number.
Grom per
Answer:
A repeating decimal is not a rational number and The product of two irrational numbers is always rational
Step-by-step explanation:
One statement that is not true is "The product of two irrational numbers is always rational". Take for example the irrational numbers √2 and √3. Their product is √6 which is also irrational.
The other false statement is "A repeating decimal is not a rational number". Take for example the repeating decimal 0.33333..... It can be written as 1/3 which is a rational number.
Find the width of a photograph whose length is 8 inches and whose proportions are the same as a photograph that is 18 inches wide by 24 inches long.
Answer:
6 Inches
Step-by-step explanation:
First Photograph
Length:Width = 24:18
Second Photograph
Let the unknown width =x
Length:Width = 8:x
Since the proportions of the two photographs are the same
[tex]8:x=24:18\\\\\dfrac{8}{x}= \dfrac{24}{18}\\\\24x=8 \times 18\\\\x=(8 \times 18) \div 24\\\\x=6$ inches[/tex]
The width of the photograph is 6 inches.
A business operated at 100% of capacity during its first month and incurred the following costs: Production costs (19,900 units): Direct materials $172,700 Direct labor 221,400 Variable factory overhead 265,400 Fixed factory overhead 92,800 $752,300 Operating expenses: Variable operating expenses $134,100 Fixed operating expenses 43,700 177,800 If 1,500 units remain unsold at the end of the month, the amount of inventory that would be reported on the absorption costing balance sheet is
Answer:
Ending inventory cost= $56,700
Step-by-step explanation:
Giving the following information:
Production costs (19,900 units):
Direct materials $172,700
Direct labor 221,400
Variable factory overhead 265,400
Fixed factory overhead 92,800
Total= $752,300
The absorption costing method includes all costs related to production, both fixed and variable. The unit product cost is calculated using direct material, direct labor, and total unitary manufacturing overhead.
Total unitary production cost= 752,300/19,900= $37.80
Units in ending inventory= 1,500
Ending inventory cost= 1,500*37.8
Ending inventory cost= $56,700
Bruce goes hiking every 2 days and swimming every 11 days . He did both kinds of exercise today . How many days from now will he next go both hiking and swimming again.
Answer:
22 more days
Step-by-step explanation:
so basically you have to find out the LCM of 2 and 11. which is 22. And that means they go hiking AND swimming in the same day the next 22 days. (basically what the other person said lol)
AND that is basically your answer :D
Suppose the coffee industry claimed that the average U.S. adult drinks 1.7 cups of coffee per day. To test this claim, a random sample of 34 adults was selected, and their average coffee consumption was found to be 1.95 cups per day. Assume the standard deviation of daily coffee consumption per day is 0.5 cups. Using a = 0.10, answer the following questions:
a. Is the coffee industryâs claim supported by this sample?
b. Determine the p-value for this test.
c. Verify your results using PHStat.
Answer:
a) This t-value obtained (2.92) is in the rejection region (t > 1.69), hence, the sample does not support the cofdee industry's claim.
b) p-value for this test = 0.006266
c) The p-value obtained for this test is lesser than the significance level at which the test was performed, hence, we can reject the nuĺl hypothesis and say that there is enough evidence to suggest that the coffee industry's claim isn't true based in results obtained from the sample data.
Step-by-step explanation:
a) Degree of freedom = n - 1 = 34 - 1 = 33
The critical value of t for a significance level of 0.10 and degree of freedom of 33 = 1.69
Since we are testing in both directions whether the the average U.S. adult drinks 1.7 cups of coffee per day using our sample,
The rejection region is t < -1.69 and t > 1.69
So, we compute the t-statistic for this sample data to test the claim.
t = (x - μ)/σₓ
x = sample mean = 1.95 cups of coffee per day
μ₀ = The standard we are comparing against = 1.7 cups of coffee per day
σₓ = standard error = (σ/√n)
σ = standard deviation = 0.5 cups
n = Sample size = 34
σₓ = (0.5/√34) = 0.0857492926 = 0.08575
t = (1.95 - 1.70) ÷ 0.08575
t = 2.9154759464 = 2.92
This t-value obtained is in the rejection region, hence, the sample does not support the cofdee industry's claim.
b) Checking the tables for the p-value of this t-statistic
Degree of freedom = df = n - 1 = 34 - 1 = 33
Significance level = 0.10
The hypothesis test uses a two-tailed condition because we're testing in both directions.
p-value (for t = 2.92, at 0.10 significance level, df = 33, with a two tailed condition) = 0.006266
c) To use PHStat, the claim that the average U.S. adult drinks 1.7 cups of coffee per day is the null hypothesis.
The alternative hypothesis is that the real number of cups of coffee that the average U.S. adult drinks as obtained from the sample data, is significantly different from the 1.7 in the coffee industry's claim.
The p-value obtained from PHstat = 0.0063
The interpretation of p-values is that
When the (p-value > significance level), we fail to reject the null hypothesis and when the (p-value < significance level), we reject the null hypothesis and accept the alternative hypothesis.
So, for this question, significance level = 0.10
p-value = 0.0063
0.0063 < 0.10
Hence,
p-value < significance level
This means that we reject the null hypothesis, accept the alternative hypothesis & say that there is enough evidence to suggest that the coffee industry's claim isn't true based in results obtained from the sample data.
Hope this Helps!!!
2x + y - z = 3
-x + 2y + 4z = -3
x – 2y - 3z = 4
Answer:
x=3, y=-2, z=1
Step-by-step explanation:
I solved by substitution
Answer:
x = 3; y = -2; z = 1.
Step-by-step explanation:
-x + 2y + 4z = -3
x – 2y - 3z = 4
(-x + x) + (2y - 2y) + (4z - 3z) = (-3 + 4)
0 + 0 + z = 1
z = 1
x - 2y - 3(1) = 4
x - 2y - 3 = 4
x - 2y = 7
x = 2y + 7
2(2y + 7) + y - (1) = 3
4y + 14 + y - 1 = 3
5y + 13 = 3
5y = -10
y = -2
x = 2(-2) + 7
x = -4 + 7
x = 3
So, your answer is (3, -2, 1).
Hope this helps!
Q1. 12.5g of medicine cost 1,075 naira. What is the cost of 1g of medicine. Q2. What is the total pay for someone who works 42 hours and gets 645 naira per hour
Step-by-step explanation:
Q1. 1,075÷12.5 =8
So Therefore 1g of medicine cost 8 naira
Q2.645÷42=15.3
so therefore 1 hour cost 15.3 naira
The cost of 1g of medicine is 86 naira and the total pay for someone who works 42 hours is 27090 naira.
What is Division?A division is a process of splitting a specific amount into equal parts.
Given that 12.5g of medicine cost 1,075 naira.
We have to find the cost of 1g of medicine.
12.5g=1075 naira
1g=1075/12.5
1g=86 naira.
the total pay for someone who works 42 hours and gets 645 naira per hour
The cost for 42 hours
42×645
27090 naira
Hence, the cost of 1g of medicine is 86 naira and the total pay for someone who works 42 hours is 27090 naira.
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5∑12 i=1 kinda hard to type but 5 is on top!!
Answer:
60
Step-by-step explanation:
We are using sigma notation to solve for a sum of arithmetic sequences:
The 5 stands for stop at i = 5 (inclusive)
The i = 1 stands for start at i = 1
The 12 stands for expression of each term in the sum
ab = cde
In order to solve the equation above for c, you must multiply both sides of the equation by the same expression
ab x _? = cde x _?
The resulting equation is
C= _?
Answer:
1) We have to multiply both sides by 1/(de)
2) c=ab/(cd)
Step-by-step explanation:
We have to achieve the right side expression be c only. To do that we have to multiply cde by 1/(de) . However we have to multiply the left side by
1/(de) as well.
So the resulting left side expression is:
ab *1/(de)=ab/(de)
So c= ab/(de)
Given equation in the question is,
ab = cde
To solve the given equation for the value of c, follow the algebraic rules,
1). Multiply both the sides of the equation with [tex]\frac{1}{de}[/tex],
[tex]ab\times \frac{1}{de} = \frac{cde}{de}[/tex]
[tex]\frac{ab}{de}= \frac{cde}{de}[/tex]
[tex]\frac{ab}{de}=c[/tex]
Therefore, resulting equation for c will be,
[tex]c=\frac{ab}{de}[/tex]
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IQ is normally distributed with a mean of 100 and a standard deviation of 15. Suppose one individual is randomly chosen. Let X = IQ of an individual. Part (a) Give the distribution of X. X ~ , Part (b) Find the probability that the person has an IQ greater than 105. Write the probability statement. P What is the probability? (Round your answer to four decimal places.) Sketch the graph. WebAssign Plot WebAssign Plot WebAssign Plot WebAssign Plot Part (c) Mensa is an organization whose members have the top 2% of all IQs. Find the minimum IQ needed to qualify for the Mensa organization. Write the probability statement. P(X > x) = What is the minimum IQ? (Round your answer to the nearest whole number.) x = Sketch the graph. WebAssign Plot WebAssign Plot WebAssign Plot WebAssign Plot Part (d) The middle 40% of IQs fall between what two values? Write the probability statement. P(x1 < X < x2) = State the two values. (Round your answers to the nearest whole number.) x1 = x2 = Sketch the graph. WebAssign Plot WebAssign Plot WebAssign Plot WebAssign Plot
Answer:
a) The normal distribution function for the IQ of a randomly selected individual is presented in the first attached image to this solution.
b) The probability that the person has an IQ greater than 105 = P(X > 105) = 0.3707
The sketch of this probability is presented in the second attached image to this solution.
c) The minimum IQ needed to qualify for the Mensa organization = 130.81. Hence, P(X > 131) = 2%
The sketched image of this probability is presented also in the second attached image to the solution. The shaded region is the required probability.
d) The middle 40% of IQs fall between 92 and 108 IQ respectively.
P(x1 < X < x2) = P(92 < X < 108) = 0.40
The sketched image of this probability is presented in the third attached image to the solution. The shaded region is the required probability.
Step-by-step explanation:
The IQ of an individual is given as a normal distribution withh
Mean = μ = 100
Standard deviation = σ = 15
If X is a random variable which represents the IQ of an individual
a) The distribution of X will then be given as the same as that of a normal distribution.
f(x) = (1/σ√2π) {e^ - [(x - μ)²/2σ²]}
The normal distribution probability density function is more clearly presented in the first attached image to this question
b) Probability that the person has an IQ greater than 105.
To find this probability, we will use the normal probability tables
We first normalize/standardize 105.
The standardized score of any value is that value minus the mean divided by the standard deviation.
z = (x - μ)/σ = (105 - 100)/15 = 0.33
P(x > 105) = P(z > 0.33)
Checking the tables
P(x > 105) = P(z > 0.33) = 1 - P(z ≤ 0.33) = 1 - 0.6293 = 0.3707
The sketch of this probability is presented in the second attached image to this question. The shaded region is the required probability.
c) Mensa is an organization whose members have the top 2% of all IQs. Find the minimum IQ needed to qualify for the Mensa organization.
We need to find x for P(X > x) = 2% = 0.02
Let the corresponding z-score for this probability be z'
P(X > x) = P(z > z') = 0.02
P(z > z') = P(z ≤ z') = 1 - 0.02 = 0.98
From the normal distribution table, z' = 2.054
z = (x - μ)/σ
2.054 = (x - 100)/15
x = 2.054×15 + 100 = 130.81 = 131 to the nearest whole number.
The sketched image of this probability is presented also in the second attached image to the solution. The shaded region is the required probability.
d) The middle 40% of IQs fall between what two values?
P(x1 < X < x2) = 0.40
Since the normal distribution is symmetric about the mean, the lower limit of this IQ range will be greater than the lower 30% region of the IQ distribution and the upper limit too is lesser than upper 30% region of the distribution.
P(X < x1) = 0.30
P(X > x2) = 0.30, P(X ≤ x2) = 1 - 0.30 = 0.70
Let the z-scores of x1 and x2 be z1 and z2 respectively.
P(X < x1) = P(z < z1) = 0.30
P(X ≤ x2) = P(z ≤ z2) = 0.70
From the normal distribution tables,
z1 = -0.524
z2 = 0.524
z1 = (x1 - μ)/σ
-0.524 = (x1 - 100)/15
x1 = -0.524×15 + 100 = 92.14 = 92 to the nearest whole number.
z2 = (x2 - μ)/σ
0.524 = (x2 - 100)/15
x2 = 0.524×15 + 100 = 107.86. = 108 to the nearest whole number.
The sketched image of this probability is presented in the third attached image to the solution. The shaded region is the required probability.
Hope this Helps!!!
Given n objects arranged in a row, a subset of these objects is called unfriendly if no two of its elements are consecutive. Show that the number of unfriendly subsets each having k elements is
Complete question is;
Given n objects are arranged in a row. A subset of these objects is called unfriendly, if no two of its elements are consecutive. Show that the number of unfriendly subsets of a k-element set is ( n−k+1 )
( k )
Answer:
I've been able to prove that the number of unfriendly subsets of a k-element set is;
( n−k+1 )
( k )
Step-by-step explanation:
I've attached the proof that the number of unfriendly subsets of a k-element set is;
( n−k+1 )
( k )
divide
a) 21564÷2
b)40565÷5
c)6365÷8
d)1436÷7
answer please fast
Answer:
21564 ÷ 2 = 10782
40565 ÷ 5 = 8113
6365 ÷ 8 = 795.625
1436 ÷ 7 = 205.142857143
Solve for X. (nearest WHOLE degree)
Answer:
x = 32°Step-by-step explanation:
To solve for x we use sine
sin ∅ = opposite / hypotenuse
From the question
38 is the hypotenuse
20 is the opposite
So we have
sin x = 20/38
sin x = 10/19
x = sin-¹ 10/19
x = 31.75
x = 32° to the nearest degreeHope this helps you
pls help me pls pls pls
Answer:
B. A shirt costs $15, and a pair of shoes costs $20.
Step-by-step explanation:
Let s = price of 1 shirt.
Let p = price of 1 pair of shoes.
Adam:
5s + 4p = 155
Friend:
3s + 2p = 85
We have a system of simultaneous equations.
5s + 4p = 155
3s + 2p = 85
Rewrite the first equation. Multiply both sides of the second equation by -2 and write below it. Add the equations.
5s + 4p = 155
(+) -6s - 4p = -170
--------------------------
-s = -15
s = 15
A shirt costs $15.
Now we replace s with 15 in the first original equation and solve for p.
5s + 4p = 155
5(15) + 4p = 155
75 + 4p = 155
4p = 80
p = 20
A pair of shoes costs $20.
Assume in a ICU room, the arrival rate of the infect follows a Poisson distribution with mean = 3 / hour. (a) What is the probability of the infected is more than 8 in a hour.
Answer:
The probability of the infected is more than 8 in a hour is 0.00384
Step-by-step explanation:
Given that the Mean of the arrival rate of the infect follows a Poisson distribution = x`= 3 / hour
The Poisson distribution formula is given by
P(X) = e-ˣ` x`ˣ/ x!
The mean is 3 and we have to find the probability of 8 or more which means
1 -X where X takes the values of 0,1,2,3,------,8.
P( more than 8 ) = 1- P( X ≤ 8 ) =1- {e-³ (3)⁸/8! +e-³ (3)⁷/7! +e-³ (3)⁶/6! +e-³ (3)⁵/5! +e-³ (3)⁴/4! +e-³ (3)³/3! +e-³ (3)²/2!+ e-³ (3)¹/1! +e-³ (3)⁰/0!}
Putting the Values
P( more than 8 ) = 1- P( X ≤ 8 ) =1- [ 0.04979*6561 / 40320 +0.04979*2187 / 5040 + 0.04979*729 / 720 +0.04979*243 / 120+0.04979*81 / 24 + 0.04979 *27 / 6 + 0.04979 *9 /2 + 0.04979*3/ 1 + 0.04979*1/1 }
Solving
P( more than 8 ) = 1- P( X ≤ 8 ) =1- [ 0.0081 + 0.0216 + 0.0504 + 0.1008 + 0.1680 + 0.2240 + 0.2241+ 0.14937 + 0.04979]
P( more than 8 ) = 1- P( X ≤ 8 ) =1-0.99616
P( more than 8 ) = 1- P( X ≤ 8 ) =0.00384
Write the value of the money in dollars 4-8 Brainliest Awnser gets 7 points for greatness
4. 12 cent
5. $2.06
6. $1.56
7. $1.30
8. 86 cent
I'm doing a practice, and I'm really confused by this question. Help would really be appreciated!!! **100 PTS!**
Great Question!
The problem we have at hand is known to be a function, which maps elements from one set of objects, ( the domain ) onto another, the range. If we were to consider an ordered pair, say ( x, y ), then the function would map x onto y. The inverse function is simply the reverse. Take the ordered pair (-4,0). Function g would map - 4 onto 0, such that [tex]g( - 4 ) = 0[/tex]. Therefore, the inverse function would map 0 onto - 4, resulting in [tex]g^{-1}( 0 ) = - 4[/tex]. And there you have it! Our first part is answered!
____
This second bit here is interesting. Let [tex]y = h( x )[/tex] -
[tex]y = 4x + 3[/tex] - Switch x and y,
[tex]x = 4y + 3[/tex] - And now solve this equation for y,
[tex]x - 4y = 3,\\- 4y = - x + 3,\\y = 1 / 4x - 3 / 4[/tex]
As you can see, we have taken the inverse of h( x ). As y = h( x ), we can thus conclude the following -
[tex]h^{-1}(x) = 1 / 4x - 3 / 4[/tex]
____
The composition (h^-1 o h)(-5) is, in other words, h^-1(h(-5)). We can therefore calculate h(-5) and then take it's inverse -
[tex]h(-5) = 4(-5) + 3,\\h(-5) = - 20 + 3,\\h(-5) = - 17[/tex]
Now we can take it's inverse -
[tex]h^{-1}(-17) = 1 / 4( - 17 ) - 3 / 4,\\- 17 / 4 - 3 / 4,\\= - 5![/tex]
Our solution for this last bit is - 5. And, if you don't feel like reading through this entire explanation just take a look at the " summed up " answer below,
[tex]g^{-1}( 0 ) = - 4,\\\\h^{-1}( x ) = 1 / 4x - 3 / 4,\\\\( h * h^{-1} )( - 5 ) = - 5[/tex] I do hope that helps you!
Answer:
Or 50
Step-by-step explanation:
Expand the expression
Answer:
C.
Step-by-step explanation:
Easiest and quickest way to do this is to plug it into your calc. Using the Binomial Theorem would be a time killer for this question, especially when it's an evaluation question.
Answer:
The answer is option C
Step-by-step explanation:
I just got it right
In the figure, qj= 2x+100 and sj=6x+52 what is sj ?
Answer:
124
Step-by-step explanation:
2x+100=6x+52
solve for variable x = 12
plug it in
2(12)+100
sj= 124
Which equation has a constant of proportionality equal to 10 choose 1 answer a, y=2/20x b, y=30/3x c, y=12/2x d, y=5/5x
Answer:
b
Step-by-step explanation:
30/3x=10
Please help me on this question please
Answer:
-5°C < 5°C
The temperature was higher on Wednesday than on Tuesday.