Answer:
The mean and standard deviation of the number of trials where the contestant guesses correctly are 12.50 and 3.062.
Step-by-step explanation:
Total number of cards presented to the contestants, N = 4.
Number of cards that has a star printed on it is, x = 1.
The probability of selecting the correct card is:
[tex]P(X)=\frac{x}{N}=\frac{1}{4}=0.25[/tex]
It is provided that each contestant attempts to identify which card has the star on it for a series of n = 50 trials.
Each trial's outcome is independent of other outcomes.
The success of each trial is denoted by the correct selection of the card with a star.
The random variable X can be explained by the Binomial distribution.
So, X follows a Binomial distribution with parameters n = 50 and p = 0.25.
The mean and standard deviation of a Binomial distribution are:
[tex]\text{Mean}=np\\\\\text{SD}=\sqrt{np(1-p)}[/tex]
Compute the mean and standard deviation of the number of trials where the contestant guesses correctly as follows:
[tex]\text{Mean}=np=50\times 0.25=12.50\\\\\text{SD}=\sqrt{np(1-p)}=\sqrt{50\times 0.25\times (1-0.25)}=3.062[/tex]
Thus, the mean and standard deviation of the number of trials where the contestant guesses correctly are 12.50 and 3.062.
[tex]N = 4[/tex] is the overall number of points distributed to the contestant, [tex]x = 1[/tex] reflects the number of decks with a star on them. The probability of selecting the correct card is as follows:
[tex]\to P(X)=\frac{x}{N}=\frac{1}{4}=0.25[/tex]
For a total of n = 50 trials, each competitor must determine whichever card has the star on it.The result of each trial is different from the results of the others.A proper selection of a card with such a star shows the success of each trial.The Binomial distributions can account for such a random value of x, As a result, X has a binomial distribution having values [tex]n = 50[/tex] and [tex]p = 0.25[/tex].The Binomial distribution does have the following mean and standard deviation:[tex]\to \text{Mean =np}\\\\\to \text{SD}=\sqrt{np(1-p)}\\\\[/tex]
Determine the mean difference of the number of tests where the contender correctly guesses:[tex]\to \text{Mean =np}= 50 \times 0.25= 12.5\\\\[/tex]
[tex]\to SD=\sqrt{np(1-p)}[/tex]
[tex]=\sqrt{50 \times 0.25 \times (1-0.25)}\\\\=\sqrt{50 \times 0.25 \times (0.75)}\\\\= \sqrt{12.5 \times 0.75}\\\\=\sqrt{9.375}\\\\=3.061[/tex]
As just a result, the standard deviation of the number most right guesses by the competitor are [tex]12.50 \ \ and\ \ 3.061[/tex], correspondingly.
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What is the slope of the line
Answer:
4/5
Step-by-step explanation:
There are so many points on the graph whose coordinates are impossible to estimate. Look for two "nice" points--points with integer coordinates. The line passes through (-2, 0) and (3, 4).
Slope = rise / run. It's the ratio of vertical change to horizontal change as you move from one point on the line to another.
Moving from (-2, 0) to (3, 4), the vertical change is 4 - 0 = 4.
The horizontal change is 3 - (-2) = 5.
The slope is 4/5
Can someone answer I barely have any points now :(
A. True, a rhombus is a parallelogram with equal sides. A rhombus has four congruent sides.
B. True, but there are two other ways to find the area of a rhombus: there is the "diagonals" method and the "trigonometry" method.
C. False, the area of a rhombus is not less than the area of a parallelogram because it will depend on the diagonals.
D. False, a parallelogram is not always a rhombus because the dimensions and other attributes of a parallelogram may vary while the rhombus will remain equal for all aspects.
E. True, if you use the base times height formula but if you used any of the other formulas this would be false.
Find the slope, if it exists, of the line containing the points (-1,-15) and (-17,-20)
The slope is _____________________
1 min to fill 16.50 gallons what is the constant
Answer:constant is 2/33
Step-by-step explanation:
1 min to fill 16.50 gallons
Time(t) varies directly as volume(v)
t α v
t =k x v Where k is constant
1=k x 16.50
k=1/16.50
k=2/33
Constant is 2/33
Easy math, but not sure what I did wrong.
Alex took 31 exams during 5 years studying at the MaPhAs University. Each year, he took more exams than the previous year. During his 5th year, he took three times as many exams as in the 1st year. How many exams did Alex take during his 4th year at the university?
Answer:
8
Step-by-step explanation:
In his 5th year, he took 3 times as many exams as the first year. So the number of exams taken in the 5th year must be a multiple of 3.
If a₁ = 1, then a₅ = 3. However, this isn't possible because we need 4 integers between them, and a sum of 31.
If a₁ = 2, then a₅ = 6. Same problem as before.
If a₁ = 3, then a₅ = 9. This is a possible solution.
If a₁ = 4, then a₅ = 12. If we assume a₂ = 5, a₃ = 6, and a₄ = 7, then the sum is 34, so this is not a possible solution.
Therefore, Alex took 3 exams in his first year and 9 exams in his fifth year. So he took 19 exams total in his second, third, and fourth years.
3 < a₂ < a₃ < a₄ < 9
If a₂ = 4, then a₃ = 7 and a₄ = 8.
If a₂ = 5, then a₃ = 6 and a₄ = 8.
If a₂ = 6, then there's no solution.
So Alex must have taken 8 exams in his fourth year.
What’s the correct answer for this?
1 hour is equal to how many seconds
Answer: 3600 seconds
Step-by-step explanation:
60 seconds in a minute
60 minutes in an hour
(60)(60) = 3600
Answer:
3600
Step-by-step explanation:
There are 60 seconds in 1 minute
30 minutes equal 1800
So, 1800 + 1800 is 3600.
Hope this helps! :)
What if f(x)=(1/7)(7x), what is f(3)
Answer:
3
Step-by-step explanation:
f(x) = (1/7)(7x) can be simplified to ...
f(x) = x
Then for x=3, ...
f(3) = 3
a businesswoman sells a bag for $52.32, thereby making a profit of 9% on the cost of her. calculate the selling price the businesswoman should ask in order to make 20% profit
Answer: $57.6
Step-by-step explanation:
Given : A businesswoman sells a bag for $52.32.
Let cuurent selling price : SP = $52.32
As they are making 9% profit now.
That means SP= Cp +0.09 CP , where Cp is the cost price of bag.
i..e [tex]52.32=Cp(1+0.09) \ \text{[Substituted value of SP in LHS and taking Cp common outside in RHS]}[/tex]
[tex]\Rightarrow\ 52.32=Cp(1.09)\Rightarrow\ CP=\dfrac{52.32}{1.09}=48[/tex]
i..e Cost price of bag = 48
Selling price to gain 20% profit = Cp+0.20CP
= CP(1+0.20)
=48 (1.20)
= 57.6
Hence, the selling price the businesswoman should ask in order to make 20% profit = $57.6
Trina has a total of 32 crayons. How much boxes of crayons did she buy.
Answer:
Depends on the type of box, but most likely one box of crayons because 32 packs are sold.
Do you have answer choices?
The area of the rectangle is 70 yd2? What is the length of side
y?
yards
Answer:
7 yds
Step-by-step explanation:
The area of a rectangle is
A = l*w
70 = 10*y
Divide each side by 10
70/10 = 10y/10
7 = y
Answer:
7
Step-by-step explanation:
To find Area is Length x Width
The Length is 10 and the Area is 70
70= 10x
Divide both sides by 10
70/19=7
The height of a triangle is 18 inches. Find the length of the base if the area of the triangle is 63 square inches
Answer:
7 inches
Step-by-step explanation:
The area of a triangle is found by
A = 1/2 bh
We know the height is 18 and the area is 63
63 = 1/2 (b)(18)
63 = 9b
Divide each side by 9
63/9 = 9b/9
7 = b
The base is 7 inches
Answer:
7 inches
Step-by-step explanation:
Area = ½ base × height
63 = ½ × base × 18
63 = 9 × base
base = 7 inches
Find the following trigonometric values.
Express your answers exactly.
cos(315) =
sin(315)=
The value of cos(315°) is 0.7071 and the value of sin(315°) is -0.7071.
What are trigonometric ratios?The sides and angles of a right-angled triangle are dealt with in Trigonometry. The ratios of acute angles are called trigonometric ratios of angles. The six trigonometric ratios are sine (sin), cosine (cos), tangent (tan), cotangent (cot), cosecant (cosec), and secant (sec).
Given that, cos(315°) and sin(315°).
So, the values are
Simplify the expression.
Exact Form:√2/2
Decimal Form:0.70710678…
sin(315°)
Simplify the expression.
Exact Form: -√2/2
Decimal Form: -0.70710678…
Therefore, the value of cos(315°) is 0.7071 and the value of sin(315°) is -0.7071.
Learn more about the trigonometric ratios here:
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Write a recursive formula to describe the sequence: 1, 3, 7, 13...
Answer:
f(n) = f(n - 1) + 2(n - 1) for n [tex]\geq[/tex] 1
Step-by-step explanation:
Needing help can’t seem to find the answers? ♀️
Step-by-step explanation:
19. Kim's Path = √240² + 100²
= √57600 + 10000
= √67600
= 260 ft.
Answer:
17 question: we are going to use Pythagorean Theorem :
33^2 + 56^2 = x^2
1089+3165 = x^2
4225=x^2
x=-65
x=65
the answer is c)65
18 question i dont know :((
19 question : we are going to use same method as the first question : the answer is 260 ft
that's all that i can do for you
Step-by-step explanation:
hope this helps you :)
what is 1+1+5+6+7+8+9 equal to
Answer:
37
Step-by-step explanation:
Ellis is 6 feet tall. If she currently has a 4 foot shadow, what angle are the sunrays making with the ground? Round decimal to the nearest hundredth.
Answer:
19.70
Step-by-step explanation:
For this case we have the following trigonometric relationship:
Tan (x) = (4/6)
Clearing the angle we have:
x = Atan (4/6)
x = 19.77
Rounding off we have:
x = 19.70 degrees
What is the next term of the arithmetic sequence?
-2,3, 8, 13, 18,
Answer:
23
Step-by-step explanation:
difference between number is 5
5n-7 to get to next term
Need help on this assignment it is due VERY SOON
All have something to do with area of composite figures. Please help. I'd be very greatful.
Answer
the first photo answer is 174 (2nd photo is A) Answer to 3rd photo is 72. The last photo is 8100 ft²
Step-by-step explanation:
1st Photo
12 x 12 is 144
5 times 12 divided by 6 - (5 x 6) 30
144 plus 30 is 174
2nd Photo
3 x 5 15
15 is A
3rd Photo
6 x 12 is 72
72 for 3rd Photo
4th Photo
90 x 90 is
8,100
A store sells gift cards in preset amounts. You can purchase gift cards for $20 or $30. You have spent $680 on gift cards. Write an equation in standard form to represent this situation. What are three combinations of gift cards you could have purchased?
Let x be the number of gift cards for $20, and let y be the number of gift cards for $30. Write an equation in standard form to represent this situation
Answer:
20x + 30y = 680
Step-by-step explanation:
Give me a good rating please!
An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
The equation represents the number of $20 and $30 gift cards bought.
20x + 30y = 680
What is an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
We have,
Number of gift cards for $20 = x
Number of gift cards for $30 = y
Total amount spend on gift card = $680
The equation represents the number of $20 and $30 gift cards bought.
20x + 30y = 680
Thus,
The equation represents the number of $20 and $30 gift cards bought.
20x + 30y = 680
Learn more about equations here:
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To generate leads for new business, Gustin Investment Services offers free financial planning seminars at major hotels in Southwest Florida. Gustin conducts seminars for groups of 25 individuals. Each seminar costs Gustin $3,500, and the commission for each new account opened is $5,000. Gustin estimates that for each individual attending the seminar, there is a 0.01 probability that he/she will open a new account.
(a) Determine the equation for computing Gustin's profit per seminar, given values of the relevant parameters. Profit = (New Accounts Opened × ) –
(b) What type of random variable is the number of new accounts opened? (Hint: Review Appendix 11.1 for descriptions of various types of probability distributions.)
(c) Choose the appropriate spreadsheet simulation model to analyze the profitability of Gustin's seminars. (I) (II) (III) (IV) Would you recommend that Gustin continue running the seminars?
(d) How many attendees (in a multiple of five, i.e., 25, 30, 35, . . .) does Gustin need before a seminar's average expected profit is greater than zero?
Answer:
a) profit = (new account opened x 5000) -3500
b) Opening account is binomial distribution with n =25 and p = 0.01
c) Probability of loss is 0.77781 --I don't recommend the company that it running the seminar
d) n ≅ 71
Step-by-step explanation:
See attached image
What is the sixth term in the sequence 3, 6, 11, 18
Answer:
38
Step-by-step explanation:
3 to 6 is an add by 3 then 6 to 11 is an add by 5 then 11 to 18 is an add by 7 each add is increased by 2 so the next add will be 9 giving you 27 then you will add 11 because it's increased by two giving you 38
Select the three side lengths, in centimeters (cm) that form a right triangle.
5 cm
6 cm
8 cm
10 cm
11 cm
12 cm
A right triangle can be made using the side lengths 3,4 5, so we can find multiples of those numbers. If you multiply 3,4 and 5 by 2 you get 6,8,10
The answer would be 6cm, 8cm, 10cm
Answer:
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
Step-by-step explanation:
What is the median of the following set of data ?
56.2 112.8 90.4 95.5 103.7 87.6 99.1 112.4 59.7
Answer: 95.5
Step-by-step explanation:
If you order the numbers from least to greatest and alternate revoking numbers the number in the middle, or median will be 95.5
Please help ASAP! giving BRAINLIEST if correct! What is the factorization of the polynomial below?
Answer:
2(x+6)(x+6)
Step-by-step explanation:
splitting the middle term:
2x²+12x+12x+72
then2x(x+6)+12(x+6)
=(2x+12)(x+6)
=2(x+6)(x+6)(by takin common factor out)
plzz mark me brainliest
How many feet would a 27-inch object measure?
Answer:
2 feet 3 inches
Step-by-step explanation:
So we know there are 12 inches in one foot. so 27/3= 2 remainder 3. So the answer is 2 feet 3 inches
complete the recursive formula of the geometric sequence 0.2,-1,5,-25
Answer:
s[1] = 0.2; s[n] = -5·s[n-1]
Step-by-step explanation:
To write a recursive formula, you need to know how a given term relates to the ones before it. Here, each term is -5 times the one before. So part of the formula is ...
s[n] = -5·s[n-1]
The other part of a recursive formula is the part that tells the initial values necessary to make this recursive function work. Here, one initial value is needed. We know that the first term is 0.2, so that's what we need to say:
s[1] = 0.2
__
The recursive formula is ...
s[1] = 0.2s[n] = -5·s[n-1]Answer:
0.2
-5
Step-by-step explanation:
Including a 8% sales tax, an inn charges $150.12 per night. Find the inn's nightly cost before tax is added.
Answer:$139.00
Step-by-step explanation:
150.12/1.08
Determine two pairs of polar coordinates for (4,4) when 0° < θ < 360°
a(4√2, 45°), (-4√2, 225°)
b(4√2, 315°), (-4√2, 135°)
c(4√2, 135°), (-4√2, 315°)
d(4√2, 225°), (-4√2, 45°)
Answer: option a.
Step-by-step explanation:
In polar coordinates we have that:
x = r*cos( θ)
y = r*sin( θ)
we know that x = 4 and y = 4. now let's analyze the options:
a) x = 4√2*cos(45°) = 4 nice.
y = -4√2*sin(225°) = 4 nice
Option a is correct
b) x = 4√2*cos(315°) = 4 nice
y = -4√2*sin(135°) = -4 incorrect
option b is not correct
c) x = 4√2*cos(135°) = -4 incorrect
Option c is not correct
d) x = 4√2*cos(225°) = -4 incorrect
option d is not correct
Education professionals refer to science, technology, engineering, and mathematics as the STEM disciplines. A research group reported that 27% of freshmen entering college in a recent year planned to major in a STEM discipline. A random sample of 85 freshmen is selected. Round the answer to at least four decimal places
Answer:
1) It is appropriate to use the normal curve, since np = 22.95 ≥ 10 and n(1 - p) = 62.05 ≥ 10
2) The probability that less than 28% of the freshmen in the sample are planning to major in a STEM discipline = 0.5832
Step-by-step explanation:
Concluding part of the question
1) Is it appropriate to use the normal approximation to find the probability that less than 28% of the freshmen in the sample are planning to major in a STEM discipline?
2) Find the probability that less than 28% of the freshmen in the sample are planning to major in a STEM discipline?
Solution
1) The condition for a distribution (binomial) to approximate a normal distribution is that
np ≥ 10 and n(1-p) ≥ 10
where n = sample size = 85
p = population proportion = sample proportion = 0.27
np = 85 × 0.27 = 22.95 ≥ 10
n(1-p) = 85 × 0.73 = 62.05 ≥ 10
2) To obtain the required probability, we need the standard deviation of the sampling distribution
σₓ = √[p(1-p)/n] = √(0.27×0.73/85) = 0.0481541642 = 0.04815
To obtain the probability that less than 28% of the freshmen in the sample are planning to major in a STEM discipline, we need to standardize 28%
The standardized score for any value is the value minus the mean then divided by the standard deviation.
z = (x - μ)/σ = (0.28 - 0.27)/0.04815 = 0.21
To obtain the probability that less than 28% of the freshmen in the sample are planning to major in a STEM discipline
P(x < 0.28) = P(z < 0.21)
We'll use data from the normal probability table for these probabilities
P(x < 0.28) = P(z < 0.21) = 0.58317 = 0.5832 to 4 d.p
Hope this Helps!!!
