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
Simplify (1+√3) (2-√3).
Answer:
[tex] \sqrt{3} - 1[/tex]
Step-by-step explanation:
[tex](1 + \sqrt{3} )(2 - \sqrt{3} ) \\ 2 - \sqrt{3} + 2 \sqrt{3} - 3 \\ = \sqrt{3} - 1[/tex]
not sure help please
Answer:
The area of a trapezoid is 1/2 (b₁ + b₂) * h where b₁ and b₂ are the bases and h is the height. The answer is 1/2 * (3 + 4) * 1 = 3.5.
Calculating conditional probability
G
The usher at a wedding asked each of the 80 guests whether they were a friend of the bride or of the groom.
Here are the results:
Bride
Groom
29
30
20
1
Given that a randomly selected guest is a friend of the groom, find the probability they are a friend of the bride.
P (bride groom)
Complete Question
Calculating conditional probability
The usher at a wedding asked each of the 80 guests whether they were a friend of the bride or of the groom.
Here are the results:
Bride :29
Groom :30
BOTH : 20
Given that a randomly selected guest is a friend of the groom, find the probability they are a friend of the bride.
P (bride | groom)
Answer:
The probability is [tex]P(B|G) = \frac{2}{3}[/tex]
Step-by-step explanation:
The sample size is [tex]n = 80[/tex]
The friend of the groom are [tex]G = 30[/tex]
The friend of the groom are [tex]B = 29[/tex]
The friend of both bride and groom are [tex]Z = 20[/tex]
The probability that a guest is a friend of the bride is mathematically represented as
[tex]P(B) = \frac{29}{80}[/tex]
The probability that a guest is a friend of the groom is mathematically represented as
[tex]P(G) = \frac{30}{80}[/tex]
The probability that a guest is both a friend of the bride and a friend of the groom is mathematically represented as
[tex]P(B \ n \ G) = \frac{20}{80}[/tex]
Now
[tex]P(B|G)[/tex] is mathematically represented as
[tex]P(B|G) = \frac{P(B \ n \ G)}{P(G)}[/tex]
Substituting values
[tex]P(B|G) = \frac{\frac{20}{80} }{\frac{30}{80} }[/tex]
[tex]P(B|G) = \frac{2}{3}[/tex]
Answer:
the answer is 3/5
Step-by-step explanation:
on Khan
Simplify the expression and then evaluate it for the given value of the variable:
(6−2x)+(15−3x) for x=−0.2
PLEASE HELP!!!!!!!!!!!!!!!!!
Answer:
-5x+2122Step-by-step explanation:
There are no factors outside the parentheses that need to be distributed, so the parentheses can be simply dropped:
6 -2x +15 -3x
The terms can be rearranged to put like terms next to each other:
-2x -3x +6 +15
and the like terms can be combined.
-5x +21 . . . . simplified expression
__
Put the value of x where x is, then do the arithmetic.
-5(-0.2) +21 = 1 +21 = 22
A triangle with side lengths is 5,5,8 is what type of triangle
Answer:
isosceles triangle
Step-by-step explanation:
Solve (x + 1 < 4) ∩ (x - 8 > -7).
Answer:
[tex]1<x<3[/tex]
Step-by-step explanation:
Let simplify each of these inequalities individually and then look at where they intersect afterwards
[tex]x+1<4\\\\x<3[/tex]
And
[tex]x-8>-7\\\\x>1[/tex]
This means that for these two inequalities to intersect, x must be greater than 1, but less than 3.
This can be represented by the following inequality [tex]1<x<3[/tex]
Seven students were surveyed on the number of hours of TV they watch each week. The results are shown below.
8, 12, 13, 15, 16, 17, 17
What is the mode of the data set?
7
14
15
17
Find the balance at the end of 4 years if $10000 is deposited at a rate of 1.5% simple interest
Answer:
$9400
Step-by-step explanation:
1.5x4=6%
100-6=94
0.94x10000=9400
Assume that SAT scores are normally distributed with mean mu equals 1518 and standard deviation sigma equals 325. If 1 SAT score is randomly selected, find the probability that it is greater than 1600. If 81 SAT scores are randomly selected, find the probability that they have a mean greater than 1600.
Answer:
[tex]P(X>1600)=P(\frac{X-\mu}{\sigma}>\frac{1600-\mu}{\sigma})=P(Z>\frac{1600-1518}{325})=P(z>0.252)[/tex]
And we can find this probability using the z score formula and the complement rule and we got:
[tex]P(z>0.252)=1-P(z<0.252) =1-0.599= 0.401 [/tex]
[tex] z =\frac{1600-1518}{\frac{325}{\sqrt{81}}}= 2.27[/tex]
And we can find this probability using the z score formula and the complement rule and we got:
[tex]P(z>2.27)=1-P(z<2.27) =1-0.988=0.012[/tex]
Step-by-step explanation:
Let X the random variable that represent the SAT scores of a population, and for this case we know the distribution for X is given by:
[tex]X \sim N(1518,325)[/tex]
Where [tex]\mu=1518[/tex] and [tex]\sigma=325[/tex]
We want to find this probability:
[tex]P(X>1600)[/tex]
And we can use the z score formula given by:
[tex]z=\frac{x-\mu}{\sigma}[/tex]
Using this formula we got:
[tex]P(X>1600)=P(\frac{X-\mu}{\sigma}>\frac{1600-\mu}{\sigma})=P(Z>\frac{1600-1518}{325})=P(z>0.252)[/tex]
And we can find this probability using the z score formula and the complement rule and we got:
[tex]P(z>0.252)=1-P(z<0.252) =1-0.599= 0.401 [/tex]
For the other part we need to take in count that the distribution for the sampel mean if the sample size is large (n>30) is given by:
[tex]\bar X \sim N(\mu, \frac{\sigma}{\sqrt{n}})[/tex]
And we can use the z score formula given by:
[tex]z=\frac{x-\mu}{\frac{sigma}{\sqrt{n}}}[/tex]
And replacing we got:
[tex] z =\frac{1600-1518}{\frac{325}{\sqrt{81}}}= 2.27[/tex]
And we can find this probability using the z score formula and the complement rule and we got:
[tex]P(z>2.27)=1-P(z<2.27) =1-0.988=0.012[/tex]
If z=32 and z/2+37=x what is x
Answer:
53
Step-by-step explanation:
Plugging in 32 for z, you get:
(32)/2+37=x
16+37=x
x=53
Hope this helps!
The solution of the linear equation z/2 + 37 = x at x at z = 32 will be 53.
What is the solution to the equation?The distribution of weights to the variables involved that establishes the equilibrium in the calculation is referred to as a result.
A relationship between two or more parameters that, when shown on a graph, produces a linear model. The degree of the variable will be one.
The linear equation is given below.
z/2 + 37 = x
Then the solution of the linear equation z/2 + 37 = x at z = 32. Then the equation will be
x = 32/2 + 37
x = 16 + 37
x = 53
Thus, the solution of the linear equation z/2 + 37 = x at z = 32 will be 53.
More about the solution of the equation link is given below.
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3) Washing your hands kills germs. If there are 275 germs chilling on your hands and
you kill 4.75% per second of washing, how many germs left on your hands after 10
seconds. Round your answer to the nearest whole germ. (Remember, keep washing
those hands)
Answer:
So we can use geometric progression each time multiplying by 0.0475
so thats (275*0.0475)*10
So that means that we would get
130.625 so we subtract that from 275
275-130.625=144.375
That would be
Step-by-step explanation:
Chris is constructing a diagram for a deck he is restructuring in his backyard. The deck will be in the shape of a square, and he
has labeled a side length with the equation below, where x represents the original deck area.
side length = V1 + 12
Answer:
Increase the area of the deck by 12 square feet.
Step-by-step explanation:
The area of the deck increased by 12 square feet.
What is area?Area is the amount of space occupied by a two-dimensional figure. In other words, it is the quantity that measures the number of unit squares that cover the surface of a closed figure. The standard unit of area is square units which is generally represented as square inches, square feet, etc.
Given that, Chris is constructing a diagram for a deck he is restructuring in his backyard.
The deck will be in the shape of a square, and he has labeled a side length with the equation below, where x represents the original deck area. Side length = V1 + 12
Increase the area of the deck by 12 square feet.
Therefore, the area of the deck increased by 12 square feet.
Learn more about the area here:
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Let the velocity of a particle be given by v(t) = 2t+a.(a) Find the number a such that the average value of v(t) on the interval [0,1] is -2.(b) Using v(t) from part (a), find the distance traveled by the particle during the time period from [0,4].
Answer:
The velocity is v(t) = 2*t + a
a) we want to find the average velocity betwen t = 0 and t = 1.
We can do this as:
Average = (v(1) + v(0))/2 = (2*1 + a + 2*0 + a)/2 = 1 + a
b) now we want to find the total distance traveled in the time lapse from t = 0 to t = 4.
For this we can see the integral:
[tex]d = \int\limits^4_0 {2*t + a} \, dt = 4^2 + a*4 - 0^2 - a*0 = 4^2 + a*4 = 16 + a^2[/tex]
NEED HELP ASP Find the common difference of the arithmetic sequence -8, -15, -22, ...
Answer:
-7
Step-by-step explanation:
To find the differences in a sequence, subtract the term before:
-15 -(-8) = -7
-22 -(-15) = -7
These differences are the same, so constitute the "common" difference.
The common difference of the sequence is -7.
Please answer this correctly
Answer:
A = 1/2 b*h
A = 24
b = 8
h = ?
24 = 1/2 * 8 * h
24 = 4h
h = 6
The height is 6 cm.
Hope this helps.
Two fair coins are flipped at the same time What is the probability that both display tails?
1/8
1/4
1/3
1/2
Answer:
Step-by-step explanation:
Your answer would be 1/2.
Because they are 2 coins and each have a probability of landing on tails.
The probability that both display tails are 1/2.
We have given that,
Two fair coins are flipped at the same time
We have to determine the, what is the probability that both display tails.
What is the probability?
Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true. The probability of an event is a number between 0 and 1, where, roughly speaking, 0 indicates the impossibility of the event and 1 indicates certainty.
Because they are 2 coins and each has a probability of landing on tails.
To learn more about the probability visit:
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A can of beans has surface area 320cm squared . Its height is 14 cm. What is the radius of the circular top?
Steps:
All cans take on the shape of a cylinder, unless you have seen interesting shape of cans like a starfish.
The formula for surface area of a cylinder is
SA = 2πr2 + 2πrh
where:
r = radius
h = height
Since we know the surface area and height, we can plug them in. Note that we can factor out the 2π. You will see why we factor out 2π rather than 2πr.
2π(r2 + (20)r) = 396
2π(r2 + 20r) = 396
Divide both sides of the equation by 2π to isolate the r terms.
r2 + 20r = 63.025
Subtract 63.025 on both sides of the equation.
r2 + 20r - 63.025 = 0
Use the quadratic formula to solve for r:
r = (-b ± √(b2 - 4ac)) / 2a
where:
a = 1
b = 20
c = -63.025
Plug in these values into the formula. You should get two solutions because of the plus/minus sign. Accept the positive value of r.
Please mark brainliest
Hope this helps.
Idaho is shaped like a triangle with a base of approximately 320 miles and a height of approximately 520 miles. Calculate the area of Idaho and write the answer in scientific notation
Answer:
8.32 × 10^4
Step-by-step explanation:
The formula for the area of a triangle is 1/2×b×h.
1/2(320)(520) = 83,2000
83,200 in scientific notation is 8.32 × 10^4
simplify (6^7)^3
will give brainlist
Answer:
The answer is D.
Step-by-step explanation:
You have to apply Indices Law,
[tex] { ({a}^{m}) }^{n} \: ⇒ \: {a}^{mn} [/tex]
So for this question :
[tex] { ({6}^{7}) }^{3} [/tex]
[tex] = {6}^{7 \times 3} [/tex]
[tex] = {6}^{21} [/tex]
Please answer this correctly
Answer:
0-19: Make it 4 units tall
20-39: Make it 2 units tall
40-59: Make it 5 units tall
60-79: Make it 3 units tall
80-99: Make it 1 unit tall
Step-by-step explanation:
0-19: 4, 6, 19, 19 (4 numbers)
20-39: 29, 38 (2 numbers)
40-59: 40, 41, 41, 57, 58 (5 numbers)
60-79: 62, 66, 73 (3 numbers)
80-99: 87 (1 number)
WILL GIVE BRAINLIEST 4 FIRST ANSWER.
When converted to speeds, which list is in order from slowest to fastest?
A: 17 miles in 2 minutes;
26 miles in 4 minutes;
33 miles in 6 minutes;
60 miles in 8 minutes
B: 17 miles in 2 minutes;
60 miles in 8 minutes;
26 miles in 4 minutes;
33 miles in 6 minutes
C: 33 miles in 6 minutes;
26 miles in 4 minutes;
60 miles in 8 minutes;
17 miles in 2 minutes
D: 60 miles in 8 minutes;
33 miles in 6 minutes;
26 miles in 4 minutes;
17 miles in 2 minutes
Answer:
c
Step-by-step explanation:
you should divide the distance on time
so
33/6=5.5
26/4=6.5
60/8=7.5
17/2=8.5
you can see answer in this order in c
Answer:
Answer:
c
Step-by-step explanation:
you should divide the distance on time
so
33/6=5.5
26/4=6.5
60/8=7.5
17/2=8.5
you can see answer in this order in c
Step-by-step explanation:
The Tennessean, an online newspaper located in Nashville, Tennessee, conducts a daily poll to obtain reader opinions on a variety of current issues. In a recent poll, readers responded to the following question: "If a constitutional amendment to ban a state income tax is placed on the ballot in Tennessee, would you want it to pass?
Required:
a. What was the sample size for this poll?
b. Are the data categorical or quantitative?
c. Would it make more sense to use averages or percentages as a summary of the data for this question?
d. Of the respondents, 67% said Yes, they would want it to pass. How many individuals provided this response?
Answer:
Answers below
Step-by-step explanation:
a. What was the sample size for this poll?
b. Are the data categorical or quantitative?
c. Would it make more sense to use averages or percentages as a summary of the data for this question?
d. Of the respondents, 67% said Yes, they would want it to pass. How many individuals provided this response?
what two numbers add to -7 and multiply to -60
Answer:
The answer would be 5 and -12
Which graph represents this equation-3x + 4y= -12
Answer:
C
Step-by-step explanation:
-3x+4y=-12
Add 3x to both sides:
4y=3x-12
Divide both sides by 4 to isolate y:
y=3/4x-3
This means that the line described has a slope of 3/4 and a y intercept of -3. The only graph that matches this is choice C. Hope this helps!
Answer: c
Step-by-step explanation:
2. En la ciudad de Quito, en la temporada fría, se registran temperaturas que van desde los 5 °C hasta los 18 °C. En la temporada cálida, el registro de la temperatura va desde los 4 °C hasta los 30 °C.
a. Representamos estas temperaturas en forma de intervalo y como conjunto.
b. ¿A qué intervalo pertenece la temperatura de la ciudad de Quito?
c. ¿Qué temperaturas son comunes en las temporadas fría y cálida?
d. ¿Qué temperaturas son posibles solo en la temporada fría?
e. ¿Qué temperaturas son posibles solo en la temporada cálida?
Answer:
(See explanation below for further detail/Véase la explicación abajo para mayores detalles)
Step-by-step explanation:
(This exercise is written in Spanish and explanations will be held in such language)
a) Las temperaturas quedan representadas a continuación:
Quito - Temporada Fría
Intervalo
[tex]5 ^{\circ}C \leq t \leq 18^{\circ}C[/tex] (Este intervalo indica si el dato puede pertenecer a la temporada fría)
Conjunto
[tex]C = \{\forall t \in \mathbb {R}| 5 \leq t \leq 18\}[/tex] (Este conjunto acumula todo el registro de las temperaturas de la temporada fría)
Quito - Temporada Cálida
Intervalo
[tex]4 ^{\circ}C \leq t \leq 30^{\circ}C[/tex] (Este intervalo indica si el dato puede pertenecer a la temporada cálida)
Conjunto
[tex]H = \{\forall t \in \mathbb {R}| 4 \leq t \leq 30\}[/tex] (Este conjunto acumula todo el registro de las temperaturas de la temporada cálida)
b) La temperatura de la ciudad de Quito pertenece esencialmente a dos intervalos:
Intervalo de Temporada Fría:
[tex]5 ^{\circ}C \leq t \leq 18^{\circ}C[/tex]
Intervalo de Temporada Cálida:
[tex]4 ^{\circ}C \leq t \leq 30^{\circ}C[/tex]
c) Toda temperatura mayor o igual que 4 °C y menor o igual que 30 °C.
d) Temperaturas mayores o iguales a 5 °C y menores o iguales a 18 °C.
e) Temperaturas mayores o iguales a 4 °C y menores o iguales a 30 °C.
What should be done to both sides of the equation in order to solve w - 9 1/2 = 15?
Answer:
Solve for
w
by simplifying both sides of the equation, then isolating the variable.
Exact Form:
w
=
49
2
Decimal Form:
w
=
24.5
Mixed Number Form:
w
=
24
Answer:
24
Step-by-step explanation:
A survey was sent out to re-evalute the proportion of people who play games on pc computers, as the last study on the topic had been gathered four years prior. This survey was done specifically to test the possibility that fewer people are playing games on pc computers. The previous study found that 81% of people were playing games on pc computers. The current study, with 861 participants, found that 53% of people who responded play on a pc computer.
Calculate the p-value and determine if we should accept or reject H0 under alpha = 0.05.
Answer:
[tex]z=\frac{0.53 -0.81}{\sqrt{\frac{0.81(1-0.81)}{861}}}=-20.943[/tex]
The p value would be given by:
[tex]p_v =P(z<20.943)\approx 0[/tex]
The p value is a very low value compared to the significance level given so then we have enough evidence to reject the null hypothesis and we can conclude that the true proportion is significantly less than 0.81
Step-by-step explanation:
Info given
n=861 represent the random sample
[tex]\hat p=0.53[/tex] estimated proportion of people who responded play on a pc computer
[tex]p_o=0.81[/tex] is the value that we want to test
[tex]\alpha=0.05[/tex] represent the significance level
z would represent the statistic
[tex]p_v[/tex] represent the p value
Hypothesis to test
We want to verify if the true proportion decreases from 81%, the system of hypothesis are.:
Null hypothesis:[tex]p\geq 0.81[/tex]
Alternative hypothesis:[tex]p < 0.81[/tex]
The statistic is given by:
[tex]z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}[/tex] (1)
Replacing the info given we got:
[tex]z=\frac{0.53 -0.81}{\sqrt{\frac{0.81(1-0.81)}{861}}}=-20.943[/tex]
The p value would be given by:
[tex]p_v =P(z<20.943)\approx 0[/tex]
The p value is a very low value compared to the significance level given so then we have enough evidence to reject the null hypothesis and we can conclude that the true proportion is significantly less than 0.81
In a Washington town, the charge for commerical waste collection is $694.55 for 5 tons of waste and $1098.56 for 8 tons of waste. (a) Find a linear formula for the cost, C. of waste collection as a function of the weight, w, in tons.
Answer:
[tex] m =\frac{1098.56-694.55}{8-5}= 134.67[/tex]
And we can find the intercept like this:
[tex] 694.55 = 134.67*5 +b[/tex]
[tex] b = 694.55 -673.35= 21.2[/tex]
And the equation would be given by:
[tex] C = 134.67 w + 21.2[/tex]
Step-by-step explanation:
For this case we want a function given by:
[tex] C = mw +b[/tex]
Where C is the cost, m the slope, w the weight and b the intercept.
We have the following info (w=5, C= 694.55) and (w=8, C=1098.56) and we can find the slope with this formula:
[tex] m =\frac{1098.56-694.55}{8-5}= 134.67[/tex]
And we can find the intercept like this:
[tex] 694.55 = 134.67*5 +b[/tex]
[tex] b = 694.55 -673.35= 21.2[/tex]
And the equation would be given by:
[tex] C = 134.67 w + 21.2[/tex]
A linear function is a function that changes at a constant rate.
The formula of the linear relationship is [tex]C = 134.67w + 21.2[/tex]
The given parameters are:
w = 5, C = 694.55 ---- Charges for 5 tonsw = 8, C = 1098.56 ---- Charges for 8 tonsStart by calculating the slope (m)
[tex]m = \frac{C_2 - C_1}{w_2 - w_1}[/tex]
This gives
[tex]m = \frac{1098.56 - 694.55 }{8- 5}[/tex]
Simplify
[tex]m = \frac{404.01}{3}[/tex]
This gives
[tex]m = 134.67[/tex]
The equation is then calculated as:
[tex]C = m(w -w_1) + w_1[/tex]
This gives
[tex]C = 134.67(w -5) + 694.55[/tex]
Expand
[tex]C = 134.67w -673.35 + 694.55[/tex]
[tex]C = 134.67w + 21.2[/tex]
Hence, the formula of the linear relationship is [tex]C = 134.67w + 21.2[/tex]
Read more about linear equations at:
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Write this number in expanded notation:178.25
Answer:
100+70+8+0.2+0.05. is the answer
Answer:
178.25 as a fraction is 178 1/4 or 713 / 4
Step-by-step explanation:
hope it works out !!
Express the following ratio in its simplest form.
4:12
Answer:
1:3
Step-by-step explanation:
divide 4 ...............
.............
ps: idk the explanation