Answer:
$140
Step-by-step explanation:
You can add up the prices to find the total. Most of us find it easier to multiply the price by the number of items.
cost of 2 shirts = (2)($25.00) = $50
cost of 4 pants = (4)(22.50) = $90
The total was $50 +90 = $140.
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.
If a line crosses the y-axis at (0,1) and has a slope of 4/5 what is the equation of the line
Answer:
y = 4/5x + 1
Step-by-step explanation:
y = mx + b
m = slope
b = y-intercept
y = 4/5x + 1
Answer:4y-5x=5
Step-by-step explanation:
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)
Does this graph represent a function? Why or why not?
A
B
C
D
Answer:
B
Step-by-step explanation:
As said in B, use the vertical line test. For any vertical line, does it hit the graph in two points? No. Therefore, the answer is B.
This particular function is f(x)=x^2.
Hope that helped,
-sirswagger21
Answer:
Yes is passes the vertical line test
Step-by-step explanation:
This parabola is a function. it has a one to one correspondence and passes the vertical line test
Which of the following is the perimeter of a triangle with side lengths of 18 cm, 26 cm, and 32 cm?
Answer:
76 cm
Step-by-step explanation:
To find the perimeter, add up all of the side lengths.
18 cm + 26 cm + 32 cm = 76 cm
I hope this helps :))
Please answer this correctly
Answer:
A=450
Step-by-step explanation:
A=a+b
2h=12+33
2·20=450
Answer:
Area=450
Step-by-step explanation:
[tex]a+b/2h[/tex]
What is the formula to find the area of parallelogram
Step-by-step explanation:
area of parallelogram= height * length of base
Isaac is a professional swimmer who trains, in part, by running. She would like to
estimate the average number of miles she runs in each week. For a random sample
of 20 weeks, the mean is
x
= 17.5 miles with standard deviation s = 3.8 miles. Find
a 99% confidence interval for the population mean number of weekly miles Isaac runs.
(a) 15.01 to 19.99 miles (b) 15.07 to 19.93 miles
(c) 15.34 to 19.66 miles (d) 15.31 to 19.69 miles
(e) 15.08 to 19.92 miles
Answer: (b) 15.07 to 19.93 miles
Step-by-step explanation:
Confidence interval is written in the form,
(Sample mean - margin of error, sample mean + margin of error)
The sample mean, x is the point estimate for the population mean.
Margin of error = z × s/√n
Where
s = sample standard deviation = 3.8
n = number of samples = 20
From the information given, the population standard deviation is unknown and the sample size is small, hence, we would use the t distribution to find the z score
In order to use the t distribution, we would determine the degree of freedom, df for the sample.
df = n - 1 = 20 - 1 = 19
Since confidence level = 99% = 0.99, α = 1 - CL = 1 – 0.99 = 0.01
α/2 = 0.02/2 = 0.005
the area to the right of z0.005 is 0.025 and the area to the left of z0.025 is 1 - 0.005 = 0.995
Looking at the t distribution table,
z = 2.861
Margin of error = 2.861 × 3.8/√20
= 2.43
the lower limit of this confidence interval is
17.5 - 2.43 = 15.07 miles
the upper limit of this confidence interval is
17.5 + 2.43 = 19.93 miles
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:
The web publisher www.exploreiceland.is (Links to an external site.)Links to an external site. provides information on traveling to Iceland. Access to the website is free but revenues are generated by selling ads that are posted on the website. In the following month, the website has committed to displaying ads to 650,000 viewers, i.e., 650,000 impressions. Based on data from previous months the traffic to the website is estimated to be normally distributed with a mean of 850,000 viewers and a standard deviation of 150,000.
How many impressions should the web publisher have taken on, to be able to guarantee a 95% service level?
Answer:
1096750 impressions
Step-by-step explanation:
Given that :
Mean = 850,000
Standard deviation = 150,000
If we assume that X should be the numbers of impressions created;
Then ;
[tex]X \approx N (\mu , \sigma^2)[/tex]
Now ; representing x as the value for the number of impression needed ; Then ;
[tex]P(X>x) = 0.95[/tex]
[tex]P(\dfrac{X- \mu}{\sigma} > \dfrac{x -850000}{150000}) = 0.95[/tex]
[tex]P(Z> \dfrac{ x -850000}{150000}) = 0.95[/tex]
From normal tables:
[tex]P(Z >1.645) = 0.95[/tex]
[tex]\dfrac{x - 850000}{150000} =1.645[/tex]
(x- 850000) = 1.645(150000)
x - 850000 = 246750
x = 246750 + 850000
x = 1096750 impressions
The following is a Markov (migration) matrix for three locations
[1/5 1/5 2/5
2/5 2/5 1/5
2/5 2/5 2/5]
(a) Initially, there are 130 individuals in location 1, 300 in location 2, and 70 in location 3. How many are in each location after two time periods?
(b) The total number of individuals in the migration process is 500. After a long time, how many are in each location?
Answer:
(a) [tex]\mathbf{P_2 = \left[\begin{array}{c}140 \\ 160 \\ 200 \end{array}\right]}[/tex]
(b) After an infinite period of time; we will get back to a result similar to after the two time period which will be [tex]= \left[\begin{array}{c}140 \\ 160 \\ 200 \end{array}\right]}[/tex]
Step-by-step explanation:
The Markov Matrix can be interpret as :
[tex]M = \left[\begin{array}{ccc} \dfrac{1}{5} & \dfrac{2}{5} &\dfrac{1}{5} \\ \\ \dfrac{2}{5}&\dfrac{2}{5}&\dfrac{1}{5}\\ \\ \dfrac{2}{5}& \dfrac{2}{5}& \dfrac{2}{5} \end{array}\right][/tex]
From (a) ; we see that the initial population are as follows: 130 individuals in location 1, 300 in location 2, and 70 in location 3.
Le P represent the Population; So ; [tex]P = \left[\begin{array}{c}130 \\ 300 \\ 70 \end{array}\right][/tex]
The objective is to find How many are in each location after two time periods;
So, after two time period ; we have the population [tex]P_2 = [M]^2 [P][/tex]
where;
[tex][M]^ 2 = \left[\begin{array}{ccc} \dfrac{1}{5} & \dfrac{2}{5} &\dfrac{1}{5} \\ \\ \dfrac{2}{5}&\dfrac{2}{5}&\dfrac{1}{5}\\ \\ \dfrac{2}{5}& \dfrac{2}{5}& \dfrac{2}{5} \end{array}\right] \left[\begin{array}{ccc} \dfrac{1}{5} & \dfrac{2}{5} &\dfrac{1}{5} \\ \\ \dfrac{2}{5}&\dfrac{2}{5}&\dfrac{1}{5}\\ \\ \dfrac{2}{5}& \dfrac{2}{5}& \dfrac{2}{5} \end{array}\right][/tex]
[tex][M]^ 2 = \dfrac{1}{25} \left[\begin{array}{ccc} 1+2+4 & 1+2+4 &1+2+4 \\ \\ 2+2+4&2+2+4&2+2+4\\ \\ 2+4+4&2+4+4& 2+4+4 \end{array}\right][/tex]
[tex][M]^ 2 = \dfrac{1}{25} \left[\begin{array}{ccc}7&7&7 \\ \\ 8 &8&8\\ \\10&10& 10 \end{array}\right][/tex]
Now; Over to after two time period ; when the population [tex]P_2 = [M]^2 [P][/tex]
[tex]P_2 = \dfrac{1}{25} \left[\begin{array}{ccc}7&7&7 \\ \\ 8 &8&8\\ \\10&10& 10 \end{array}\right] \left[\begin{array}{c}130 \\ 300 \\ 70 \end{array}\right][/tex]
[tex]\mathbf{P_2 = \left[\begin{array}{c}140 \\ 160 \\ 200 \end{array}\right]}[/tex]
(b) The total number of individuals in the migration process is 500. After a long time, how many are in each location?
After a long time; that is referring to an infinite time (n)
So; [tex]P_n = [M]^n [P][/tex]
where ;
[tex][M]^n \ can \ be \ [M]^2 , [M]^3 , [M]^4 .... \infty[/tex]
; if we determine the respective values of [tex][M]^2 , [M]^3 , [M]^4 .... \infty[/tex] we will always result to the value for [tex][M]^n[/tex]; Now if [tex][M]^n[/tex] is said to be a positive integer; then :
After an infinite period of time; we will get back to a result similar to after the two time period which will be [tex]= \left[\begin{array}{c}140 \\ 160 \\ 200 \end{array}\right]}[/tex]
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.
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ASAP! GIVING BRAINLIEST! Please read the question THEN answer CORRECTLY! NO guessing. I say no guessing because people usually guess on my questions. CHECK ALL THAT APPLY.
Answer:
B, E
Step-by-step explanation:
A line has a negative slope when it decreases going left to right.
As the absolute value of the slope gets larger (-2 to -3 would be 2 to 3), the graph gets steeper (-3 is steeper than -2).
Answer:
B & E
Step-by-step explanation:
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 !!
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.
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It is thought that prehistoric Indians did not take their best tools, pottery, and household items when they visited higher elevations for their summer camps. It is hypothesized that archaeological sites tend to lose their cultural identity and specific cultural affiliation as the elevation of the site increases. Let x be the elevation (in thousands of feet) of an archaeological site in the southwestern United States. Let y be the percentage of unidentified artifacts (no specific cultural affiliation) at a given elevation. The following data were obtained for a collection of archaeological sites in New Mexico. x = 5.22 5.69 6.25 6.75 7.25 y 17 12 33 37 62What percentage of the variation in y can be explained by the corresponding variation in x and the least-squares line? a. 95.7% b. 0.7% c. 8.4% d. 91.6% e. 4.3%
Answer:
(B) 0.7%
Step-by-step explanation:
X = Land Elevation (in ,000 feet)
Y = Unidentified Artifacts (in %)
The hypothetical theory says that:
The higher the elevation, the higher the percentage of unidentified artifacts in the location.
To find the percentage of variation in Y that can be explained by variations in X, we find the slope of the graph of X on Y.
Transforming X to thousand feets, we have 5220, 5690, 6250, 6750, 7250. This is in the attachment, plotted against 17, 12, 33, 37 and 62 respectively.
Further calculations, along with the graph, are in the attachment below. The answer therein is (B) 0.7%
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
Set F1 = 5N at 0 degrees, F2= 5N at 90 degrees, F3 = 5N at 270 degrees and run the simulation. Using trigonometry, what net force of F4 in the negative x-direction is necessary to produce an angle of 15 degrees between F2 and F3 and the y-axis? Set F4 to that value and run the simulation. Does the angle formed approximate 15 degrees?
Answer: find the solution in the explanation
Step-by-step explanation:
Let's use resolution of forces by resolving into x - component and y- component.
X - component.
Sum of forces = F1 - F3 - F4cos 15
Sum of forces = 0
5 - 5 - 0.97F4 = 0
- 0.97 F4 = 0
F4 = 0
Y - component
Sum of forces = F2 + F4 sin 15
Sum of forces = 0
5 + 0.26F4 = 0
0.26 F4 = -5
F4 = -5/0.26
F4 = -19.23 N
Simulating F4 back into the equation
Sum of forces = F1 - F3 - F4cos 15
- F4cos Ø = 0
- (-19.23) cos Ø = 0
Cos Ø = 0
Ø = 1
Does the angle formed approximate 15 degrees ? NO
What is the area of the circle?
Answer:
A =50.24 in ^2
Step-by-step explanation:
The diameter is 8 inches
The radius is 1/2 diameter
r = d/2 = 8/2 = 4
The area of the circle is given by
A = pi r^2
A = 3.14 (4)^2
A =50.24 in ^2
Answer:
C. 50.24 in²
Step-by-step explanation:
d= 8 in
r= 8/2= 4 in
Area= πr²= 3.14×4²= 50.24 in²
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?
if you’re good with probability in math 30 please help and answer the question below!!
A six-sided number cube has faces with the numbers 1 through 6 marked on it. What is the probability that a number less than 3 will occur on one toss of the number cube?
a) 1/6
b) 1/2
c) 1/3
d) 2/3
Answer: b) 1/3
Step-by-step explanation:
The numbers LESS THAN 3: 1, 2
[tex]\dfrac{\text{Quantity of numbers less than 3}}{Total\ number}\quad =\dfrac{2}{6}\quad \rightarrow \large\boxed{\dfrac{1}{3}}[/tex]
Rewrite the expression in the form z^n
[tex] \sqrt[5]{z {}^{4}z {{}^{ \frac{ - 3}{2} } } } [/tex]
Answer:
[tex]z^{0.5}[/tex]
Step-by-step explanation:
So first simplify inside:
[tex]z^4z^{-1.5}=z^{2.5}[/tex]
Now divide that by 5:
[tex]z^{0.5}[/tex]
Dora likes to explore. Recently, she explored southeast Australia where she found some very large trees known as Eucalyptus regnans or Mountain Ash. She wondered if they were taller, on average, than the coastal Douglas Firs of her native state of Oregon in the United States, which have an average height of 250 feet in old growth areas. Dora measured the heights of 15 Mountain Ash trees in southeast Australia and found an average height of these trees of 293 feet. Suppose s 25 feet. Assume the heights of the 15 trees in Dora's sample are representative of the heights of all Mountain Ash trees in southeast Australia. The t-statistic for this problem is 6.661. Based on this t-statistic, which of the following is true? Choose the correct answer below.
A. With a p-value of 0.999, there is sufficient evidence to accept the null hypothesis as true.
B. With a p-value less than 0.0001, there is not sufficient evidence to reject the null hypothesis and accept the alternative as true. y
C. With a p-value less than 0.0001, there is sufficient evidence to reject the null hypothesis and accept the alternative as true.
D. With a p-value less than 0.0001, there is not sufficient evidence to accept the null hypothesis as true. 0 E. With a p-value of 0.999, there is not sufficient evidence to reject the null hypothesis and accept the alternative as true.
Answer:
C. With a p-value less than 0.0001, there is sufficient evidence to reject the null hypothesis and accept the alternative as true.
Step-by-step explanation:
She performed an hypothesis test with the sample of size n=15 that she takes. The t-statistic has a value of 6.661.
The degrees of freedom for this sample size are:
[tex]df=n-1=15-1=14[/tex]
The P-value for a statistic t=6.661 and 14 degrees of freedom is:
[tex]\text{P-value}=P(t>6.661)=0.00001[/tex]
With these P-value we know that the effect is significant and the null hypothesis is rejected. There is enough evidence to support the claim that the mean height of Mountain Ash trees is greater than the coastal Douglas Firs.
A spinner has 10 equally sized sections, 8 of which are gray and 2 of which are blue. The spinner is spun twice. What is the probability that the first spin lands on gray and the second spin lands on blue ? Write your answer as a fraction in simplest form.
Answer:
4/25
Step-by-step explanation:
The probability the first spin lands on gray is 8/10 = 4/5.
The probability the second spin lands on blue is 2/10 = 1/5.
The probability of both events is 4/5 × 1/5 = 4/25.
Are the two terms on each tile like terms? Sort the tiles into the appropriate categories.
-7y^2and y^2
-4p and p^2
0.5kt and -10kt
6 and 9
5x and 5
3ad and 2bd
Answer:
LIKE TERMS: 6 and 9, 0.5kt and -10kt, and -7y2 and y2. UNLIKE TERMS: 3ad and 2bd, 5x and 5, and the last one is -4p and p2
Step-by-step explanation:
Answer: like terms: 6&9 , 0.5kt&-10kt , -7y^2&y^2
unlike terms 3ad&2bd, 5x&5, -4p&p^2
Step-by-step explanation:
passed
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.
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.
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.
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g A psychic was tested for extrasensory perception (ESP). The psychic was presented with cards face down and asked to determine if each of the cards was one of four symbols: a star, cross, circle, or square. Let p represent the probability that the psychic correctly identified the symbols on the cards in a random trial. How large a sample n would you need to estimate p with margin of error 0.01 and 95% confidence?
Answer:
Step-by-step explanation:
Hello!
The objective is to test ESP, for this, a psychic was presented with cards face down and asked to determine if each of the cards was one of four symbols: a star, cross, circle, square.
Be X: number of times the psychic identifies the symbols on the cards correctly is a size n sample.
p the probability that the psychic identified the symbol on the cards correctly
You have to calculate the sample size n to estimate the proportion with a confidence level of 95% and a margin of error of d=0.01
The CI for the population proportion is constructed "sample proportion" ± "margin of error" Symbolically:
p' ± [tex]Z_{1-\alpha /2} * (\sqrt{\frac{p'(1-p')}{n} } )[/tex]
Where [tex]d= Z_{1-\alpha /2} * (\sqrt{\frac{p'(1-p')}{n} } )[/tex] is the margin of error. As you can see, the formula contains the sample proportion (it is normally symbolized p-hat, in this explanation I'll continue to symbolize it p'), you have to do the following consideration:
Every time the psychic has to identify a card he can make two choices:
"Success" he identifies the card correctly
"Failure" he does not identify the card correctly
If we assume that each symbol has the same probability of being chosen at random P(star)=P(cross)=P(circle)=P(square)= 1/4= 0.25
Let's say, for example, that the card has the star symbol.
The probability of identifying it correctly will be P(success)= P(star)= 1/4= 0.25
And the probability of not identifying it correctly will be P(failure)= P(cross) + P(circle) + P(square)= 1/4 + 1/4 + 1/4= 3/4= 0.75
So for this experiment, we'll assume the "worst case scenario" and use p'= 1/4 as the estimated probability of the psychic identifying the symbol on the card correctly.
The value of Z will be [tex]Z_{1-\alpha /2}= Z_{0.975}= 1.96[/tex]
Now using the formula you have to clear the sample size:
[tex]d= Z_{1-\alpha /2} * (\sqrt{\frac{p'(1-p')}{n} } )[/tex]
[tex]\frac{d}{Z_{1-\alpha /2}} = \sqrt{\frac{p'(1-p')}{n} }[/tex]
[tex](\frac{d}{Z_{1-\alpha /2}})^2 =\frac{p'(1-p')}{n}[/tex]
[tex]n*(\frac{d}{Z_{1-\alpha /2}})^2 = p'(1-p')[/tex]
[tex]n = p'(1-p')*(\frac{Z_{1-\alpha /2}}{d})^2[/tex]
[tex]n = (0.25*0.75)*(\frac{1.96}{0.01})^2= 7203[/tex]
To estimate p with a margin of error of 0.01 and a 95% confidence level you have to take a sample of 7203 cards.
I hope this helps!
Answer:
The sample size should be 6157
Step-by-step explanation:
Given that the margin of error (e) = ± 0.01 and the confidence (C) = 95% = 0.95.
Let us assume that the guess p = 0.25 as the value of p.
α = 1 - C = 1 - 0.95 = 0.05
[tex]\frac{\alpha }{2} =\frac{0.05}{2}=0.025[/tex]
The Z score of α/2 is the same as the z score of 0.475 (0.5 - 0.025) which is 1.96. Therefore [tex]Z_\frac{\alpha }{2}=Z_{0.025}=1.96[/tex]
To determine the sample size n, we use the formula:
[tex]Z_{0.025}*\sqrt{\frac{p(1-p)}{n} }\leq e\\Substituting:\\1.96*\sqrt{\frac{0.2(1-0.2)}{n} } \leq 0.01\\\sqrt{\frac{0.2(0.8)}{n} }\leq \frac{1}{196}\\\sqrt{0.16} *196 \leq \sqrt{n}\\78.4\leq \sqrt{n}\\ 6146.56\leq n\\n=6157[/tex]
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]