Answer:
There are 4 scores in the sample.
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
In this question, we have that:
[tex]\mu = 40, \sigma = 8, X = 36, Z = -1, s = \frac{8}{\sqrt{n}}[/tex]
We want to find n. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]-1 = \frac{36 - 40}{\frac{8}{\sqrt{n}}}[/tex]
[tex]-4\sqrt{n} = -8[/tex]
[tex]4\sqrt{n} = 8[/tex]
Simplifying by 4
[tex]\sqrt{n} = 2[/tex]
[tex](\sqrt{n})^2 = 2^2[/tex]
[tex]n = 4[/tex]
There are 4 scores in the sample.
(5,-6) and (2,-6) find the distance between each pair points in units
Answer:
The distance between the points is 3.
Step-by-step explanation:
Hope it helps ;)
Box A contains 3 red and 2 blue marbles while Box B contains 2 red and 8 blue marbles. A fair coin is tossed. If the coin turns up heads, a marble is chosen from Box A; if it turns up tails, a marble is chosen from Box B.
A. Find the probability that a red marble is chosen.
B. Referring to above information, suppose that the person who tosses the coin does not reveal whether it has turned up heads or tails (so that the box from which a marble was chosen is not revealed) but does reveal that a red marble was chosen. What is the probability that Box A was chosen (i.e., the coin turned up heads)?
Answer:
A. [tex]\frac{4}{10}[/tex]
B. [tex]\frac{3}{4}[/tex]
Step-by-step explanation:
Given - Box A contains 3 red and 2 blue marbles while Box B contains 2
red and 8 blue marbles. A fair coin is tossed. If the coin turns up
heads, a marble is chosen from Box A; if it turns up tails, a marble
is chosen from Box B.
To find - A. Find the probability that a red marble is chosen.
B. Referring to above information, suppose that the person who
tosses the coin does not reveal whether it has turned up
heads or tails (so that the box from which a marble was
chosen is not revealed) but does reveal that a red marble was
chosen. What is the probability that Box A was chosen (i.e.,
the coin turned up heads)?
Proof -
As given ,
Box A : 3 red marbles and 2 blue marbles.
Box B : 2 red marbles and 8 blue marbles.
a.)
As we have to find the probability that a red marble is chosen.
A red marble is chosen in two different ways - either it can be from Box A or Box be .
If Box A is chosen , then Probability of red ball is [tex]\frac{3}{5}[/tex]
If Box B is chosen , Then Probability of Red ball is [tex]\frac{2}{10} = \frac{1}{5}[/tex]
Now,
Probability of Box A is Chosen = [tex]\frac{1}{2}[/tex]
Probability of Box B is chosen = [tex]\frac{1}{2}[/tex]
∴ we get
Probability that a Red marble is chosen = [tex]\frac{1}{2}[/tex]×[tex]\frac{3}{5}[/tex] + [tex]\frac{1}{2}[/tex]×[tex]\frac{1}{5}[/tex] = [tex]\frac{3}{10} + \frac{1}{10} = \frac{4}{10}[/tex] = 0.4
b.)
Now,
Probability that Box A is chosen given that Red marble is chosen is
P(Box A | Red marble ) = [tex]\frac{(\frac{3}{5})(\frac{1}{2}) }{(\frac{3}{5})(\frac{1}{2}) + (\frac{1}{5})(\frac{1}{2})} = \frac{\frac{3}{10} }{\frac{3}{10} + \frac{1}{10} } = \frac{\frac{3}{10} }{\frac{4}{10}}[/tex] = [tex]\frac{3}{4}[/tex]
6) The coordinates of the origin are
Answer:
(0,0)
Step-by-step explanation:
Required
Determine the coordinates of the origin
In geometry, the coordinates of the origin is the point where x and y are 0.
i.e.
[tex]x = 0[/tex] and [tex]y = 0[/tex]
So, the coordinate (x,y) is (0,0)
What percent is equivalent to 1/10?
Answer: 10%
Step-by-step explanation:
1/10 is equal to .10 or 10%
Answer:
10%
Step-by-step explanation:
Divide 1 by 10 and you get 0.10 :)
what does l-7l mean and whats its value NEED HELP
determine the scale factor
Answer:
The scale factor is (2/3)
Step-by-step explanation:
[tex]9 \times \frac{2}{3} = 6 \\ 12 \times \frac{2}{3} = 8[/tex]
I hope that is useful for you :)
27. The length and breadth of a rectangle are in the ratio 7:5 and the perimeter is 240m, find the area of
the rectangle
Answer:
[tex]Area = 3500[/tex]
Step-by-step explanation:
Given
[tex]Length : Breadth = 7 : 5[/tex]
[tex]Perimeter = 240m\\[/tex]
Required
Determine the area
The perimeter is:
[tex]Perimeter = 2(Length + Breadth)[/tex]
This is then represented as:
[tex]240 = 2(7x + 5x)[/tex]
[tex]240 = 2 * 12x[/tex]
[tex]240 = 24x[/tex]
[tex]10 = x[/tex]
[tex]x = 10[/tex]
So, the area is:
[tex]Area = Length * Width[/tex]
[tex]Area = 7x * 5x[/tex]
[tex]Area = 7*10 * 5*10[/tex]
[tex]Area = 3500[/tex]
HELP HELP HELP!!! NUMBER 3 PLEASE!!!
Answer:
see the attachment, answers there
Lula has two dogs, one 35 pounds, the other 25 pounds. What is the average weight of Lula's dogs?
Answer:
30
Step-by-step explanation:
25+35= 60
60/2=30
Answer: 30
Step-by-step explanation:
The term average has a number of different meanings. Most generally, it is a single number that is used to represent a collection of numbers. In the context of mathematics, "average" refers to the mean, specifically, the arithmetic mean. It is a relatively simple statistical concept that is widely used in many areas.
The equation below is one of the more commonly understood definitions of the average: [tex]Average =[/tex] [tex]\frac{Sum}{Count}[/tex]
a number added to one third of itself equals 12 . what is the number
Answer:
9
Step-by-step explanation:
x+1/3x=12
(3x+1x)/3=12
4x/3=12
4x=12×3
4x=36
x=36/4
x=9
Answer:
1/3+x=12(cross multiply)
x+1=12*3
x+1=36(collect like terms)
x=36-1
x=35
If g(x) is 11 then what is x
Quadrilateral ABCD is reflected over the x-axis. What are the coordinates of
quadrilateral A'B'C'D?
Answer: A
Step-by-step explanation:
X values to the right of the y axis are positive. X values to the left of the y axis are negative.
Y values above the x axis are positive.
Y values below the x axis are negative.
Pairs of coordinates are always noted as (x,y) with the x value of a point given first and the y value of that same point given second.
Answer:
AStep-by-step explanation:
Let A=(a,b) then the reflected over the x-axis will be A'=(a,-b)
A=(5,5) --> A'=(5,-5)
B=(5,1) --> B'=(5,-1)
C=(2,1) --> C'=(2,-1)
D=(1,5) ---> D'=(1,-5)
What is the perimeter of the triangle?
Answer: 3y + 5 cm
Step-by-step explanation: The perimeter of a triangle
is just the distance around the outside of the figure.
So just add up all the sides.
So we have y + y + y + 5 and we get 3y + 5.
g Suppose the population 10-year cumulative incidence of prostate cancer among 70-year old men is 0.06. Further, suppose 260 men without prostate cancer, aged 50 years were randomly sampled and 13 of them developed prostate cancer within 10 years. Is there evidence at the 0.05 significance level to conclude that the cumulative incidence of prostate cancer among 50-year old men differs from that of 70-year old men
Answer:
There is not enough statistical evidence to conclude that the cumulative incidence of prostrate cancer among 50-year old men differs from that of 70-year old men
Step-by-step explanation:
The population 10 year cumulative incidence of prostrate cancer among 70 year old men, p = 0.06
The number of 50 year old men in the sample, n = 260 men
The number of the sampled men that developed prostrate cancer = 13 men
The significance level, α = 0.05
Let the null hypothesis, H₀: [tex]\hat{p}[/tex] = p
The alternative hypothesis, Hₐ: [tex]\hat{p}[/tex] ≠ p
The standard score, [tex]z_{\alpha /2}[/tex] = 1.96
The test statistic, 'z', is given as follows;
[tex]z=\dfrac{\hat{p}-p}{\sqrt{\dfrac{p \cdot q}{n}}}[/tex]
[tex]\hat{p}[/tex] = 13/260 = 0.05
q = 1 - p = 1 - 0.06 = 0.94
[tex]Therefore, \ z=\dfrac{0.05-0.06}{\sqrt{\dfrac{0.06 \times 0.94}{260}}} = \dfrac{\sqrt{9165} }{141} \approx -0.68[/tex]
From the z-table, we find the p-value as follows;
P(z ≈ -0.68) = 0.24825
Therefore, given that the p-value, 0.24825 is larger than the significance level, α/2 = 0.025, we fail to reject the null hypothesis, and therefore, there is not enough statistical evidence to conclude that the cumulative incidence of prostrate cancer among 50-year old men differs from that of 70-year old men
The sum or two numbers is 59. the larger number is 15 more than the smaller number. What are the numbers
Answer: 37 and 22
Step-by-step explanation:
x + y = 59
x = 15 + y (substitute x as 15 + y into the first equation)
15 + y + y = 59
2y + 15 = 59
2y = 44
y = 22
substitute y as 22 into one of the equations
x = 15 + 22
x = 37
Horatio recorded the daily high temperatures. On 66 days, the high temperature was greater than 88°F. This was 75% of the days that Horatio recorded. How many days was the high temperature less than or equal to 88°F?
Answer:
The answer is 22
Step-by-step explanation:
The total number of days recorded by Horatio was 88,
The number of days with high temperatures less than or equal to 88°F is 22 days.
What is an expression?An expression contains one or more terms with addition, subtraction, multiplication, and division.
We always combine the like terms in an expression when we simplify.
We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.
Example:
1 + 3x + 4y = 7 is an expression.
3 + 4 is an expression.
2 x 4 + 6 x 7 – 9 is an expression.
33 + 77 – 88 is an expression.
We have,
We know that the high temperature was greater than 88°F on 75% of the days, which means it was less than or equal to 88°F on the remaining 25% of the days.
So we can set up an equation to solve for the number of days the high temperature was less than or equal to 88°F:
So,
25% x total number of days = number of days with high temperature less than or equal to 88°F
Or in other words:
0.25 x total number of days = number of days with high temperature less than or equal to 88°F
We are given that the number of days with high temperatures greater than 88°F is 66.
Let's use x to represent the total number of days:
0.25x = number of days with high temperature less than or equal to 88°F
0.25x = x - 66
(since the number of days with high temperatures less than or equal to 88°F is the remainder)
0.25x - x = -66
-0.75x = -66
x = 88
The total number of days recorded by Horatio was 88,
The number of days with high temperatures less than or equal to 88°F.
= 0.25 x 88
= 22 days.
Thus,
The total number of days recorded by Horatio was 88,
The number of days with high temperatures less than or equal to 88°F is 22 days.
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The area of the parallelogram is___ cm2
Answer:
Step-by-step explanation:
Area of parallelogram=base×perpendicular height
Area of para.= 7×14
Area of para.= 98cm²
8,626 round to the nearest thousand?
Answer:
9000
Step-by-step explanation:
What is the multiplicative inverse of y?
Answer:
The multiplicative inverse of y is [tex]\frac{1}{y}[/tex].
Step-by-step explanation:
Multiplicative inverse implies a value that you would multiply with the given value so as to give 1.
Let the multiplicative inverse of y be represented by a, so that;
a x y = 1
ay = 1
divide both sides by y to have,
a = [tex]\frac{1}{y}[/tex]
Thus, the multiplicative inverse of y is [tex]\frac{1}{y}[/tex].
This is applicable to any given value. Examples:
i. Given 2, the multiplicative inverse is [tex]\frac{1}{2}[/tex].
⇒ 2 x [tex]\frac{1}{2}[/tex] = 1
ii. What is the multiplicative inverse of 5?
The required answer is [tex]\frac{1}{5}[/tex].
Mia buys 4 ¼ pounds of plums. Her total cost after using a coupon for 55 cents off her entire purchase was $3.23. Write an equation to represent this situation.
Try to answer these
What is the total?
What will make the total - in words (be precise)
Write the words out as an equation
What don’t you know?
Write the algebraic equation.
Answer: I tried to help but i just got confused
Sorrry I didnt know the answer
I need to multiply 10,170 by 0.775
Answer:
7881.75
Step-by-step explanation:
10,170x0.775
Answer:
7881.75
Step-by-step explanation:
Find the radius of a circle if its center is (2,3) and one point on the circle is (5,3).
Answer:
Step-by-step explanation:
radius = distance between (2,3) and (5,3) = √[(5-2)² + (3-3)²] = 3
The required radius of the circle is
center is (2,3)
point on the circle is (5,3).
What is radius?
Radius of the circle is the distance between the center to the circumference.
Radius = [tex]\sqrt{(X_2-X_1)^2+(Y_2-Y_1)^2}[/tex]
=[tex]\sqrt{(5-3)^2-(3-3)^2}[/tex]
Radius = [tex]\sqrt{4}[/tex]
Radius = 2
Thus, the required radius is 2 .
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You NEVER distribute a coefficient of an absolute value. True or False?
Answer:
TRUE!!!!!!!!!
Step-by-step explanation:
What is the measure of angle A?
Enter your answer as a decimal in the box. Round your final answer to the nearest hundredth.
Answer: 45 degrees
Step-by-step explanation:
What is the area of the triangle?
8
4
Al abrir su alcancía Beatriz encontró que entre monedas de 5, 10 y 25 centavos completaba $ 9.50. Encontró igualmente que el número de monedas de 10 centavos era el triple de las de 25 centavos y que las de 5 centavos era el doble de las de 10 centavos. ¿Cuántas monedas de cada denominación había en la alcancía?}
Answer:
67 monedas de 5, 34 de 10 y 11 de 25.
Step-by-step explanation:
Representemos el primer enunciado de manera algebraica:
[tex]5x+10y+25z =950[/tex] (1)
Donde:
x es el numero de monedas de 5y es el numero de monedas de 10 z es el numero de monedas de 25Ahora, el número de monedas de 10 centavos era el triple de las de 25 centavos y que las de 5 centavos era el doble de las de 10 centavos, se puede representar como:
[tex]y=3z[/tex] (2)
[tex]x=2y[/tex] (3)
Combinado las eacuaciones (1), (2) y (3) tenemos:
[tex]5(2y)+10y+25(\frac{y}{3}) =950[/tex]
[tex]10y+10y+\frac{25}{3}y =950[/tex]
[tex]\frac{85}{3}y =950[/tex]
[tex]y =34[/tex]
Por lo tanto el valor de x y z seran:
[tex]x=2(34)[/tex]
[tex]x=68[/tex]
[tex]z=11[/tex]
Si ponemos cada valor en la equacion (1), tenemos:
[tex]5(68)+10(34)+25(11) =955[/tex]
Como el resultado da 955 hay un excedente de 5 pesos, asi que finalmente tendremos.
x = 67
y = 34
z = 11
Espero te haya serrvido!
What is the sum (2 – 3i) + (-4-2i) ?
The sum of the complex numbers (2 – 3i) and (-4-2i) is -2 - 5i.
Complex numbers are numbers of the form a + bi, where a and b are real numbers and i is the imaginary unit, satisfying the equation [tex]i^2[/tex] = -1. The real part of a complex number is denoted by Re(z) = a, and the imaginary part is denoted by Im(z) = b.
Complex numbers can be added, subtracted, multiplied, and divided in a similar way to real numbers. The addition and subtraction of complex numbers is done by adding or subtracting the real and imaginary parts separately.
To find the sum of complex numbers, we add their real parts and their imaginary parts separately. Let's calculate the sum of the given complex numbers:
(2 - 3i) + (-4 - 2i)
Real part: 2 + (-4) = -2
Imaginary part: (-3i) + (-2i) = -5i
Therefore, the sum of (2 - 3i) + (-4 - 2i) is -2 - 5i.
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Solve the inequality for v.
5v-9> 66
Answer:
v>15
Step-by-step explanation:
add 9 to 66
5v>75
v>15
Answer: v>15
Step-by-step explanation:
The inequality can be treated as an equal sign and solved normally. Add 9 to both sides to get 5v>75, then divide to get v>15.
NOTE: If an inequality is divided by a negative number, the sign flips (> to <, etc.)
6. Cynthia walks 6 miles at a rate of 2 miles
per hour. How long will it take her to
arrive at her destination?
Answer:
3
Step-by-step explanation:
6 / 2 = 3 hours
A body starts from rest and
accelerates uniform at 5 ms2.
calculate the time taken
by the body to cover a
distance of
1km