Using the Normal distribution, the Empirical rule and the Central limit theorem, it is found that n is 36.
In a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
It 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, which is the percentile of X. The empirical rule states that 68% of the measures are within 1 standard deviation of the mean.The central limit theorem states that for sampling distribution of sample means of size n, the standard deviation is [tex]s = \frac{\sigma}{\sqrt{n}}[/tex]In this problem, since 68% of the students had sample means between 48.5 and 51.5 mm, we have that:
When X = 51.5, Z = 1.When X = 48.5, Z = -1.Using one of them, we can find the standard error. So:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]1 = \frac{51.5 - 50}{s}[/tex]
[tex]s = 1.5[/tex]
Then, since [tex]\sigma = 9[/tex], the sample size is found solving the following equation:
[tex]s = \frac{\sigma}{\sqrt{n}}[/tex]
[tex]1.5 = \frac{9}{\sqrt{n}}[/tex]
[tex]1.5\sqrt{n} = 9[/tex]
[tex]\sqrt{n} = \frac{9}{1.5}[/tex]
[tex](\sqrt{n})^2 = (\frac{9}{1.5})^2[/tex]
[tex]n = 36[/tex]
n is 36.
A similar problem is given at https://brainly.com/question/13002303
what is the product of r and t if R equals 5.33 and T equals 0.5
HELP
______________________
Answer:
The answer is the third option/choice.
Ben buys a car for $50,000. The value of the car decreases at a rate of 4% per year. How much will the car be worth in 3 years? A. $48,000 B. $44,237 C. $45,082 D. $43,270
Evaluate: 18.4 ÷ 2.3 × 3.4 + 13.812 =
What is the null hypothesis if we want to test the hypothesis that the mean score on campus 1 is higher than on campus 2? h0: µ1 = 0?
No, the null hypothesis will be, there is no difference between the mean scores of campus 1 and campus 2.
Therefore, the null hypothesis would be:
H₀: µ₁ - µ₂ = 0
where µ₁ is the population mean score of campus 1 and µ₂ is the population mean score of campus 2.
What is mean by Subtraction?Subtraction in mathematics means that is taking something away from a group or number of objects. When you subtract, what is left in the group becomes less.
Now, We test this null hypothesis against the alternative hypothesis that the mean score on campus 1 is higher than on campus 2:
Hₐ: µ₁ > µ₂
Hence, if there is sufficient evidence to reject the null hypothesis and conclude that there is a significant difference between the mean scores of campus 1 and campus 2.
Thus, No, the null hypothesis will be, there is no difference between the mean scores of campus 1 and campus 2.
Therefore, the null hypothesis would be:
H₀: µ₁ - µ₂ = 0
where µ₁ is the population mean score of campus 1 and µ₂ is the population mean score of campus 2.
Learn more about the subtraction visit:
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Help ASAP PLEASE!!! match the term with the appropriate definition.
kaelyn has 14 coins that have a vaule of $ 1.20. she only has dimes and nickles. how many nickles does kaely have
Kaelyn has 14 coins made of dimes and nickels valued at $1.20. By setting up a system of equations and solving for the number of nickels, we determine that she has 4 nickels.
The student is asking a mathematical question involving coin values and combinations. When working with combinations of coins, we typically use a system of equations or algebraic expressions. Kaelyn has 14 coins consisting of dimes and nickels with a total value of $1.20. To systematize, let's let D be the number of dimes and N be the number of nickels. The following equations represent the relationships between the coins:
D + N = 14 (since there are 14 coins in total)0.10D + 0.05N = 1.20 (representing the total value of the coins in dollars)Multiply the second equation by 100 to deal with whole numbers:
10D + 5N = 120From the first equation, we can express D as:
D = 14 - NSubstitute this into the second equation:
10(14 - N) + 5N = 120140 - 10N + 5N = 120-5N = -20N = 4So, Kaelyn has 4 nickels and the rest are dimes.
If you have 2500 to invest at 6 interest compounded quarterly. For how many years will the money need to be invested for that amount to triple?
PLz help!
Write the equation of the line that passes through (3, −2) and has a slope of 4 in point-slope form. (2 points)
1 y + 2 = 4(x − 3)
2 y − 3 = 4(x + 2)
3 x − 3 = 4(y + 2)
4 x + 2 = 4(y − 3)
hey can you please help me posted picture of question
Root plot for : y = 3x2+7x+2
Axis of Symmetry (dashed) {x}={-1.17}
Vertex at {x,y} = {-1.17,-2.08}
x -Intercepts (Roots) :
Root 1 at {x,y} = {-2.00, 0.00}
Root 2 at {x,y} = {-0.33, 0.00}
BRAINLIEST!!!
Which statement about a dilation with a scale factor of 3 is true?
The statement which is true about the dilation is:
[tex]\dfrac{3}{2}=\dfrac{6}{4}[/tex]
Step-by-step explanation:We know that the dilation transformation changes the size of the original figure but the shape is preserved.
The dilation transformation either reduces the size of the original figure i.e. the scale factor is less than 1 or enlarges the size of the original figure i.e. the scale factor is greater than 1.
The ratio of the corresponding sides of the two figure are equal.
i.e.
[tex]\dfrac{3}{2}=\dfrac{6}{4}[/tex]
Solve the equation 3x+5y=4
for y
Answer:
y = (4 -3x)/5
Step-by-step explanation:
Find the terms containing y. If they are all on one side of the equation (it is), then identify the terms not containing y. Subtract those. Then, divide by the coefficient of y.
3x +5y = 4
5y = 4 - 3x . . . . . non-y term subtracted
y = (4 -3x)/5 . . . . divide by the coefficient of y
_____
If you like, you can rearrange this to slope-intercept form:
... y = -3/5x +4/5
The circle belowis centered at the point (-2 ,1) and has a radiusof length 3
Answer:
Option A, (x + 2)² + (y - 1) = 9
Explanation:
The equation form of a circle is (x - h)² + (y - k)² = r², where the center is ordered pair (h, k) and r represents the radius.
From the given information, the center is point (-2, 1) and the radius (r) is 3 units. With this, we can plug the information in and simplify:
(x - (-2))² + (y - (1))² = (3)²
(x + 2)² + (y - 1)² = 9
The equation for the given circle is (x + 2)² + (y - 1)² = 9
What is the area of sector GPH?
The area of sector GPH is [tex]\(\frac{1}{4}\pi r^2\).[/tex]
To find the area of sector GPH, we use the formula for the area of a sector of a circle, which is given by [tex]\(\frac{\theta}{360^\circ} \times \pi r^2\)[/tex], where [tex]\(\theta\)[/tex] is the central angle of the sector in degrees, and [tex]\(r\)[/tex] is the radius of the circle.
Given that the central angle of sector GPH is [tex]\(90^\circ\) (or \(\frac{\pi}{2}\)[/tex] radians, since[tex]\(180^\circ\) is \(\pi\) radians)[/tex], and the radius [tex]\(r\)[/tex] is unspecified, we can express the area of the sector in terms of [tex]\(r\).[/tex]
Using the formula for the area of a sector:
[tex]\[ \text{Area of sector GPH} = \frac{\theta}{360^\circ} \times \pi r^2 \][/tex]
Substituting [tex]\(\theta = 90^\circ\):[/tex]
[tex]\[ \text{Area of sector GPH} = \frac{90^\circ}{360^\circ} \times \pi r^2 \][/tex]
Simplifying the fraction:
[tex]\[ \text{Area of sector GPH} = \frac{1}{4} \times \pi r^2 \][/tex]
So, the area of sector GPH is [tex]\(\frac{1}{4}\pi r^2\)[/tex], which is one-fourth of the area of the entire circle. This makes sense because the sector represents a quarter of the circle's area due to its [tex]\(90^\circ\)[/tex] central angle.
Which ordered pair is the vertex of y = [x - 3]+ 2?
A.(2, –3)
B.(–3, 2)
C.(3, 2)
D.(2, 3)
Unsaved If you are studying the effects of UV rays on eyesight and you group 10 people together and make them wear sunglasses for 10 weeks and see if their eyesight is affected and then take another group and do not give them sunglasses and test their vision after 10 weeks, what is the treatment ? note this is not an ethical study.
sunglasses.
10 weeks.
eyesight.
vision test.
Answer:
Sunglasses
Step-by-step explanation:
A cirlce with a radius of 8 cm rotates 30 degrees in one second. Determine the angle of rotation in radians.
Angle:___ w:___ v:___
Yanis fires pottery in a kiln. He decides to measure the rate of change of temperature of the pottery over time. What would be an appropriate unit for Yanis's purpose?
Answer with explanation:
Pottery is on a Kiln.
Unit of temperature can be Kelvin(°K) or Degree Celsius(°C) or Fahrenheit(°F).
Unit of time is second, minute and hour.
Rate of change of temperature of the pottery over time can be written as
[tex]1.=\frac{\text{Degree Celsius}}{\text{Second}}\\\\2.=\frac{\text{Degree Celsius}}{\text{Minute}}[/tex]
Internationally , Kelvin is used as S.I unit of Temperature.
So,Yanin can use
[tex]1.=\frac{\text{Kelvin}}{\text{Second}}\\\\2.=\frac{\text{Kelvin}}{\text{Minute}}[/tex]
as Rate of change of temperature of the pottery over time.
The table shows the number of boys and girls that have black, blonde, brown, or red hair color. What is the probability that a student is a boy with red hair? (round to nearest hundredth)
Hair Color Boys Girls
Black 4 5
Blonde 4 6
Brown 10 8
Red 2 1
Answer:
0.05
Step-by-step explanation:
Given :
Hair Color Boys Girls
Black 4 5
Blonde 4 6
Brown 10 8
Red 2 1
Solution :
Since ware required to find the probability that a student is a boy with red hair.
Total no. of boys with red hair = 2
Total no. of students = 4+4+10+2+5+6+8+1=40
Thus the probability that a student is a boy with red hair = [tex]\frac{\text{No. of boys with red hair }}{\text{total no. of students }}[/tex]
⇒[tex]\frac{2}{40}[/tex]
⇒[tex]\frac{1}{20}[/tex]
⇒[tex]0.05[/tex]
Hence the probability that a student is a boy with red hair is 0.05
ln(x+2)-ln(4x+3)=ln(1/2*x)
Given: KLMN is a trapezoid, KF =10 MF ║ LK AKLMF = AFMN Find: KN
In a trapezoid with parallel sides, if a pair of opposite sides are equal, then the other pair of opposite sides are also equal. Therefore, in the given trapezoid KLMN, KN is equal to AN + 10.
Explanation:In the given trapezoid KLMN, the sides KF and LM are parallel. We are given that KF = 10 and AFMN = AKLMF. We need to find KN.
Since KF and LM are parallel, KF = LM. Therefore, LM = 10.
Since AFMN = AKLMF, we can say that AN = KL. So, AN + LM = KL + KF. Substituting the given values, we get AN + 10 = KL + 10. Therefore, AN = KL.
Hence, KN = KL + LM = AN + LM = AN + 10.
Therefore, KN = AN + 10.
Amy has 5 yards of border to put around a garden. She uses all the border to make four sections that are the same length. Which expession does not equal the length of one these sections in yards?
Answer:
4 ÷ 5
Step-by-step explanation: becuz i said so
Which of the following functions are their own inverses? Select all that apply.
a. t(p) = p
b. y(j) = -1/j
c. w(y) = -2/y
d. d(p) = 1/x^2
Answer:
a,b and c.
Step-by-step explanation:
We have to find the the functions that are their own inverses.
a.t(p)=p
Then the inverse function of given function is
[tex]p=t^{-1}(p)[/tex]
Therefore, the given function is inverse function of itself.
Hence, option a is true.
b.y(j)=[tex]-\frac{1}{j}
Let y(j)=y then we get
[tex]y=-\frac{1}{j}[/tex]
[tex]j=-\frac{1}{y}[/tex]
[tex]j=-\frac{1}{y(j)}[/tex]
[tex]j=-\frac{1}{\frac{-1}{j}}[/tex]
[tex]j=j[/tex]
Hence, the function is inverse of itself.Therefore, option b is true.
c.[tex]w(y)=-\frac{2}{y}[/tex]
Suppose that w(y)=w
Then [tex]w=-\frac{2}{y}[/tex]
[tex]y=-\frac{2}{w}[/tex]
[tex]w(y)=-\frac{2}{-\frac{2}{w}}[/tex]
[tex]w(y)=w[/tex]
[tex]w(y)=-\frac{2}{y}[/tex]
Hence, the function is inverse function of itself.Therefore, option c is true.
d.[tex]d(p)=\frac{1}{x^2}[/tex]
Let d(p)=d
If we replace [tex]\frac{1}{x^2}by p then we get
[tex]d=\frac{1}{x^2}[/tex]
[tex]x^2=\frac{1}{d}[/tex]
[tex]x=\sqrt{\frac{1}{d}}[/tex]
[tex]x=\sqrt{\frac{1}{d(p)}[/tex]
Hence, the function is not self inverse function.Therefore, option d is false.
Chloe puts 4 soaps and two bottles of lotion in each gift basket. She has 127 soaps and 85 bottles of lotion. How many gift baskets can Chloe complete?
A right triangle has one side, s, and a hypotenuse of 12 meters. Find the area of the triangle as a function of s.
A) A(s) = 2s
144 - s2
B) A(s) = s
144 - s2
C) A(s) = 2s
12 - s2
D) A(s) = 12s
144 - s2
10)
The base of a ladder is placed 5 feet away from a 13 foot tall wall. What is the minimum length ladder needed to reach the top of the wall (rounded to the nearest foot)?
A) 12 ft
B) 13 ft
C) 14 ft
D) 15 ft
Answer: A(s) = [tex]\frac{s\sqrt{144-s^{2} } }{2}[/tex] ; 10) c) 14ft
Step-by-step explanation: Area of a triangle is: A = [tex]\frac{b.h}{2}[/tex]
where:
b is base of a triangle
h is height of a triangle
For this right triangle, it is known one side, s, and hypotenuse, 12. To determine the other side, we use Pythagoras Theorem:
hypotenuse² = side² + side²
[tex]12^{2} = s^{2} + x^{2}[/tex]
[tex]x^{2} = 12^{2} - s^{2}[/tex]
[tex]x^{2} = 144 - s^{2}[/tex]
x = [tex]\sqrt{144 - s^{2} }[/tex]
To determine the Area of the right triangle as function of s:
A = [tex]\frac{b.h}{2}[/tex]
A = [tex]\frac{1}{2}[/tex](s.x)
A = [tex]\frac{1}{2}[/tex] . (s.[tex]\sqrt{144 - s^{2} }[/tex])
Therefore, the area of the right triangle is:
A = [tex]\frac{1}{2}[/tex] . (s.[tex]\sqrt{144 - s^{2} }[/tex])
The ladder and the wall form a right triangle. The height of it is 13 ft, the base is 5ft and the hypotenuse is the length of the ladder. So, to find the minimum length, use Pythagoras Theorem:
hypotenuse² = side² + side²
h² = 13² + 5²
h² = 169 + 25
h = [tex]\sqrt{194}[/tex]
h = 14
The minimum length the ladder has to have to reach the top is 14 ft.
Factor \2x^2-11x+5=0
The quadratic equation [tex]2x^2[/tex]-11x+5=0 is factored into (2x - 1)(x - 5), and it has solutions x = 0.5 and x = 5.
Explanation:The question asks us to factor the quadratic equation[tex]2x^2[/tex]-11x+5=0. To do this, we need to find two numbers that multiply to give ac (where a is the coefficient of x^2 and c is the constant term) and add to give b (the coefficient of x). Here, ac is (2)(5)=10, and b is -11. The two numbers that satisfy this are -10 and -1 because -10 * -1 = 10 and -10 + -1 = -11.
We rewrite the middle term using these two numbers and then group the terms to factor by grouping:
[tex]2x^2[/tex]- 10x - x + 5 = 0The factored form of the quadratic equation is (2x - 1)(x - 5). Therefore, the solutions to the equation are x = 0.5 and x = 5, found by setting each factor equal to zero.
which transformations are needed to change the parent some function to the sine function below?
help me out with this
Two events are independent when the following is true:
a. the outcome of one event determines the outcome of the other event
b. there is no correlation between the two events
c. the outcome of one event does NOT determine the outcome of the other event
d. The outcome of the event is determined by the theoretical probability of the event
Solution:
Independent Events:
Consider an experiment of Rolling a die, then getting an even number and multiple of 3.
Total favorable outcome = {1,2,3,4,5,6}=6
A=Even number = {2,4,6}
B=Multiple of 3 = {3,6}
A ∩ B={6}
P(A)=[tex]\frac{3}{6}=\frac{1}{2}[/tex], P(B)= [tex]\frac{2}{6}=\frac{1}{3}[/tex]
P(A ∩ B)=[tex]\frac{1}{6}[/tex]
So, P(A)× P( B)=[tex]\frac{1}{2}\times\frac{1}{3}=\frac{1}{6}[/tex]=P(A ∩ B)
Hence two events A and B are independent.
Option (c). the outcome of one event does NOT determine the outcome of the other event
Answer:
C on edge or the outcome of one event does NOT determine the outcome of the other event
Step-by-step explanation:
What is the vertex of the quadratic function f(x) = (x - 8)(x - 2)
Answer: (5, -9)
What is the vertex of the quadratic function f(x) = (x – 8)(x – 2)?