Answer:
0.0721 = 7.21% probability that the mean height for the sample is greater than 65 inches.
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 z-score 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 p-value, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem establishes 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.
Mean of 64.4 inches, standard deviation of 2.91
This means that [tex]\mu = 64.4, \sigma = 2.91[/tex]
Sample of 50 women
This means that [tex]n = 50, s = \frac{2.91}{\sqrt{50}}[/tex]
What is the probability that the mean height for the sample is greater than 65 inches?
This is 1 subtracted by the p-value of Z when X = 65. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{65 - 64.4}{\frac{2.91}{\sqrt{50}}}[/tex]
[tex]Z = 1.46[/tex]
[tex]Z = 1.46[/tex] has a p-value of 0.9279
1 - 0.9279 = 0.0721
0.0721 = 7.21% probability that the mean height for the sample is greater than 65 inches.
What is y=4/5x+2 written in standard form?
Chose 1 answer:
A.−4/5x+y−2=0
B. 5y=4x+10
C. y=4/5(x+5/2)
D. −4x+5y=10
Answer:
The "Standard Form" for writing down a Linear Equation is
Ax + By = C
A shouldn't be negative, A and B shouldn't both be zero, and A, B and C should be integers.
--------------------------------
y = 4/5x + 2
Multiply both sides by 5 to clear the fraction
5y = 4x + 10
Subtract 4x from both sides
-4x + 5y = 10 This is answer D, BUT A shouldn't be negative
Multiply both sies by -1
4x - 5y = -10 This is correct Standard Form, BUT it is not one of the choices
Answer D is closest to being correct
► What is the mean of the following data set? 98, 208, 189, 94, 117
Answer:
mean of data is 141.2
Step-by-step explanation:
mean of data = sum of data / no of data
=98 + 208 + 189 + 94 + 117 / 5
=706 / 5
=141.2
Answer:
141.2Step-by-step explanation:
98 + 208 +189 +94 +1117 =709
706/5 = 141.2
Hope this helps!
In the short run, higher demand will not influence the price, it will influence
A. output.
B. price.
ОО
C. investment.
D. input.
Answer:
c espero q passe na prova tudo de bom pra vc
Write an equation and solve for x. Show all your work.
Answer:
x=63
Step-by-step explanation:
Because we know that the total angle is a right angle (see the square in the top right of the problem), and 25 and x+2 constitute as the only two angles making up the total angle, we can say that 25 and x+2 are complementary, meaning they add up to 90 degrees. We can then write our equation as follows:
25 + (x+2) = 90
27+x=90
Subtract 27 from both sides
x=63
What is the slope of the line shown in the graph?
A coordinate plane is shown with points graphed at −2 comma 2 and 0 comma 1. The points are joined by a line.
−2
−1
−1 over 2
1 over 2
Answer:
-1 over 2
Step-by-step explanation:
Answer:
-1/2
Step-by-step explanation:
The line joins (-2, 2) and (0, 1).
Remember that slope equals change in y all divided by the change in x.
Here,
change in y = 1 - 2 =- 1
change in x = 0 -(-2) = 2
Thus, slope =- 1/2
Choose the correct vertex of the function f(x) = x2 - X + 2.
Answer:
The vertex of the function is [tex](\frac{1}{2}, \frac{7}{4})[/tex]
Step-by-step explanation:
Vertex of a quadratic function:
Suppose we have a quadratic function in the following format:
[tex]f(x) = ax^{2} + bx + c[/tex]
It's vertex is the point [tex](x_{v}, y_{v})[/tex]
In which
[tex]x_{v} = -\frac{b}{2a}[/tex]
[tex]y_{v} = -\frac{\Delta}{4a}[/tex]
Where
[tex]\Delta = b^2-4ac[/tex]
If a<0, the vertex is a maximum point, that is, the maximum value happens at [tex]x_{v}[/tex], and it's value is [tex]y_{v}[/tex].
f(x) = x² - X + 2.
Quadratic equation with [tex]a = 1, b = -1, c = 2[/tex]
So
[tex]\Delta = b^2-4ac = (-1)^2 - 4(1)(2) = 1 - 8 = -7[/tex]
[tex]x_{v} = -\frac{(-1)}{2} = \frac{1}{2}[/tex]
[tex]y_{v} = -\frac{-7}{4} = \frac{7}{4}[/tex]
The vertex of the function is [tex](\frac{1}{2}, \frac{7}{4})[/tex]
Find the equation (in terms of x ) of the line through the points (-2,5) and (3,4)
y=
Answer:
[tex]{ \boxed{ \bf {general \: equation : y = mx + c}}} \\ m \: is \: the \: slope \\ { \green{slope = \frac{ \triangle \: y}{ \triangle \: x} }} \\ m = \frac{(4 - 5)}{(3 - ( - 2))} \\ m = - \frac{1}{5} \\ \therefore \: { \red{y = - \frac{1}{5} x + c}} \\ consinder \: the \: first \: point : \\ 5 = ( - \frac{1}{5} \times - 2) + c \\ c = \frac{23}{5} \\ \therefore \: { \boxed{ \bf{answer : 5y = - x + 23}}} \\ \\ { \underline{ \blue{ \tt{becker \: jnr}}}}[/tex]
The height of a square pyramid where the lateral area equals 240 cm sq. and the edges of the base are 12cm
Answer:
The height is 8cm
Step-by-step explanation:
Given
[tex]L_A = 240cm^2[/tex] --- lateral area
[tex]a = 12cm[/tex] --- base lengths
Required
The height of the pyramid
The lateral area of a square pyramid is:
[tex]L_A = a\sqrt{a^2 + 4h^2[/tex]
So, we have:
[tex]240 = 12\sqrt{12^2 + 4h^2[/tex]
[tex]240 = 12\sqrt{144 + 4h^2[/tex]
Divide both sides by 12
[tex]20 = \sqrt{144 + 4h^2[/tex]
Square both sides
[tex]400 = 144 + 4h^2[/tex]
Collect like terms
[tex]4h^2 = 400 - 144[/tex]
[tex]4h^2 = 256[/tex]
Divide by 4
[tex]h^2 = 64[/tex]
Take square roots
[tex]h = 8[/tex]
What is the area of the triangle formed from (0,-3), (0,4), and (4,-3)?
O A. 14 square units
O B. 6 square units
O c. 48 square units
O D. 24 square units
One sixth of the students of a class joined the
sports club. Three fifth of these students opted
to play table tennis. If 6 students play table
tennis, how many students are there in the
class?
Answer:
5/8 the answer answer answer
which of the following nets does not make a triangular prism?
Diagram A and Diagram B do not form a triangular prism
The sum of 5 times a number and -2, added to 8 times the number.
The algebraic expression (simplify your answer)
Step-by-step explanation:
sum of 5 times a number and -2, + 8n
becomes:
5n + (-2) + 8n, or
5n -2 +8n, or. 13n - 2
Please help ASAP thank you
Answer:
if you still need the answer its B here the explenation in a picture:
Step-by-step explanation:
k+9=7..................................................
Answer:K=-2
Step-by-step explanation:
becuase you do the opposite of +9 which is -9 and you do 7-9 which is -2 so K=-2
I’ll give u brainlest please
Answer:
315
Step-by-step explanation:
the formula is V = B * h
B is the area of the base
V = (1/2)(10)(7) * 9
What are the solutions to
96x(730) = (85/x)(15)
in decimal form?
Answer:
[tex]x = 0.1349[/tex]
Step-by-step explanation:
Given
[tex]96x (730) = (85/x)(15[/tex]
Multiply both sides by x
[tex]96x^2 (730) = 85 * 15[/tex]
[tex]96x^2 (730) = 1275[/tex]
Rewrite as:
[tex]96*730x^2 = 1275[/tex]
[tex]70080x^2 = 1275[/tex]
Divide by 70080
[tex]x^2 = 0.01819349315[/tex]
Take square roots of both sides
[tex]x = 0.1349[/tex]
Show that the set is linearly dependent by finding a nontrivial linear combination of vectors in the set whose sum is the zero vector. (Use s1, s2, and s3, respectively, for the vectors in the set.)
S = {(3,4),(−1,1),(2,0)}
Answer:
Let's define:
s1 = (3, 4)
s2 = (-1, 1)
s3 = (2, 0)
The system will be linearly dependent if we can write one of the vectors as a linear combination of the other two, so for example:
s1 = a*s2 + b*s3
where a and b are real numbers.
So let's try to solve this:
(3, 4) = a*(-1, 1) + b*(2, 0)
Note that the second term in the left only modifies the x-component. And the y-component in the left is 4, so we can conclude that a = 4 (because the first term is the only that has an y-component different than zero)
(3, 4) = 4*(-1, 1) + b*(2, 0)
(3, 4) = (-4, 4) + b*(2, 0)
Now we need to solve:
3 = -4 + b*2
3 + 4 = b*2
7 = b*2
7/2 = b
Then the linear combination is:
s1 = 4*s2 + (7/2)*s3
(3, 4) = 4*(-1, 1) + (7/2)*(2, 0)
Then the set is linearly dependent.
Help please this is so hard I don't understand it
Answer:
<ABC = 15
< BAC = 150
Step-by-step explanation:
<C = <B since this is an isosceles triangle. We know this because AC = AB
<C = 15 so <ABC = 15
The sum of the angles of a triangle is 180
A + B+ C = 180
A + 15+15 = 180
A +30 =180
A = 180-30
A = 150
< BAC = 150
Can someone help me please???!
Answer:
1) Yes, it is a right angle triangle
2)Yes, it is a right angle triangle
3) No, they are not similar.
Step-by-step explanation:
Dimension of triangle A = 48, 55 & 73
Dimension of triangle B = 36, 77 & 85
For any of the triangles to be a right angled one, then;
c = √(a² + b²)
Where a,b & c are side dimensions of a triangle.
Thus;
Triangle A: c = √(48² + 55²)
c = √5329
c = 73
This tallies with what we are given and so it is a right angled triangle.
Triangle B: c = √(36² + 77²)
c = √(7225)
c = 85
Similar to the third side dimension of 85, thus it is true.
For Triangle A & B to be similar, the ratio of the 3 corresponding sides must be in a whole number ratio.
Thus, we have;
48/36 = 1.5
55/77 = 5/7
73/85 = 73/85
Since the ratios are not similar, then we can say that the triangles are not similar.
i need help with this
Answer:
Step-by-step explanation:
64
128°
Step-by-step explanation:
The measure of the intercepted arc is twice the measure of the inscribed angle in a circle. Since the inscribed angle is given as 64°, that means that the intercepted arc x is 2×64° = 128°
In the diagram, the lines dividing parking spaces are parallel. The measure of ∠1 is 110°. Identify the measures of each labeled angle to ensure cars can park safely.
Answer:
1=110 2=70 3=70 4=110 5=110 6=70 7=70 8 =110
Step-by-step explanation:
its the answer
Mrs. Brown, Mrs. White, and Mrs. Gray are a teacher, a doctor, and a lawyer, not necessarily in that order. Each has a horse. One horse is white, one is brown, and one is gray. From the following clues, determine the occupation of each woman and the color of her horse. No one’s name is the same as the color of her horse. The teacher owns a brown horse. Mrs. Gray is a doctor.
Answers:
Mrs. Brown ( lawyer ) owns the gray horse.Mrs. White ( teacher ) owns the brown horseMrs Gray ( doctor ) owns the white horse===========================================================
Explanation:
We're given these three clues
Clue 1: No one's name is the same as the color of her horseClue 2: The teacher owns a brown horseClue 3: Mrs. Gray is a doctor.Clue 3 is what we'll start with. Since Mrs. Gray is a doctor, this means that the doctor owns either a white horse or a brown horse. The doctor can't own a gray horse because the names can't match up (eg: the last name Gray with gray horse), due to clue 1.
If Mrs. Gray owned a brown horse, then she'd be a teacher (clue 2). But clue 3 says she's a doctor. We have a contradiction if Mrs. Gray owns the brown horse. Therefore, Mrs. Gray owns the white horse.
----------------
After we concluded the last section, we now know the following:
The horses that are left are the brown and gray horse.The professions left are the teacher and lawyer.The people left are Mrs. Brown and Mrs. White.In short, we've just crossed "Mrs. Gray", "doctor", and "white horse" from the list.
Based on clue 1, we know that Mrs. Brown cannot possibly own the brown horse. Therefore, she must own the gray horse. So Mrs. White must own the brown horse.
Since Mrs. White owns the brown horse, she must be the teacher (clue 2). That leaves "lawyer" as the last profession, and that's assigned to Mrs. Brown.
----------------
Side note: I apologize for being a bit wordy, but I wanted to be very careful in the logical sense as to approach this problem. There's probably a much quicker efficient way to do this.
Simplify the expression.
33 · 32 + 12 ÷ 4
Answer:
1059
Step-by-step explanation:
33 · 32 + 12 ÷ 4
PEMDAS
Multiply and divide first from left to right
1056 + 3
Then add
1059
[tex]\huge\textsf{Hey there!}[/tex]
[tex]\mathsf{33\times32+12\div4}\\\\\mathsf{33\times32= \boxed{\bf 1,056}}\\\\\mathsf{\bold{1,056}+12\div4}\\\\\mathsf{12\div4=\boxed{\bf 3}}\\\\\mathsf{1,056+\bf 3}\\\mathsf{= \boxed{\bf 1,059}}\\\\\\\boxed{\boxed{\large\textsf{Answer: \huge \bf 1,059}}}\huge\checkmark[/tex]
[tex]\large\textsf{Good luck on your assignment and enjoy your day!}[/tex]
~[tex]\frak{Amphitrite40:)}[/tex]
Teresa is making iced tea. She has a container that has a volume of 3.95 gallons to store the iced tea.
A survey of 1000 young adults nationwide found that among adults aged 18-29, 35% of women and 30% of men had tattoos. Suppose that these percentages are based on random samples of 500 women and 500 men. Using a 2.5% level of significance, can you conclude that among adults aged 18-29, the proportion of all women who have tattoos exceeds the proportion of all men who have tattoos?
Answer:
95% confidence interval for adults in age group 18-29 is (-0.007, 0.107)
Step-by-step explanation:
Given
N1 = n2 = 500
% of males = 0.30
% of females = 0.35
95% confidence interval
(p2-p1) + z(0.025) sqrt (p1q1/n1 + p2q2/n2) and (p2-p1) - z(0.025) sqrt (p1q1/n1 + p2q2/n2)
Substituting the given values, we get –
(0.35-0.30) + 1.96 sqrt (0.3*0.7/500 + 0.35*0.65/500) and (0.35-0.30) - 1.96 sqrt (0.3*0.7/500 + 0.35*0.65/500)
0.05 + (1.96 *0.029) and 0.05 - (1.96 *0.029)
0.05 + 0.057 and 0.05 – 0.057
(-0.007, 0.107)
what is the coefficient of y in 2-5y÷2
Answer:
-5/2 because there is -5y/2 but we have to take coefficient only so -5/2
Given the triangle below, answer the following:
Answer:
Step-by-step explanation:
question no . 5
ratio of angle L
take angle as reference angle
using cos rule
cos L = base / hypotenuse
= 4/5
ratio of angle N
take angle N as reference angle
using sin rule
sin N = opposite / hypotenuse
= 4/5
for measure of angle L
cos L = 4/5
cos L = 0.8
L = [tex]cos^{-1}(0.8)[/tex]
L = 36.9
for meanure of angle N
sin N = 4/5
sin N = 0.8
N = [tex]sin^{-1}(0.8)[/tex]
N = 53.1
(2x^4+5x^3+5x^2+10+8)/(x+2)
Answer:
30
Step-by-step explanation:
You use polynomial division to divide all the numbers on the numerator by the denominator.
in an examination 45% students passed in science only 25% passed in english only and 5% students failed in both subjects if 200 students passed in english find the total number of students by using venn diagram
Step-by-step explanation:
[tex]\huge\mathfrak\pink{Answer}[/tex]
Total number of students= y
(25/100) xy= 200
25 xy = 200 x 100
25y 20000
y = 20000/25
y 800
total number of students = 800
Step-by-step explanation:
[tex]\mathfrak\pink{Answer}[/tex]
Total number of students= y
(25/100) xy= 200
25 xy = 200 x 100
25y 20000
y = 20000/25
y 800
total number of students = 800
The sum of two numbers is 50 and the difference is 18. What are the numbers?
Equations:
x + y = 50
x = y - 18
-------------------
Add and solve for "x"::
2x = 32
x = 16
-----
Solve for "y"::
16 + y = 50
y = 34
ANSWERS ARE IN BOLD