Solution :
Given :
[tex]$\mu = 24$[/tex]
n = 15
[tex]$\overline x = 24.89$[/tex]
s = 0.5902
The hypothesis :
[tex]$H_0 : \mu = 25$[/tex]
[tex]$H_a : \mu \neq 25$[/tex]
This is a 2 tailed test.
The significance level is [tex]$95 \% \ ( \alpha =0.05)$[/tex]
The test statistic :
[tex]$Z=\frac{\overline x - \mu}{\frac{\sigma}{\sqrt n}}$[/tex]
[tex]$Z=\frac{24.89-25}{\frac{0.5902}{\sqrt 15}}$[/tex]
= -0.72
The p value : The p value for Z = -0.72 is 0.4716
The critical value : the critical value at α = 0.05 is +1.96 to -1.96
The decision rule :
If [tex]$Z_{observed} > Z_{critical}$[/tex] or if [tex]$Z_{observed} < -Z_{critical}$[/tex], then reject [tex]$H_0$[/tex].
Also if p value is less than α, then reject [tex]$H_0$[/tex].
The decision :
Since the Z falls in between +1.96 and -1.96, we fail to reject the [tex]$H_0$[/tex]. Also since p value is greater than α, we fail to reject [tex]$H_0$[/tex].
The conclusion :
There is not sufficient evidence at the 95% significance level to warrant rejection of the claim that the pills come from a population in which the amount of the atorvastatin is equal to 25 mg.
Now calculating the mean and the standard deviation :
[tex]$\text{Mean} = \frac{\text{sum of observation}}{\text{total observations}}$[/tex]
Standard deviation = [tex]$\sqrt{\text{variance}}$[/tex]
Variance = [tex]$\frac{\text{sum of squares(SS)}}{n-1}$[/tex]
Where, SS = [tex]$\sum (X - \text{mean})^2$[/tex]
X Mean [tex]$(X-\text{mean})^2$[/tex]
24.1 24.89 0.62
24.4 24.89 0.24
24.3 24.89 0.35
24.9 24.89 0
24.1 24.89 0.62
24.2 24.89 1.72
24.1 24.89 0.04
26.2 24.89 0.04
25.1 24.89 0.24
25 24.89 0.01
24.7 24.89 0.04
25.1 24.89 0.04
25.3 24.89 0.17
25.5 24.89 0.37
25.5 24.89 0.37
n 15
Sum 373.3
Average 24.89
SS 4.8775
Variance = [tex]$\frac{SS}{n-1}$[/tex] 0.348392857
Standard deviation 0.5902
What is the lateral surface area?
Answer:
The lateral surface of an object is all of the sides of the object, excluding its base and top. The lateral surface area is the area of the lateral surface
Step-by-step explanation:
Which ordered pair is a solution to the equation y = 5x + 2?
A (-2, -8)
B (22, 4)
C (8, 40)
D (-5, 2)
Which of the following is a solution to 10x^2-x=3?
Answer:
g
Step-by-step explanation:
It took Kai 9 hours to mow 6 lawns. If Kai worked at the same rate, how many lawns could he mow in 33 hours?
Answer:
so im not sure it can either be 33, 1.5 or 49.5
Step-by-step explanation:
Have an amazing day :)
Will give brainlst
Answer:
1 1/2. Hope this helps u :D
Answer:
Square root of
20square-13square
= √231
Christy is painting pinwheels to sell at a fair. It takes her 1.5 hours to paint each pinwheel. How many pinwheels will she be able to paint in 13.5 hours?
Answer: 9 hours
Step-by-step explanation:
13.5 hours / 1.5 hours = 9 hours
A sphere has a volume of 36 pi in 3rd power. Find the radius of the sphere. Use 3.14 for pi.
Answer:
3 inches
Step-by-step explanation:
1. Volume of a sphere
V = 4/3πr^3
2. Plug in numbers
V = 36π
r = ?
36π = 4/3πr^3
27=r^3
[tex]r=\sqrt[3]{27}[/tex]
r = 3
I need help with this
Can anyone help me out on this
Answer: y=x+60
So y=mx+b is slope intercept form
y=x+60
m=1/1 because we go equally up as we go right so just put x
b=60 because we start at 60
Hope this helps
What is a characteristic of people who live in a nation-state?
Answer:
Ethnically diverse people loving in the same area
Identify the vertex of the quadratic function below.
Carlotta has 2/3 of a bag of dog food. She gives her dog 2/9 of the bag at each feeding. How many times can she feed her dog with what is left in this bag of dog food?
A. 3
B. 4
C. 18
D. 27
Answer:
27
Step-by-step explanation:
Carlotta can feed 3 times her dog with leftover in this bag of dog food
What is the unitary method?
The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value. If an event can occur in m different ways and if following it, a second event can occur in n different ways, then the two events in succession can occur in m × n different ways.
WE have been given that Carlotta has 2/3 of a bag of dog food and She gives her dog 2/9 of the bag at each feeding.
The bag of dog food = 2/3
Let she feed her dog with leftover in this bag of dog food = X
Therefore, X = 2/3 × 9/2
X = 18 / 6
X = 3
Hence, Carlotta can feed 3 times her dog with leftover in this bag of dog food
Learn more about the unitary method, please visit the link given below;
https://brainly.com/question/23423168
#SPJ5
You have two numbers. If you double the first number and add it to the second number, the sum is 10.
Let x represent the first number and let y represent the second number.
1) Write an equation showing the relationship between x, y, and 10.
Answer:
probably 2,5&10 because they are all multiples of 2
WILL GIVE BRAINLST
HAVE A GOOD DAY
Answer:
6.633249581 and I would say it's irrational
Step-by-step explanation:
:)
Find the following F distribution values from Table 4 of Appendix B.
answer this pls !!!!?!?!??!
Answer:
A
Step-by-step explanation:
Please help I'll give brainliest! And 100 points this is due tonight!!!
Answer:
You can try searching it up or going to math.way
Step-by-step explanation:
what two consecutive whole numbers that 12 lie between
The order pair for the equation y =2x+3(-1----)
Answer:
Y=-1
Step-by-step explanation:
2(-1)+3=y
-2+3= -1
WILL GIVE BRAINLIEST!!! As part of an offseason training program, the Lane Tech cross county team must sprint up a ramp with a 28% grade. To the nearest degree, what angle does with ramp make with the ground?
Answer:
20%
Step-by-step explanation:
Which value of x makes this equation true?
-8(x+5) = -3x - 7+ X-3
A. = 7 1/2
B. X=-5
c. X = 1 1/4
D. X= 12
Answer:
B: x = -5
Step-by-step explanation:
A person on a moving sidewalk travels 6 feet in 3 seconds. The moving sidewalk has a length of 60 feet. How long will it take to move from one end of the sidewalk to the other?
Answer:
Speed = distance / time
= 6/3 =2 ft/sec
Time = distance / speed
= 60/2
= 30 seconds
The first three terms of a sequence are given. Round to the nearest thousandth (if
necessary).
5,4,16/5
Find the 7th term
Answer:
Step-by-step explanation:
a₂/a₁ = ⅘
This is a geometric sequence with initial term = 5 and common ratio = ⅘
a₇ = a₁(⅘)⁷⁻¹ = 5(⅘)⁶ = 4⁶/5⁵= 4096/3125 ≅ 1.311
Can someone help me with these questions and show work please and thank you
Answer:
11. 78
12. 4x² - 3x - 1
Step-by-step explanation:
11. Sum of n whole numbers = ½(n² + n)
Multiply
½*n² + ½*n
= n²/2 + n/2
To find the sum of the first 12 whole number, substitute 12 for n into the equation.
= 12²/2 + 12/2
= 144/2 + 12/2
= 72 + 6
= 78
12. Area of trapezoid = ½(a + b)*h
Where,
a = 5x - 4
b = 3x + 2
h = x + 1
Area = ½(5x - 4 + 3x + 2)*(x + 1)
Area = ½(8x - 2)*(x + 1)
Area = ½[8x(x + 1) -2(x + 1)]
= ½[8x² + 8x - 2x - 2]
Add like terms
= ½(8x² - 6x - 2)
= ½(8x²) - ½(6x) - ½(2)
= 4x² - 3x - 1
Ms. Katie had a pizza party with the art club. There are 8 students and each student ate 1/3 of a pizza. How many pizzas did they eat altogether?
Answer:
1.7 or 38/5
Step-by-step explanation:
Hope this helps!
FIND THE ERROR: Chun and Traci are determining the value of x in the figure. Chun says to find the value of x, solve the proportion = 1, but
Treci says to find the value of 1, the proportion is should be solved. Is either of them correct? Explain your reasoning
9514 1404 393
Answer:
Chun is correct
Step-by-step explanation:
The angle bisector divides the sides of the triangle proportionally. Any proportion that is written should equate ratios of corresponding sides.
Chun's proportion correctly relates the top-side measures to their corresponding bottom-side measures:
top short : bottom short = top long : bottom long
5 / 8 = 15 / x
__
Traci's error is that she mixes top-side and bottom-side measures. Her incorrect relation is ...
top short : bottom long = bottom short : top long
She has used top:bottom for short measures and bottom:top for long measures. This mixing will give Traci an incorrect solution.
__
Chun's proportion correctly gives x=24.
Answer:
Step-by-step explanation:
Chun; by the Triangle Angle Bisector Theorem, the correct proportion is 58=15x.
1. Solve. Draw a rectangular fraction to explain your thinking. Then, write a number sentence.
1/3 of 3/7
2. In a cookie jar, 1/4 of the cookies are chocolate chip, and 1/2 of the rest of the are peanut butter?
9514 1404 393
Answer:
1. 1/3 × 3/7 = 1/7
2. 1/2×(1 -1/4) = 3/8
Step-by-step explanation:
Attached is my attempt at the required drawings. Yours may be different, based on the methods used by your teacher.
please help me please brainliest
Answer:19
Step-by-step explanation:perimeter is everything added since it’s a rectangle 10 on both length sides will be 20 so 58-20 is 38 divide that by 2 and that’s your answer.
Suppose we want to choose 2 objects, without replacement, from the 4 objects pencil, eraser, desk, and chair
Answer: First off. Question or statement? Secondly. What?
Step-by-step explanation: Third. What?
Find the point on the line 2x+6y+1=0 which is closest to the point (-5,-3)
Answer:
(-1.875, -1.625)
Step-by-step explanation:
We want to find the point on the equation 2*x + 6*y + 1 = 0 which is closest to the point (-5, -3)
Remember that the distance between two points (a, b) and (c, d) is:
D = √( (a - c)^2 + (b - d)^2)
First we can write our equation as a line in the slope intercept form:
y = -(2/6)*x - 1
Now we could minimize the equation:
D = √( (x - (-5))^2 + (y - (-3))^2) = √( (x + 5)^2 + (y + 3)^2)
D = √( ( x + 5)^2 + ( -(2/6)*x - 1 + 3) ^2)
Then we can minimize:
D^2 = (x + 5)^2 + ( -(2/6)*x + 2)^2
= x^2 + 10*x + 25 + (4/36)*x^2 - (8/6)*x + 4
= (1 + 4/36)*x^2 + (10 - 8/6)*x + 29
= (40/36)*x^2 + (52/6)*x + 29
This is a quadratic equation whose leading coefficient is positive, then the minimum of this equation is at the vertex.
The vertex is at the x-value such that (D^2)' = 0
Then:
(D^2)' = 2*(40/36)*x + (52/6)
This needs to be zero then:
0 = 2*(40/36)*x + (52/6)
-52/6 = (80/36)*x
(-52/6)*(36/80) = x
-1.875 = x
And the y-value when x = -1.875 is:
y = -(2/6)*-1.875 - 1
y = -1.625
Then the point on the line 2x+6y+1=0 that is closest to (-5,-3) is the point (-1.875, -1.625)