Company a samples 16 workers, and their average time with the company is 5.2 years with a standard deviation of 1.1. Company b samples 21 workers and their average time with the company is 4.6 years with a standard deviation 4.6 years
The populations are normally distributed. Determine the:
Hypothesis in symbolic form?
Determine the value of the test statistic?
Find the critical value or value?
determine if you should reject null hypothesis or fail to reject?
write a conclusion addressing the original claim?
Answer:
Step-by-step explanation:
GIven that :
Company A
Sample size n₁ = 16 workers
Mean [tex]\mu[/tex]₁ = 5.2
Standard deviation [tex]\sigma[/tex]₁ = 1.1
Company B
Sample size n₂ = 21 workers
Mean [tex]\mu[/tex]₂ = 4.6
Standard deviation [tex]\mu[/tex]₂ = 4.6
The null hypothesis and the alternative hypothesis can be computed as follows:
[tex]H_o : \mu _1 = \mu_2[/tex]
[tex]H_1 : \mu _1 > \mu_2[/tex]
The value of the test statistics can be determined by using the formula:
[tex]t = \dfrac{\overline {x_1}- \overline {x_2}}{\sqrt{\sigma p^2( \dfrac{1}{n_1}+\dfrac{1}{n_2})}}[/tex]
where;
[tex]\sigma p^2= \dfrac{(n_1 -1) \sigma_1^2+ (n_2-1)\sigma_2^2}{n_1+n_2-2}[/tex]
[tex]\sigma p^2= \dfrac{(16 -1) (1.1)^2+ (21-1)4.6^2}{16+21-2}[/tex]
[tex]\sigma p^2= \dfrac{(15) (1.21)+ (20)21.16}{35}[/tex]
[tex]\sigma p^2= \dfrac{18.15+ 423.2}{35}[/tex]
[tex]\sigma p^2= \dfrac{441.35}{35}[/tex]
[tex]\sigma p^2= 12.61[/tex]
Recall:
[tex]t = \dfrac{\overline {x_1}- \overline {x_2}}{\sqrt{\sigma p^2( \dfrac{1}{n_1}+\dfrac{1}{n_2})}}[/tex]
[tex]t = \dfrac{5.2- 4.6}{\sqrt{12.61( \dfrac{1}{16}+\dfrac{1}{21})}}[/tex]
[tex]t = \dfrac{0.6}{\sqrt{12.61( \dfrac{37}{336})}}[/tex]
[tex]t = \dfrac{0.6}{\sqrt{12.61(0.110119)}}[/tex]
[tex]t = \dfrac{0.6}{\sqrt{1.38860059}}[/tex]
[tex]t = \dfrac{0.6}{1.178388981}[/tex]
t = 0.50917
degree of freedom df = ( n₁ + n₂ - 2 )
degree of freedom df = (16 + 21 - 2)
degree of freedom df = 35
Using Level of significance ∝ = 0.05, From t-calculator , given that t = 0.50917 and degree of freedom df = 35
p - value = 0.3069
The critical value [tex]t_{\alpha ,d.f}[/tex] = [tex]t_{0.05 , 35}[/tex] = 1.6895
Decision Rule: Reject the null hypothesis if the test statistics is greater than the critical value.
Conclusion: We do not reject the null hypothesis because, the test statistics is lesser than the critical value, therefore we conclude that there is no sufficient information that the claim that company a retains it workers longer than more than company b.
How to find the area of the shaded region
Answer:
61 cm^2.
See below.
Step-by-step explanation:
P(x) =2x3 -11x2 -4x +1 g(x) =2x +1
Answer:
see explanation
Step-by-step explanation:
If (2x + 1) is a factor then x = - [tex]\frac{1}{2}[/tex] is a root and P(- [tex]\frac{1}{2}[/tex] ) = 0 ← Factor theorem
P(- [tex]\frac{1}{2}[/tex] )
= 2(- [tex]\frac{1}{2}[/tex] )³ - 11(- [tex]\frac{1}{2}[/tex] )² - 4(- [tex]\frac{1}{2}[/tex] ) + 1
= - [tex]\frac{1}{4}[/tex] - [tex]\frac{11}{4}[/tex] + 2 + 1
= - [tex]\frac{12}{4}[/tex] + 3
= - 3 + 3
= 0
Since P(- [tex]\frac{1}{2}[/tex] ) = 0 then g(x) is a factor of P(x)
Please Help!!! What is 2x = 40?
Answer:
Friend your answer is 20
Step-by-step explanation:
You divide 40 by the co-efficient of 2=20
[tex]\boxed{x = 20}[/tex]
There is only one step to this equation. We use inverse operations to isolate the x by dividing 2 on both sides; because 2 is being multiplied by x, and the inverse operation for multiplication is division.
2x/2 = x
40/2 = 20
The equation now looks like:
x = 20
This is your answer.
there are 400 pages-to be read from a book.yesterday you read 1/4 of the pages. today you read 2/3 of the remains pages from the book.how many pages are left in the book
Answer:
100 pages
Step-by-step explanation:
Yesterday, there were 400 pages left unread so you read 1/4 * 400 = 100 pages yesterday. Today, there are 400 - 100 = 300 pages left unread so today, you read 2/3 * 300 = 200 pages. This means that there are 300 - 200 = 100 pages left in the book.
Please answer these 3 questions for 70 points 1 thanks 5 stars and brainiest
Answer:
Step-by-step explanation:
Problem 14: Mean 5.5, Range: 5.8
Problem 15: question #1 4, mode: 63
Probelm 16: Median 63, Range: 8.3
Answer:
14: Mean is 5.5 Hours
Range is 7.9 Hours
15: 4 Numbers
Mode is 6.3
16: Median is 6.3
Range is 8.3
Step-by-step explanation:
(I'll edit in the explanations momentarily)
The width of a rectangle measures (2.3a + 9.9) centimeters, and its length
measures (6.3a - 2.6) centimeters. Which expression represents the perimeter, in
centimeters, of the rectangle?
12.2a +3.7
O 7.3 + 8.60
O 17.2a + 14.6
O 7.4 +24.4a
Answer:
17.2a+14.6
Step-by-step explanation:
Which geometric figure has 120 rotational symmetry?
Answer:
Triangle
Step-by-step explanation:
Has 120° degrees of rotation and measure of the central angle and has 3-fold rotational symmetry
Calculate the perimeter of a semi-circle
whose diameter is 14cm
perimeter of a semicircle is [tex]\frac{2\pi r}{2}+2r=\frac{d\pi}2 +d[/tex]
$d=14$
so, perimeter= $14\cdot\frac{22}7\cdot \frac{1}2+14=22+14=36$ cm
Answer:
Perimeter of semi-circle = 36 cm
Step-by-step explanation:
diameter = d = 14 cm
Perimeter of semicircle = Circumference of semi-circle + diameter
= [tex]\frac{1}{2}\pi d + d[/tex]
= [tex]\frac{1}{2}*\frac{22}{7}*14 +14\\[/tex]
= 22 + 14
= 36 cm
What is the value of x?
7
7 square root 2
14
14 square root 2
Answer:
14
Step-by-step explanation:
Using the sine ratio in the right triangle and the exact value
sin45° = [tex]\frac{1}{\sqrt{2} }[/tex] , thus
sin45° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{7\sqrt{2} }{x}[/tex] = [tex]\frac{1}{\sqrt{2} }[/tex] ( cross- multiply )
x = 7[tex]\sqrt{2}[/tex] × [tex]\sqrt{2}[/tex] = 7 × 2 = 14
Answer:
x = 14i hope it helps :)Step-by-step explanation:
[tex]Hypotenuse = x \\Opposite = 7\sqrt{2} \\\alpha = 45\\\\\Using \: SOHCAHTOA\\Sin \alpha = \frac{Opposite}{Hypotenuse}\\ \\Sin 45 = \frac{7\sqrt{2} }{x} \\\\\frac{\sqrt{2} }{2} = \frac{7\sqrt{2} }{x} \\\\\sqrt{2x} = 14\sqrt{2} \\\\\frac{\sqrt{2x} }{2} = \frac{14\sqrt{2} }{2} \\x = 14[/tex]
X+2/x-2 - x+3/x-1 solve
●✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎❀✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎●
Hi my lil bunny!
❧⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯☙
[tex]x+\frac{2}{x} -2-x+\frac{3}{x} -1[/tex]
[tex]= \frac{-3x + 5}{x}[/tex]
❧⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯☙
●✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎❀✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎●
Hope this helped you.
Could you maybe give brainliest..?
❀*May*❀
PLZ HELP! please answer both if you can!!
1. What is the area of the following triangle in square meters? Do not round your answer. A = a0 m 2
2.What is the average of the two bases in the following trapezoid in feet? 18 ft 11 ft 14.75 ft 22 ft
Answer:
0.324m^2 ; 18 ft
Step-by-step explanation:
Given the triangle :
Base (b) of triangle = 54cm
Height (h) of triangle = 1.2m
Area(A) of a triangle is given by:
0.5 * base * height
Base = 54cm = 54/100 = 0.54 m
Therefore,
A = 0.5 * 0.54m * 1.2m
A = 0.324m^2
2.) Average of the two bases in the trapezoid :
From the trapezium Given :
Base 1 = 15 feets
Base 2 = 7 yards
1 yard = 3 Feets
Therefore, base 2 in Feets = 7 * 3 = 21 Feets
Average of the two bases :
(21 Feets + 15 Feets) / 2
= 36 Feets / 2
= 18 Feets
Which of the following describes a change in a shape's position or size?
A. reflection symmetry
B. image
O C. transformation
D. rotational symmetry
Answer:
The correct option is;
C. Transformation
Step-by-step explanation:
In mathematics, transformation refers to the relocation of an object called the pre-image from initial position to another new location at which point the object will be known as the image whereby there is a one to one mapping from each point on the pre-image to the image
The types of transformation includes reflection, rotation, and translation which involve changes in position and dilation, which involves changes in the size of the pre-image.
Pete earns graduated commission on his sales each month. He earns 7% commission on the first $35,000 in sales and 9% on anything over that. If Pete had $43,000 in sales this month, how much commission did he earn?
a. $2,610
b. $3,170
c. $3,870
d. $6,880
Please select the best answer from the choices provided A B C D
Answer:
b.$3170
Step-by-step explanation:
43,000-35,000=8,000
SO you would find 9% commission on 8,000
8,000x.09=720
then, you would find his normal commission if he only made 35,000
so you would do 35,000x.07=2450
you would, then, add the two together to get his entire commission, which is $3170
Answer:
b
Step-by-step explanation:
PLS HELP I REALLY NEED IT
Answer:
x=9
Step-by-step explanation:
<B = <E from the concurrency statement
5x = 45
Divide by 5
5x/5 = 45/5
x = 9
Answer:
Hey there!
These are similar triangles, and similar triangles have congruent angles.
Thus, we have 5x=45
Simplifying, we have x=9
Let me know if this helps :)
which of these correctly rearranges the terms in this polynomial so like terms are next to each other ? 3-6x+4x^2+3x-6x^2-4 PLEASE HELP!!
Answer:
A is the answer
Step-by-step explanation:
Answer:
the answer is A.
Step-by-step explanation:
Factorise : x^2-9x-70 Step by Step
Answer:
Step-by-step explanation:
x^2 - 9x - 70
we need to find two numbers whose sum is -9 and product id -17
The numbers are -14 and 5
By splitting the middle term,
x^2 - 14x + 5x - 70
= x ( x - 14 ) + 5 ( x - 14 )
( x + 5 ) ( x - 14 )
Hope this helps
Plz mark as brainliest!!!!!
Answer:
Step-by-step explanation:
Sum = -9
Product = -70
Factors = -14 , 5
x² - 9x - 70 = x² + 5x - 14x + (-14) * 5
=x(x + 5) - 14(x + 5)
= (x + 5)(x - 14)
(3)/(22)+(-(1)/(11) find the sum without use of a number line
Answer:
1/22
Step-by-step explanation:
Simplify it.
It becomes 3/22-1/11
Change the denominator to 22 becasue that is the LCM.
It becomes 3/22-2/22 which is 1/22. :)
1) UN MOVIL A SE MUEVE DESDE UN PUNTO CON VELOCIDAD CONSTANTE DE 20m/s EN EL MISMO INSTANTE A UNA DISTANCIA DE 1200m, OTRO MOVIL B SALE Y PERSIGUE AL MOVIL A CON VELOCIDAD CONSTANTE DE 40m/s.¿ EN QUE TIEMPO Y A QUE DISTANCIA B ALCANZA a
Answer:
El móvil B necesita 60 segundos para alcanzar al móvil A y le alcanza una distancia de 2400 metros con respecto al punto de referencia.
Step-by-step explanation:
Supóngase que cada movil viaja en el mismo plano y que el móvil B se localiza inicialmente en la posición [tex]x = 0\,m[/tex], mientras que el móvil A se encuentra en la posición [tex]x = 1200\,m[/tex]. Ambos móviles viajan a rapidez constante. Si el móvil B alcanza al móvil A después de cierto tiempo, el sistema de ecuaciones cinemáticas es el siguiente:
Móvil A
[tex]x_{A} = 1200\,m+\left(20\,\frac{m}{s} \right)\cdot t[/tex]
Móvil B
[tex]x_{B} = \left(40\,\frac{m}{s} \right)\cdot t[/tex]
Donde:
[tex]x_{A}[/tex], [tex]x_{B}[/tex] - Posiciones finales de cada móvil, medidas en metros.
[tex]t[/tex] - Tiempo, medido en segundos.
Si [tex]x_{A} = x_{B}[/tex], el tiempo requerido por el móvil B para alcanzar al móvil A es:
[tex]1200\,m+\left(20\,\frac{m}{s} \right)\cdot t = \left(40\,\frac{m}{s} \right)t[/tex]
[tex]1200\,m = \left(20\,\frac{m}{s} \right)\cdot t[/tex]
[tex]t = \frac{1200\,m}{20\,\frac{m}{s} }[/tex]
[tex]t = 60\,s[/tex]
El móvil B necesita 60 segundos para alcanzar al móvil A.
Ahora, la distancia se obtiene por sustitución directa en cualquiera de las ecuaciones cinemáticas:
[tex]x_{B} = \left(40\,\frac{m}{s} \right)\cdot (60\,s)[/tex]
[tex]x_{B} = 2400\,m[/tex]
El móvil B alcanza al móvil A a una distancia de 2400 metros con respecto al punto de referencia.
Compare the slopes of the linear functions f(x) and g(x) and choose the answer that best describes them.
A. The slope of f(x) is greater than the slope of g(x).
B. The slope of f(x) is less than the slope of g(x).
C. The slope of f(x) is equal to the slope of g(x).
D. The slope of g(x) is undefined
Answer:
The slope of f(x) is equal to the slope of g(x).
Step-by-step explanation:
The question is incomplete. Here is the complete question.
Compare the slopes of the linear functions f(x) and g(x) and choose the answer that best describes them.
a graph of a line labeled f of x passing through 0, negative 1 and 3, 1
x g(x)
0 2
3 4
6 6
Slope is defined as the change of the y axis to the z axis of a plane.
Slope = ∆y/∆x
Slope = y2-y1/x2-x1
For f(x) with coordinates (0, -1) and (3,1)
x1 = 0, y1 = -1, x2 = 3 and y2 = 1
Slope of f(x) = 1-(-1)/3-0
Slope = 1+1/3
Slope = 2/3
For g(x), we will choose any two of the coordinates from the table. Using the coordinates (3,4) and (6,6)
x1 = 3, y1 = 4, x2 = 6 and y2 = 6
Slope of g(x) = 6-4/6-3
Slope of g(x) = 2/3
It can be seen that the value of both slopes are equal. Hence, the slope of f(x) is equal to the slope of g(x) is the correct option.
Answer:
The answer is C. The slope of f(x) is equal to the slope of g(x).
Step-by-step explanation:
Did the test.
how many seconds are there in a month of 30 days express it in scientific notation
The house Trevor's family lives in has 6 people (including Trevor) and 3 bathrooms. In the past month, each person showered for an average of 480 minutes and used an average 72 liters of shower water (over the entire month). Water costs 0.20 dollars per liter.
Answer:
$86.40
Step-by-step explanation:
The house Trevor's family lives in has 6 people (including Trevor) and 3 bathrooms. In the past month, each person showered for an average of 480 minutes and used an average 72 liters of shower water (over the
entire month). Water costs 0.20 dollars per liter.
How much did Trevor's family pay per minute on shower water
Average person=72 liters of water
6 people=72*6= 432 liters
Each person = 480 minutes
6 people=480*6= 2,880 minutes
Water=$0.20 per liter
Total cost of water= 432 * 0.20
= $86.40
Answer:
o.o3
Step-by-step explanation:
Evaluate -3(8).
I know the answer is -24 but I don’t know who to work it out, can someone please help me
Answer:
-24
Step-by-step explanation:
-3 multiply 8 = -24
Because when ever you multiply a negative number with a positive number result will always be negative and 3 multiply 8 is 24.
Answer: -24
Step-by-step explanation: When you're asked to multiply
positives and negatives together, the rules are simple.
positive times a positive is a positive
positive times a negative is a negative
negative times a positive is a negative
negative times a negative is a positive
One way that I think will help you is to think
about the problem in terms of the signs.
If the signs are the same, the product will always be positive.
For example, (+3) · (+6) = +18 and (-6) · (-2) = +12.
If the signs are different, the product is negative.
So (+6) · (-4) is -24 and (-10) · (+5) is -50.
So don't get caught up on the signs.
Do the problem first, then determine if the
signs are the same or if they are different.
please help me
Expand ( p + 6 )( p - 3 )
Answer:
(p^2) + 3p - 18
Step-by-step explanation:
Have a nice day!
Answer:
2p+3
Step-by-step explanation:
(p+6)(p-3)
you have to open the brackets i.e
p+p+6-3
add p+p and you get 2p then you subtract positive 6 from 3 and you get 3
so your answer will be 2p+3
Convert to slope-intercept from: y-4=9(x-7)
Answer:
y = 9x - 59
Step-by-step explanation:
y - 4= 9(x-7)
y - 4 = 9x - 63
y - 4 + 4 = 9x - 63 + 4
y = 9x - 59
Answer:
Below
Step-by-step explanation:
● y-4 = 9(x-7)
Multiply 9 by (x-7)
● y-4 = 9x - 63
Add 4 to both sides
● y-4+4 = 9x-63 +4
● y = 9x - 59
I need helpp!! match the building block of geometry to the statement that defines it.
1)DIAGRAM
A)a formal statement declaring the meaning of
a word
2)DEFINITION
B)a visual tool representing mathematical
ideas to be interpreted
3)THEOREM
C)a mathematical statement proven using
postulates and definitions
4)POSTULATE
D)a mathematical statement taken as a fact
Answer:
1) [tex]DIAGRAM \mapsto B[/tex]
2) DEFINITION [tex]\mapsto A[/tex]
3) THEOREM [tex]\mapsto C[/tex]
4) POSTULATE [tex]\mapsto D[/tex]
Step-by-step explanation:
1) DIAGRAM B) A visual tool representing mathematical ideas to be interpreted
A diagram is the depiction or representation of information using symbols
2) DEFINITION A) A formal statement declaring the meaning of a word
A definition is a statement that outlines the meaning of a word or a group of words or a diagram, or a symbol or sign
3) THEOREM C) A mathematical statement proven using postulates and definitions
A general statement of a proposition that is by itself not evident, but given proof by a combination of postulates
4) POSTULATE D) A mathematical statement taken as a fact
An assumed truth taken as the foundation for further reasoning
if "f" varies directly with "m," and f = -19 when m = 14, what is "f" when m = 2
Answer:
f = - [tex]\frac{19}{7}[/tex]
Step-by-step explanation:
Given f varies directly with m then the equation relating them is
f = km ← k is the constant of variation
To find k use the condition f = - 19 when m = 14, thus
- 19 = 14k ( divide both sides by 14 )
- [tex]\frac{19}{14}[/tex] = k
f = - [tex]\frac{19}{14}[/tex] m ← equation of variation
When m = 2, then
f = - [tex]\frac{19}{14}[/tex] × 2 = - [tex]\frac{19}{7}[/tex]
How do you solve
n= (2s-1)+(s-1)
Answer:
n=3s-2
Step-by-step explanation:
Step 1: Remove unnecessary parentheses (2s-1)
Step 2: Collect "Like Terms" (2s+s= 3s)
Last Step: Put them all together (n=3s - 2)
Solve for x. This is for my math class, and I’ve been stuck on this for a while. Please help!
Answer:
Hey there!
Angles in a triangle add to 180 degrees.
24+134+2x=180
158+2x=180
2x=22
x=11
Let me know if this helps :)
multiple choice
a. 126 pie cm^3
b. 84 pie cm^3
c. 504 pie cm*3
Answer:
a. 126 pie cm^3
Step-by-step explanation:
Area of a circle = pi*r²
Volume = area*height
(pi*r²)*14
Since your answers are with Pi omit the Pi and times 3² * 14 = 126 pie cm³
Answer:
A. 126pi cm^3
Step-by-step explanation:
The volume of a cylinder can be found using the following formula.
[tex]v=\pi r^2 h[/tex]
First, we must find the radius. The radius is half of the diameter.
[tex]r=\frac{d}{2}[/tex]
The diameter of the cylinder is 6 cm.
[tex]r=\frac{6cm}{2}[/tex]
[tex]r= 3cm[/tex]
The radius is 3 cm.
Now, we can substitute values into the formula.
[tex]v=\pi r^2 h[/tex]
[tex]r= 3cm\\h=14 cm[/tex]
[tex]v=\pi (3cm)^2*14 cm[/tex]
Evaluate the exponent.
[tex](3cm)^2=3cm*3cm=9cm^2[/tex]
[tex]v=\pi*9cm^2*14cm[/tex]
Multiply 9 cm^2 and 14 cm
[tex]9 cm^2*14cm=126cm^3[/tex]
[tex]v=\pi*126cm^3[/tex]
The answer choices are in terms of pi, so we can simply rearrange our answer:
[tex]v=126\pi cm^3[/tex]
The volume of the cylinder is 126pi cubic centimeters and A is the correct answer.
PLEASE ANSWER!!! Select the correct answer from each drop-down menu. Consider the function f(x) = 3x + 1 and the graph of the function g(x) shown below.
Function transformation involves changing the position of a function.
The graph of g(x) is the graph of f(x) translated 2 units right, and [tex]\mathbf{g(x) = 3(x -2) + 1}[/tex]
The function is given as:
[tex]\mathbf{f(x)=3x + 1}[/tex]
The graph of g(x) passes through (2,1) and (0,-5).
Start by calculating the slope (m)
[tex]\mathbf{m = \frac{y_2 - y_1}{x_2 - x_1}}[/tex]
So, we have:
[tex]\mathbf{m = \frac{-5-1}{0-2}}[/tex]
[tex]\mathbf{m = \frac{-6}{-2}}[/tex]
[tex]\mathbf{m = 3}[/tex]
The equation is then calculated as:
[tex]\mathbf{g(x) = m(x -x_1) + y_1}[/tex]
So, we have:
[tex]\mathbf{g(x) = 3(x -2) + 1}[/tex]
By comparing [tex]\mathbf{f(x)=3x + 1}[/tex] and [tex]\mathbf{g(x) = 3(x -2) + 1}[/tex]
The graph of f(x) is shifted 2 units to the right
Read more about function transformation at:
https://brainly.com/question/13810353
