According to the typist claim, we build an hypothesis test, find the test statistic and the p-value relative to this test statistic, reaching a conclusion that:
The p-value of the test is 0.1333 > 0.05, which means that there is not enough evidence to reject the typist's claim.
-------------------------------------------------------------
In an interview for a secretary position at the dealer, a typist claims a tying speed of 45 words per minute.
At the null hypothesis, we test if the mean is of at least 45, that is:
[tex]H_0: \mu \geq 45[/tex]
At the alternative hypothesis, we test if the mean is of less than 45, that is:
[tex]H_1: \mu < 45[/tex]
-------------------------------------------------------------
The test statistic is:
We have the standard deviation for the sample, so the t-distribution is used to solve this question
[tex]t = \frac{X - \mu}{\frac{s}{\sqrt{n}}}[/tex]
In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, s is the standard deviation and n is the size of the sample.
-------------------------------------------------------------
45 is tested at the null hypothesis:
This means that [tex]\mu = 45[/tex]
On the basis of 70 trials, she demonstrated an average speed of 43 words per minute with a standard deviation of 15 words per minute.
This means that [tex]n = 70, X = 43, s = 15[/tex]
Value of the test statistic:
[tex]t = \frac{X - \mu}{\frac{s}{\sqrt{n}}}[/tex]
[tex]t = \frac{43 - 45}{\frac{15}{\sqrt{70}}}[/tex]
[tex]t = -1.12[/tex]
-------------------------------------------------------------
P-value of the test and decision:
The p-value of the test is found using a left-tailed test(test if the mean is less than a value), with 70 - 1 = 69 degrees of freedom and t = -1.12.
Using a t-distribution calculator, the p-value is of 0.1333.
The p-value of the test is 0.1333 > 0.05, which means that there is not enough evidence to reject the typist's claim.
A similar problem can be found at https://brainly.com/question/24241851
If Acot theta + Bcot theta =4 and
Bcot theta + Acot theta = q, then p^2-q^2=? .
(Please Answer Quickly!!! I will mark you as Brainliest)
Answer is: B
Step-by-step explanation: correct answer is B
b
2
−a
2
Given, acotθ+bcscθ=p
bcotθ+acscθ=q
⇒p
2
−q
2
=(p−q)(p+q)
=[acotθ+bcscθ−bcotθ−acscθ][acotθ+bcscθ+bcotθ+acscθ]
=[cotθ(a−b)−cscθ(a−b)][cotθ(a+b)+cscθ(a+b)]
=(a−b)(cotθ−cscθ)(a+b)(cotθ+cscθ)
=(a
2
−b
2
)(cot
2
θ−csc
2
θ)
=(−1)(a
2
−b
2
)[∵csc
2
θ−cot
2
θ=1]
=(b
2
−a
2
)
i need help i don’t know the answer
Answer:
(3x - 4) (2x + 15)
Step-by-step explanation:
6x² + 37x - 60
Using "splitting the middle term" method,
we get;
6x² + 45x - 8x - 60
= 3x (2x + 15) - 4 (2x + 15)
= (3x -4) (2x + 15)
Suppose a line passes through (a, -11) and (7,13), and is parallel to the line
y =2x + 8, What is the value of a? Write the equation of the line
Answer:
a=19
Step-by-step explanation:
The slope of the equation is - 2 as it's parallel to the given line. Using two point slope form, (13-(-11))/(7-a)=-2. 24=-2(7-a), - 12=7-a, a=19
Answer:
see explanation
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
y = 2x + 8 ← is in slope- intercept form
with slope m = 2
Parallel lines have equal slopes
Calculate the slope between the 2 given points and equate to 2
Using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (a, - 11) and (x₂, y₂ ) = (7, 13)
m = [tex]\frac{13-(-11)}{7-a}[/tex] = [tex]\frac{13+11}{7-a}[/tex] = [tex]\frac{24}{7-a}[/tex] , then
[tex]\frac{24}{7-a}[/tex] = 2 ( multiply both sides by 7 - a )
2(7 - a) = 24 ( divide both sides by 2 )
7 - a = 12 ( subtract 7 from both sides )
- a = 5 ( multiply both sides by - 1 )
a = - 5
--------------------------------------------------
y = 2x + c ← is the partial equation
To find c substitute (7, 13) into the partial equation
13 = 14 + c ⇒ c = 13 - 14 = - 1
y = 2x - 1 ← equation of parallel line
An airplane is descending as it approaches the airport. If the angle of depression from the plane to the ground is 7 degrees and the plane is 2,000 feet above the ground, what is the distance from the plane to the airport?
Answer:
The distance from the plane to the airport is around 245.57 feet.
Step-by-step explanation:
Angle of depression = 7 degrees
Height (Vertical portion of a right-angle triangle) = 2,000 feet
We are looking for the base of the right-angle triangle, which represents the distance from the plane to the airport. Therefore, we must use SOH or CAH or TOA to help us determine the length of the base. In this case, it is most convenient to use TOA:
tanΘ=[tex]\frac{Opposite}{Adjacent}[/tex]
Rearrange the equation to solve for 'Opposite':
Opposite=(tanΘ)(Adjacent)
Opposite=(tan[7])(2,000)
Opposite=0.12278456*2,000
Opposite=245.5691218 feet
Thus, the distance from the plane to the airport is around 245.57 feet.
Find the real or imaginary solutions by factoring.
X^4 -3x^2 = -2x^2
Look in the images it is solved.
plz help me..... ....
Answer:
Step-by-step explanation:
1) Tính a) (x+3)^2
b) (2x-1)^2
c) x^2 - 2y^2
d) ( x+2)^3
e)(x-3)^3
Answer:
1. a) x^2 + 6x + 27
b) 4x^2 - 4x + 1
c) x^2 - 4y^2
d) x^3 + 6x^2 + 12x + 8
e) x^3 - 9x^2 + 27x - 27
According to the rules of Major League Baseball, the infield must be 30 feet by 30 feet in a diamond shape with perpendicular (90°) corners. Answer the following questions regarding the shape of the infield.
Answer:
No Major League ballparks are exactly alike, but certain aspects of the field of play must be uniform across baseball.
The infield must be a square that is 90 feet on each side, and the outfield is the area between the two foul lines formed by extending two sides of said square (though the dirt portion of the field that runs well past the 90-foot basepaths in all Major League parks is also commonly referred to as the infield). The field must be constructed so that the bases are the same level as home plate.
The rulebook states that parks constructed by professional teams after June 1, 1958, must have a minimum distance of 325 feet between home plate and the nearest fence, stand or other obstruction on the right- and left-field foul lines, and 400 feet between home plate and the nearest fence, stand or other obstruction in center field. However, some clubs have been permitted to construct parks after that date with dimensions shorter than those specified.
The pitcher's plate must be a 24-inch by 6-inch slab of whitened rubber that is 10 inches above the level of home plate and 60 feet, 6 inches away from the back point of home plate. It is placed 18 inches behind the center of the mound -- which is erected within an 18-foot diameter circle -- and surrounded by a level area that is 5 feet by 34 inches. The slope of the pitcher's mound begins 6 inches in front of the pitcher's plate and must gradually decrease by 1 inch every foot for 6 feet in the direction of home plate.
Home plate is a 17-inch square of whitened rubber with two of the corners removed so that one edge is 17 inches long, two adjacent sides are 8 1/2 inches each and the remaining two sides are 12 inches each and set at an angle to make a point. The 17-inch side faces the pitcher's plate, and the two 12-inch edges coincide with the first- and third-base lines. The back tip of home plate must be 127 feet, 3 and 3/8 inches away from second base.
The other bases must be 15-inch squares that are between 3 and 5 inches thick, covered by white canvas or rubber and filled with soft material.
Step-by-step explanation:
The rules for two lines are y=x+2 and y=5 - 2x. At what point do they intersect?
Answer:
(1,3)
Step-by-step explanation:
SEE THE IMAGE FOR SOLUTION
HOPE IT HELPS
HAVE A GREAT DAY
D= -2
E = [1 2]
17. Multiply matrix D by matrix E.
A. 2
B. [
48]
5 101
C.-2-4
1 2
D.
5-2 1
4 2
Answer:
here's the answer to your question
3. The volume of a cube is 216 cm'. What is the length of one side?
O 6 cm
6 cm3
72 cm
O 72 cm
Answer:
6 cm
Step-by-step explanation:
6 cm×6cm×6cm=216 cm³
4. Find the center and radius of the circle given by this equation: x2 – 8x + y2 + 4y - 16 = 0
Answer:
Center ( 4 , -2) and r = 6
Step-by-step explanation:
x² - 8x + y² + 4y - 16 = 0
x² - 8x + y² + 4 y = 16
x²- 2*4x + y² + 2 *2y = 16
(x² - 2*4x + 16 ) - 16 + (y² + 2*2y + 4) -4 = 16
(x - 4)² + (y + 2)² = 16 + 16 + 4
(x - 4)² + (y -[-2])² = 36
(x- 4)² + ( y - [-2] )² = 6²
Compare with (x - h)²+ (y - k)² = r²
Center ( 4 , -2) and r = 6
Sonia works at a bakery. The function f(x) represents the amount of money Sonia earns per loaf, where x is the number of loaves she makes. The function g(x) represents the number of bread loaves Sonia bakes per hour, where x is the number of hours she works. Show all work to find f(g(x)), and explain what f(g(x)) represents.
f(x)=9x^2+1
g(x)=square root 2x^3
Answer:
18x^3+1
Step-by-step explanation:
since g(x)=√2x^3 and f(x)=9x^2+1 then
f(g(x))= 9(g(x))^2 +1 = 9(√2x^3)^2 +1 = 18x^3+1
this represents the amount of money Sonia earns baking loaves in x hours
The equation of f(g(x)) is [tex]f(g(x)) = 9(\sqrt{2x^3})^2 + 1[/tex], and it represents the amount of money Sonia makes when she bakes for x hours
The functions are given as:
[tex]f(x) = 9x^2 + 1[/tex]
[tex]g(x) = \sqrt{2x^3}[/tex]
Recall that:
[tex]f(x) = 9x^2 + 1[/tex]
Substitute g(x) for x
[tex]f(g(x)) = 9(g(x))^2 + 1[/tex]
Substitute [tex]g(x) = \sqrt{2x^3}[/tex]
[tex]f(g(x)) = 9(\sqrt{2x^3})^2 + 1[/tex]
Hence, the equation of f(g(x)) is [tex]f(g(x)) = 9(\sqrt{2x^3})^2 + 1[/tex]
Read more about composite functions at:
https://brainly.com/question/10687170
the square of 5 is divided by the cube root of 27. what is the remainder
Step-by-step explanation:
square of 5 is 25 and it divided by the cube root of 27 means 3
Now ,
#25÷3
= 8 [1] (•°• 3×8 = 24)
Here,
we got 1 as a reminder .
Hope it is helpful to you
✌️✌️✌️✌️✌️✌️✌️
The remainder will be 1.
What is Division method?Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications. For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.
Given that;
The square of 5 is divided by the cube root of 27.
Now,
Since, The square of 5 is divided by the cube root of 27.
Hence, We get;
⇒ 5² / ∛27
⇒ 25 / 3
After divide we get;
3 ) 25 ( 8
24
--------
1
Thus, The value of remainder = 1
Learn more about the divide visit:
https://brainly.com/question/28119824
#SPJ2
pls help pls pls pls pls
Answer:
B' - (3,1)
C' - (3,8)
D' - (6,-1)
Step-by-step explanation:
P varies directly with T and p=10 when T=500. When T=509, find T
Answer:
Let,
P= kT
P = 10, when T = 500
So, 10=k500
or, k=10/500
or, k=1/50
When T=509
P=kT
or, P=(1/50)×509
or, P=508/50
or, P = 10.18
And when P = 509 (since the question isn't clear)
509=(1/50)×T
or, T=509×50
or, T=25450
Hellllpppppp PLLLEASE! I need answer RIGHT NOW!!!!
Answer:
0.25 as a fraction is 25/100, which further simplified becomes 1/4
HELPPPP!!! FAST I WILL GIVE BRAINLIEST!!!!
Answer:
36% of the muffins sold were carrot.
Step-by-step explanation:
How many carrot muffins we have? 9
How many muffins we have in total? 25
So, 9/25. Convert 9/25 to percentage.
9/25 = 0.36
0.36×100
=36%
Answer:
36%
Step-by-step explanation:
Hello! I hope you are having a great day!! I am happy to help you with this problem.
We know that in total there were 25 muffins sold (you can count them) and 9 of which were carrot. This means that 9/25 of the muffins were carrot. Now we must turn 9/25 into a percentage.
9/25 * 100 = 0.36. 0.36 * 100 = 36%
And thats your answer!!
please help me
solve (x+3) (x+7)
Step-by-step explanation:
Here, we'll need to multiply these two values together. I'll use the expansion formula, which goes as follows:
[tex](a+b)(c+d)[/tex]
Expand[tex]ac + ad + bc + bd[/tex]
Lets apply this to the following equation:
[tex](x+3) (x+7)[/tex]
Expand.[tex](x*x) + (x * 7) + (3 * x) + (3 * 7)[/tex]
Simplify.[tex](x^2) + (7x) + (3x) + (21)[/tex]
Remove parenthesis and add.[tex]x^2+10x+21[/tex]
Answer:
x^2+10x+21
Plssss help plssssss
Answer:
True
Step-by-step explanation:
Just compare the numbers to the dots.
I hope this helps!
pls ❤ and give brainliest pls
Answer:
true
Step-by-step explanation:
The answer is true.
0_____ is
than all negative numbers.
Answer:
is whole number
Step-by-step explanation:
plz mrk me brainliest
Answer:
0 is larger than all negative numbers.
Step-by-step explanation:
When dealing with negative numbers, the number closer to zero is the bigger number. Zero (0) has the unique distinction of being neither positive nor negative.
factories 2x^3+ 7x^2+ 7x +2 emergency pls
hope it helps you...............
Answer:
the answer is (x+1)(x+2)(2x+1)
The path a character takes to navigate a level of a video game is given in the following graph.
What is the domain?
A. –4 ≤ x ≤ 8
B. –4 ≤ x ≤ 8, x ≠ 0, 4
C. –10 ≤ x ≤ 10
D. –10 ≤ x ≤ 10, x ≠ –4, 6
Option C is correct. The domain of the graph is –10 ≤ x ≤ 10.
The domain of a graph is the set of input values accepted by the function. They are values along the x-axis of the graph.
According to the graph shown, the values along the x-axis lies between -10 and 10. Hence the domain of the graph will be expressed as:
–10 ≤ x ≤ 10
Option C is correct. The domain of the graph is –10 ≤ x ≤ 10.
Learn more here: https://brainly.com/question/18486099
The radius of a circle is 16 ft. Find its area in terms of pi
Step-by-step explanatio
Find the number of gallons of sulferic acid in 50 gallons of solution in a tank, if the percent of sulfuric acid is 50%.
Answer:
25 gallons of sulfuric acid
Step-by-step explanation:
Find how much sulfuric acid is in the tank by finding 50% of 50 (the total gallons of solution):
50(0.5)
= 25
So, there are 25 gallons of sulfuric acid.
Evaluate the expression for c = 11.
-1 - C=
Answer:
c=-12
Step-by-step explanation:
place 11 in for C > -1-11=
subtract 11 from -1. -12
Which of the following numbers are irrational numbers? Please choose all that apply.
Question 2 options:
−67−−√
13
0.6
π
Which table has a constant of proportionality between y and x of 8/5
Answer:
A.) is my best guess
Step-by-step explanation:
Item 4
Luis reads the temperature of a solution in a lab experiment. The temperature of the solution is 5.6º F. After 6 hours, he reads the temperature of the solution again. The temperature of the solution is now −1.2°F .
Luis plots the points on the number line to determine the temperature change between these two readings.
What is the temperature change?
ANSWER:____° F
The temperature change after 6 hours is 6.8°F
Initial temperature = 5.6°F
Initial temperature = 5.6°FFinal temperature after 6 hours = -1.2°F
The temperature change can be calculated as the difference in the value of final and initial temperature.
Temperature change = (final temperature - initial temperature)
Temperature change = (5.6 - (-1.2))°F
Temperature change = (5.6 + 1.2)°F = 6.8°F
Hence, temperature change after 6 hours is 6.8°F
Learn more : https://brainly.com/question/15473063
Answer:
6.8
Step-by-step explanation:
k12
I really need help again.
Answer:
Y = -1/2X +4
Step-by-step explanation:
x1 y1 x2 y2
2 3 0 4
(Y2-Y1) (4)-(3)= 1 ΔY 1
(X2-X1) (0)-(2)= -2 ΔX -2
slope= - 1/2
B= 4
Y =-0.5X +4
