Answer:
The decision Rule is
Reject the null hypothesis
The conclusion is
There is sufficient evidence to states that tim and per's mutations lead to different mean copulation duration.
The test statistics is [tex]z =-2.2187[/tex]
Step-by-step explanation:
From the question we are told that
The Mutation Mean copulation duration is for per [tex]\= x_1 = 17.5[/tex]
The Mutation Mean copulation duration is for tim [tex]\= x_2 = 19.9[/tex]
The Mutation Standard deviation copulation duration for is per [tex]s _1 = 3.37[/tex]
The Mutation Standard deviation copulation duration for is tim [tex]s _2 = 2.47[/tex]
The sample size for per is [tex]n_1 = 14[/tex]
The sample size for tim is [tex]n_2 = 17[/tex]
The null hypothesis is [tex]H_o : \mu_1 = \mu_2[/tex]
The alternative hypothesis is [tex]H_a : \mu_1 \ne \mu_2[/tex]
Generally the test statistics is mathematically represented as
[tex]z = \frac{\=x_1 - \= x_2 }{ \sqrt{\frac{s_1^2 }{n_1} + \frac{s_2^2 }{n_2} } }[/tex]
=> [tex]z = \frac{17.5 - 19.9 }{ \sqrt{\frac{3.37^2 }{14} + \frac{2.47^2 }{17} } }[/tex]
=> [tex]z =-2.2187[/tex]
From the z table the area under the normal curve to the left corresponding to -2.2187 is
[tex]P(Z < -2.2187) = 0.013254[/tex]
Generally the p-value is mathematically represented as
[tex]p-value = 2 * P(Z <-2.2187 )[/tex]
=> [tex]p-value = 2 * 0.013254[/tex]
=> [tex]p-value = 0.02651[/tex]
Let assume that the level of significance is [tex]\alpha = 0.05[/tex]
So
From the value obtained we see that [tex]p-value < \alpha[/tex] hence
The decision Rule is
Reject the null hypothesis
The conclusion is
There is sufficient evidence to states that tim and per's mutations lead to different mean copulation duration.
Determine whether a quadratic model exists for each set of values. If so, write the model.
f(-2)=16, f(0)=0, f(1)=4
Answer:
[tex]f(x)=4x^2[/tex]
Step-by-step explanation:
Quadratic Model
The quadratic function can be expressed in the form:
[tex]f(x)=ax^2+bx+c[/tex]
Where a,b, and c are constants to be determined using the points through which the function passes.
We have the points (-2,16) (0,0) (1,4). To find the values of a,b,c we just substitute the values of x and y and solve the system of equations.
Point (0,0):
[tex]f(0)=a*0^2+b*0+c=0[/tex]
It follows that
c=0
Point (-2,16):
[tex]f(0)=a*(-2)^2+b*(-2)+c=16[/tex]
Operating:
[tex]a*(4)+b*(-2)+c=16[/tex]
Since c=0:
[tex]4a-2b=16[/tex]
Divide by 2:
[tex]2a-b=8\qquad\qquad [1][/tex]
Point (1,4):
[tex]f(1)=a*(1)^2+b*(1)+c=4[/tex]
[tex]a*(1)+b*(1)+c=4[/tex]
Since c=0:
[tex]a+b=4\qquad\qquad [2][/tex]
Adding [1] + [2]:
2a+a=12
3a=12
a=12/3=4
a=4
From [2]
b=4-a
b=4-4=0
b=0
The model is:
[tex]\boxed{f(x)=4x^2}[/tex]
How to solve m(2x-5) = 9x-k STEP BY STEP
Which equations are true?
Choose all answers that apply:
Α)
-X = -x + 3 +0
B)
-X = 0 +(-x)
с)
None of the above
Answer:
B
Step-by-step explanation:
Any value of x would make the equation true.
What is (1.7x10^4)x(8.5x10^-2) in standard form
Answer:
1.445 × 10³
Step-by-step explanation:
Standard form is a way of writing a small number or a large number easily.
We should give the final answer in standard form.
1) (1.7 × 10⁴) × (8.5 × 10⁻²)
We enter this directly into the calculator to obtain a solution.
= 1445
We write this in standard form we have :
1.445 × 10³
Answer:
1.445 × 10³ hope it helped goodluck!
15 is what percent of 90
Jordan weighed two buckets of sand for a geology project. The first bucket weighed 26.31 pounds. The other bucket weighed 4.39 pounds. How much do the two buckets of sand weigh all together?
Answer:
30.7
Step-by-step explanation:
Find the measure of angle b.
Answer:
angle b=36
Step-by-step explanation:
angle b = 90-54=36 (given b+54+90)
Given the function f(x) = 4 - 2x: If the domain is {-4,0, 5), find the range.
A)
{-4, 4,-6)
B)
{-4, 4, 14)
C)
{12, 4, -6}
D)
{12, 4, 14)
Answer:
C) -4,4,-6
Step-by-step explanation:
domain is x so plug the domain numbers into the function
4-2(-4)=12
4-2(0)=4
4-2(5)=-6
Therefore Range is (-4,4,-6)
HELPPP . sorry for cracked. screen.. Identify w as either rational or irrational
, and approximate to the tenths place. (4
points)
Answer:
Irrational: √2 = 1.4
Step-by-step explanation:
Choose an answer and tell me why u chose it
9514 1404 393
Answer:
(D) (170 -4x)°
Step-by-step explanation:
Angles 1 and 5 are corresponding, so are congruent. Angle 6 forms a linear pair with angle 5, so is its supplement. That is, angle 6 is the supplement of angle 1:
∠6 = 180° -(4x +1)° = (180 -1)° -4x°
∠6 = (179 -4x)° . . . . matches choice D
(W+4)(3w-2) please solveeed
Step-by-step explanation:
[tex]{:}\longrightarrow[/tex][tex]\sf (w+4)(3w-2)[/tex]
[tex]{:}\longrightarrow[/tex][tex]\sf w(3w-2)+4 (3w-2)[/tex]
[tex]{:}\longrightarrow[/tex][tex]\sf 3w^2-2w+12w-8[/tex]
[tex]{:}\longrightarrow[/tex][tex]\sf 3w^2+10w-8 [/tex]
greatest common factor of 24, 36, and 50
Answer:
The greatest common factor of 24, 36, and 50 is 2.
Step-by-step explanation:
Factors of 24 are 1, 2, 3, 4, 6, 8, 12, 24
Factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, 36
Factors of 50 are 1, 2, 5, 10, 25, 50
Therefore the GCF is 2.
We can see that 2 is the only common factor, hence the greatest common factor of 24, 36, and 50 is 2
For us to get the greatest common factor of 24, 36, and 50, we need to get their individual factor first as shown:
24 = 2 * 12
36 = 2 * 18
50 = 2 * 25
From all the factors, we can see that 2 is the only common factor, hence the greatest common factor of 24, 36, and 50 is 2
Learn more: https://brainly.com/question/219464
three examples of equations where there will be no solution.
Answer:
5x = 3x
4+8t-y=y-t+8
98/r=34t
Step-by-step explanation:
hope this helps!
mark me brainliest plz!
What is the answer to x - 10 + -6 + 4
Answer: x-12
Step-by-step explanation:
Simplify.
x
−
1
0
−
6
+
4
x−10−6+4
2 Collect like terms.
x
+
(
−
1
0
−
6
+
4
)
x+(−10−6+4)
3 Simplify.
x
−
1
2
x−12
PLS HELP THX PLS jrkdkekmc
Answer: No
Step-by-step explanation:
The c kind of cut off, but you can use slopes to figure it out. The rule for a perpendicular slope is the opposite reciprocal. Assuming that C is the right angle, since right triangles typically work that way, we can figure out the slopes for ac and bc. The slopes are not reciprocals:
AC= -5/2
BC= -1/3
This isn't a right triangle because the lines are not perpendicular.
3(x-1) – 1= - 7x
2 3
I need help please
if y⁻⁴ = 256 then y will be
Answer:
y = 1/4
Step-by-step explanation:
y⁻⁴ = 256
(1/y)⁴ = 256
y⁴ = 1/256
y = ⁴√1/256
y = 1/4
Thus, The value of y is 1/4
-TheUnknownScientist
Solve the Inequality:
Answer:
z > 4
Step-by-step explanation:
- 2z - 3 < 5
- 2z < 5 + 3
- 2z < 8
z > - 4
Answer:
z > -4
Step-by-step explanation:
Please see the following attachment for step by step
Jeremy's password is the combination of letters and numbers shown below. He
wants to know the ratio of letters to numbers in this password. Use Jeremy's
password to write the ratio THREE different ways. (Hint: think about the different
formats) 27 R Q A58 E 3 (plz help I know the problem mightseem long but not really)
Answer:
numbers:letters
5:4 (numbers:letters form)
Step-by-step explanation:
There are 5 numbers in the password and 4 letters
Hopefully this helps :)
2) Zoe was practicing for a marathon. She practiced for six days, running
four miles each day. How many miles did Zoe run altogether?
Answer: zoe ran 24 miles
Zach has a basic cell phone plan that does not include texting. He is going to add a texting package to his cell phone plan. He has two choices of texting packages, A and B. Package A charges $0.15 per text with no monthly fees for the texting package. Package B charges $0.10 per text, but has a $10 monthly fee for the texting package. Write an equation that represents the total cost for each texting package if any amount of texts are sent. Be sure to define the variables you are using for your equation.
Answer:
bababoeybababoey
Step-by-step explanation:
Answer: STUPID
Step-by-step explanation:
2r-7 = r + 15,
Find R
Answer: 22
Step-by-step explanation:
2r - 7 = r + 15
2r - r = 15 + 7
2r = 22
r = 22/2
r = 11
find the value of x of given figure and solve this question step by step plzz help question number D
Answer:
x=15 cm
Step-by-step explanation:
The two triangles in the diagram are:
ABC and BDC
First we have to find the third side (hypotenuse) of BDC so that we can use it to find the value of x.
Hypotenuse is the largest side of a triangle which is usually in front of the right angle.
So in BDC
[tex]Base = BD =10cm\\Hypotenuse = BC = ?\\Perpendicular = CD = 2\sqrt{11}cm[/tex]
Applying Pythagoras theorem:
[tex](Hypotenuse)^2 = (Base)^2 + (Perpendicular)^2\\BC^2 = BD^2 + CD^2\\BC^2 = (10)^2 + (2\sqrt{11})^2\\BC^2 = 100+(2^2 * 11)\\BC^2 = 100+(4*11)\\BC^2 = 100+44\\BC^2 = 144\\\sqrt{BC^2} = \sqrt{144}\\BC = 12cm[/tex]
Solving for triangle ABC
[tex]Base = BC = 12 cm\\Perpendicular = AB = 9 cm\\Hypotenuse = AC = x\\[/tex]
Applying Pythagoras theorem
[tex]AC^2 = BC^2+AB^2\\x^2 = (12)^2 + (9)^2\\x^2 = 144+81\\x^2 = 225\\\sqrt{x^2} = \sqrt{225}\\x = 15cm[/tex]
Hence,
x=15 cm
In parallelogram ABCD, if AO = 4x + 12 and OC = 5x – 6 what is the
****length of AC (be careful)
Answer:
Step-by-step explanation:
The sides of a parallelogram are equal. If O is the midpoint of its diagonal AC, them AO+OC = AC
Given
AO = 4x + 12 and
OC = 5x – 6
Required
AC
AC = 4x+12 + 5x-6
AC = 4x+5x+12-6
AC = 9x+6
Hence the length of AC is 9x+6
An estimate for - ✓ 72 is
A.- 8.1
b. - 8.5
c. -9.1
d. -9.5
What will happen to the graph of the line y = -54x + 3 if you change -54 to 54?
Answer:
Graph the line using the slope and y-intercept, or two points.
Slope:
1
y-intercept: ( 0 , 0 ) x y 0 0 1 1
I NEED HELP ASAP!!!! PLS HELP ME. WILL MARK THE FIRST ANSWER BRAINLIEST!!!
Answer:
I am too young for this type of math, but I suggest you try M-a-t-h w-a-y
a stock has a price of $58.63. This is $5.92 less than the price of stock yesterday. Write and solve an equation to find the price p (in dollars) of the stock yesterday.
Answer:
$52.71
Step-by-step explanation:
Today's price= $58.63
Yesterday's price= y
Difference= $5.92
y+5.92 = 58.63
y = 58.63 - 5.92
= $52.71
Elias’s teacher has given him a rectangle that is 15 feet by 20 feet. She has asked him to create a new rectangle using a scale factor of 8/3. Elias says that will be a reduction because the scale factor is a fraction. Is he correct?
Answer:
Yes
Step-by-step explanation:
Because for every 8 feet of the original rectangles, it will be 3 feet on the scale model, therefore it is reducing.
Answer:
Elias is not correct, A scale factor of 8/3 is an enlargement because it is greater than 1.
A reduction has a scale factor between
0 and 1.
(Verified answer)
The width of a rectangle is 3 cm less than twice its length. If the perimeter of the
rectangle is 18 cm, find its dimensions.
Answer:
length=4
Width=2×4-3=5
Step-by-step explanation:
Let length =X
Width =2x-3
Perimeter=18
2(length+width)=18
2(X+2x-3)=18
3x-3=9
3x=12
X=12/3
X=4
So length=4
Width=2×4-3=5
Answer:
[tex] \huge{ \boxed{ \bold{ \sf{Length \: = \: 4 \: cm}}}}[/tex]
[tex] \huge{ \boxed{ \bold{ \sf{Width = 5 \: cm}}}}[/tex]
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☯ Question :
The width of a rectangle is 3 cm less than twice its length. If the perimeter of the rectangle is 18 cm, find its dimensions.☯ Step - by - step explanation :
✒ First, Let length of a rectangle be ' L '.
✑ Given :
Width of a rectangle = 3 cm less than twice its length ( i.e W = 2L - 3 )Perimeter of a rectangle ( P ) = 18 cm☞ Finding value of length of a rectangle :
[tex] \boxed{ \sf{Perimeter \: of \: a \: rectangle = 2(L + W)}}[/tex]
Plug the values and solve for L
➺ [tex] \sf{18 = 2(L+ 2L - 3)}[/tex]
➺ [tex] \sf{18 = 2(3L - 3)}[/tex] { Add : 2L and L )
➺ [tex] \sf{18 = 6L - 6}[/tex] { Distribute 2 through the parentheses )
➺ [tex] \sf{6L - 6 = 18}[/tex] { Swipe the sides of the equation }
➺ [tex] \sf{6L = 18 + 6}[/tex] { Move 6 to right hand side and change it's sign )
➺ [tex] \sf{6L = 24}[/tex] { Add the numbers : 18 and 6 }
➺ [tex] \sf{ \frac{6L}{6} = \frac{24}{6}} [/tex] { Divide both sides by 6 }
➺ [tex] \boxed{ \sf{length \: ( \: L\: ) \: = \: 4 \: cm}}[/tex]
☞ Now , Evaluating 2L - 3 when L = 4 cm in order to find the value of width of a rectangle : [tex] \sf{2l - 3}[/tex]
➺ [tex] \sf{2 \times 4 - 3}[/tex] { Plug the value of length }
➺ [tex] \sf{8 - 3}[/tex] { Multiply 2 by 4 }
➺ [tex] \boxed{ \sf{Width \: ( \: W \: ) \: = \: 5 \: cm}}[/tex]
Hence ,
Length of a rectangle ( L ) = 4 cmWidth of a rectangle ( W ) = 5 cmHope I helped!
Have a wonderful day! ツ
~TheAnimeGirl ♡
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