Answer:
The null hypothesis: [tex]\mathbf{H_o: p=0.27}[/tex]
The alternative hypothesis: [tex]\mathbf{H_1: p \neq 0.27}[/tex]
Test statistics : z = −2.30
P-value: = 0.02144
Decision Rule: Since the p-value is lesser than the level of significance; then we reject the null hypothesis.
Conclusion: We accept the alternative hypothesis and conclude that under the same circumstances the proportion of offspring peas will be yellow is not equal to 0.27
Step-by-step explanation:
From the given information:
Let's state the null and the alternative hypothesis;
Since The claim is that 27% of the offspring peas will be yellow.
The null hypothesis state that the proportion of offspring peas will be yellow is equal to 0.27.
i.e
[tex]\mathbf{H_o: p=0.27}[/tex]
The alternative hypothesis state that the proportion of offspring peas will be yellow is not equal to 0.27
[tex]\mathbf{H_1: p \neq 0.27}[/tex]
The test statistics:
we are given 437 green peas and 129 yellow apples;
Hence;
[tex]\hat p = \dfrac{x}{n}[/tex]
where ;
[tex]\hat p[/tex] = sample proportion
x = number of success
n = total number of the sample size
[tex]\hat p = \dfrac{129}{437+129}[/tex]
[tex]\hat p = \dfrac{129}{566}[/tex]
[tex]\mathbf{\hat p = 0.2279}[/tex]
Now; the test statistics can be computed as :
[tex]z = \dfrac { \hat p -p }{\sqrt {\dfrac{p(1-p)}{n} } }[/tex]
[tex]z = \dfrac {0.2279 -0.27 }{\sqrt {\dfrac{0.27(1-0.27)}{566} } }[/tex]
[tex]z = \dfrac {-0.043 }{\sqrt {\dfrac{0.27(0.73)}{566} } }[/tex]
[tex]z = \dfrac {-0.043 }{\sqrt {\dfrac{0.1971}{566} } }[/tex]
[tex]z = \dfrac {-0.043 }{\sqrt {3.48233216*10^{-4} } }[/tex]
[tex]z = \dfrac {-0.043 }{0.01866} }[/tex]
z = −2.30
C. P-value
P-value = P(Z < z)
P-value = P(Z< -2.30)
By using the P-value method and the normal distribution as an approximation to the binomial distribution.
from the table of standard normal distribution
move left until the first column is reached. Note the value as –2.0
move upward until the top row is reached. Note the value as 0.30
find the probability value as 0.010724 by the intersection of the row and column values gives the area to the left of
z = -2.30
P- value = 2P(z ≤ -2.30)
P-value = 2 × 0.01072
P - value = 0.02144
Decision Rule: Since the p-value is lesser than the level of significance; then we reject the null hypothesis.
Conclusion: We accept the alternative hypothesis and conclude that under the same circumstances the proportion of offspring peas will be yellow is not equal to 0.27
If A=2+i, O=-4, P=-i, and S=2+4i, find A-O+P+S.
==================================================
Work Shown:
A = 2+i
O = -4, this is the letter 'oh' not to be confused with the number zero
P = -i
S = 2+4i
A-O+P+S = (2+i) - (-4) + (-i) + (2+4i)
A-O+P+S = (2+i) + 4 + (-i) + (2+4i)
A-O+P+S = (2+4+2) + (i-i+4i)
A-O+P+S = 8+4i
Two ships are located 200 m and 300 m respectively from a lighthouse. If the angle formed by their paths to the lighthouse is 96°. What is the distance between the two ships?
Answer:its from applications of trignometry
The distance between the two ships is 377.54 m.
Given that, two ships are located 200 m and 300 m respectively from a lighthouse and the angle formed by their paths to the lighthouse is 96°.
We need to find the distance between the two ships.
What is the cosine rule to find the side?The cosine rule is c²=a²+b²-2abcosC
Now, c²=200²+300²-2×200×300cos96°
⇒c²=40000+90000-1,20,000×(-0.1045)
⇒c²=40000+90000+12,540
⇒c=377.54 m
Therefore, the distance between the two ships is 377.54 m.
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A rectangle is placed around a semicircle as shown below. The length of the rectangle is 14mm. Find the area of the shaded region. Use the value 3.14 for pi , and do not round your answer. Be sure to include the correct unit in your answer.
Image is missing, so i have attached it
Answer:
21.07 mm²
Step-by-step explanation:
We will use the Formulas:
Area of semicircle = πr²/2
Area_rectangle = Length x width = Lw
We are given:
Length of rectangle = 14 mm
From the attached image, the diameter of the semicircle is equal to the length of the rectangle.
Thus;
diameter of semicircle = length of rectangle
Therefore,
diameter of semicircle = 14 mm
Also, from the attached image, the radius of the semicircle is equal to the width of the rectangle.
Thus;
diameter of semicircle/2 = radius of semicircle
Hence;
radius of semicircle = 14/2 = 7mm = width of rectangle
Thus;
Area of rectangle = L*w = 14 × 7 = 98 mm²
Area of semicircle = πr²/2 = π×7²/2 = 76.93 mm²
To get the area of the shaded region, we will subtract area of the semi-circle from the area of the rectangle.
Area of shaded region = Area_rectangle - Area_semicircle = 98 - 76.93 = 21.07 mm²
Find the lateral area of the cone in terms of pi.
To find the lateral area of a cone, use this formula:
[tex]\pi r\sqrt{h^2+r^2}[/tex]
where r is the radius (in this case, 11) and h is the height (in this case, 26)
Try plugging the values in. If you need additional help, feel free to ask!
I promise I will mark as brainiest How many minutes is it before 12 noon, if 48 minutes ago it was twice as many minutes past 9 a.m.? i want step by step explanation
Answer:
9:00 am -------------------- 12:00pm ( There are 180 minutes between them)
Go 48 minutes back (132 Minutes between them)
That time is divided by 2
(4x minutes past 9:00 and x minutes left to reach 12:00)
132/3 = 44 minutes are left
OR
12:00- 44 minutes = 11:16
11:16-48 minutes =10:28
9 am + 88minutes (44 x 2) = 10:28
ANY ONE PLZ HELP 25 POINTS PROVE THAT x³+y³+z³-3xyz=(x+y+z)(x+ωy+ω²z)(x+ω²y+ωz)
Answer:
Proved
Step-by-step explanation:
Taking R.H.S
=> [tex](x+y+z)[x(x+w^2y+wz)+wy(x+w^2y+wz)+w^2z(x+w^2y+wz)][/tex]
=> [tex](x+y+z)(x^2+w^2xy+wxz+wxy+w^3y^2+w^2yz+w^2xz+w^4yz+w^3z^2)[/tex]
Remember ∴ ω³ = 1
So we'll replace all ω³'s with 1
=> [tex](x+y+z)(x^2+y^2+z^2+w^2xy+wxy+w^2yz+w^4yz+w^2xz+wxz)[/tex]
=> [tex](x+y+z)[x^2+y^2+z^2+xy(w^2+x)+w^2yz+w^3*wyz+xz(w^2+w)][/tex]
Remember ∴ ω²+ω = -1
=> [tex](x+y+z)[x^2+y^2+z^2+xy(-1)+yz(w^2+w)+xz(-1)][/tex]
=> [tex](x+y+z)(x^2+y^2+z^2-xy-yz-xz)[/tex]
According to formula:
x³+y³+z³-3xyz = [tex](x+y+z)(x^2+y^2+z^2-xy-yz-xz)[/tex]
So, it becomes
=> [tex]x^3+y^3+z^3-3xyz[/tex]
Please can somebody work out the mean? I'm struggling! <3
Step-by-step explanation:
The formulae for median is
N=£f/2 that is the sum of frequency divide by two
Median =Nth term + (N + 1)th term divide by two
first of all do the cumulative frequency which is
2+0=2
2+8=10
10+4=14
14+10=24
24+6=30
therefore N=£f/2
N=30/2
=15
when you use the formulae
it will be 15+(15+1)/2
then check the cumulative frequency the value close to the range of 15 and 16 which is 14
then you trace 14 back to the conceded goals
which is 2
then you add 2+2 and divide by two
which is= 2
therefore the median is 2
Mean
formulae
mean=conceded goals multiply by the frequency/sum of frequency
0*2=0.
1*8=8
2*4=8
3*10=30
4*6=24
total is 70
sum of frequency is 10
according to the formulae 70/10=7
therefore the mean is 7
Change each of the following angles in degrees to angles in radians
(d) 〖150〗^0 (e) 〖240〗^0 (f) 〖300〗^0
Answer:
d: 2.6179, e: 4.1887, f: 5.2359 all in rad
Step-by-step explanation:
(d): 150°degrees
150° × π / 180°
= 0.83333333333π rad
= 2.6179 rad
(e):240°degrees
240° × π / 180°
= 1.3333333333π rad
= 4.1887 rad
(f): 300°degrees
300° × π / 180°
= 1.6666666667π rad
= 5.2359 rad
If all my stuff is correct please give me an 5/5 and a thanks. :)
please help me 4 1/7 + 1/2
Answer:
Exact Form:65/14
Mixed number Form:4 9/14
Step-by-step explanation:
Answer:
4 9/14
as an improper fraction: 65/14
hopefully this helped :3
URGENT MATH PROBLEM!!!!!
Helppp!!!! please!!!
Answer:
[tex]\boxed{Area = 32.5 mm^2}[/tex]
Step-by-step explanation:
Area of Triangle = [tex]\frac{1}{2} (Base)(Height)[/tex]
Where base = 13 mm, Height = 5 mm
Area = 1/2 (13)(5)
=> Area = 1/2 (65)
=> Area = 32.5 mm^2
Answer:
c. 32.5 mm²
Step-by-step explanation:
The equation for the area of a triangle is a=1/2bh. In this equation you basically multiply the length of the base of the triangle times the height of the triangle and divide that by 2 to get the area. So, you would take 13, the base, and multiply it by 5, the height to get 65. Then, you would divide that by 2 to get 32.5 mm².
6z^6-21z^4-12z^2
give in step by step explanation
This expression cannot be simplified, as you cannot add or subtract variables raised to different exponents.
Answer:
Step-by-step explanation:
6z⁶ - 21z⁴ - 12z² = 2*3*z⁶ - 3*7*z⁴ - 4*3*z²
= 3z² (2z⁴ - 7z² - 4)
In the diagram below, AB is parallel to cd what is the value of x?
Answer:
45 degrees
Step-by-step explanation:
corresponding angles have are equal
Solve this a² ÷ a⁴ × a²
Step-by-step explanation:
a^4 - a^4 = (a^2 +a^2)(a^2-a^2)
a^4 - a^4 = (a^2 + a^2)(a+a)(a-a)
there is no need of this solution, because it equal to 0 because a^4 - a^4 will be equal then it will be 0
i hope this will help you
Answer:
Hello There!
~~~~~~~~~~~~~~~
a² ÷ a⁴ × a² =
1
Step-by-step explanation: Simplify the expression.
Hope this helped you! Brainliest would be nice!
☆_____________❤︎______________☆
Any point on the parabola can be labeled (x,y), as shown. What are the distances from the point (x,y) to the focus of the parabola and the directrix? Select two answers.
distance to the focus: (x+3)2+(y−3)2−−−−−−−−−−−−−−−√
distance to the focus: (x−2)2+(y+3)2−−−−−−−−−−−−−−−√
distance to the focus: (x+3)2+(y−2)2−−−−−−−−−−−−−−−√
distance to the directrix: |x−4|
distance to the directrix: |y−4|
distance to the directrix: |y+4|
Answer:
Step-by-step explanation:
Standard form of the equation:
y = [tex]-\frac{1}{4} (x+3)^2+3[/tex]
Directrix: y=4
Focus: (-3,2)
Points on the parabola (x,y):
(-5,2) (-3,3) (-1,2)
Distance from points to focus:
(-5,2) = (-3,2)
Answer choices: (x+3)^2+(y−3)^2, (x−2)2+(y+3)2, (x+3)2+(y−2)2
(-5+3)^2+(2-3)^2=5
(-5-2)^2+(2+3)^2=74
(-5+3)^2+(2-2)^2=4
(-1,2)
convert the following to a rectangular equation
x=3t+5
y=t^2-1
Answer:
y=2x-3, x=23.5
Step-by-step explanation:
This is what i got.
The rectangular form of equation is y= x² /9 - 10x/9 - 34/9.
What is Rectangular Equation?An equation made up of variables like x and y that can be plotted on a standard Cartesian plane is referred to as a rectangular equation or an equation in rectangular form.
Given:
x=3t+5.....(1)
y=t²-1.....(2)
From equation (1), we get
t= 1/3(x-5)
Now, put t in equation (2)
y= 1/9 (x- 5)² - 1
y = 1/9 x² - 25/9 -10x/ 9 - 1
y= x² /9 - 10x/9 - 34/9
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To write a fraction as a decimal, you divide the denominator by the numerator.
Answer:
"The decimal number is just a shorthand way of writing a fraction with a denominator of one thousand. It means the very same thing as . But this is just the algorithm for dividing the numerator by the denominator to get the decimal digits ."
Step-by-step explanation:
2/3 x +3 =1/4x-7
solve with work
Answer:
x=-24
Step-by-step explanation:
2/3 x +3 =1/4x-7
8/12x+3= 3/12x-7
5/12x + 3 = -7
5/12x = -10
5/12x (12/5) = -10(12/5)
x=-120/5
x=24
Find the measurement of both complementary angles, if One is 30° greater than the other one.
Answer:
30° and 60°
Step-by-step explanation:
Step 1: Write out equation
x + (x + 30) = 90
Step 2: Solve for x
2x + 30 = 90
2x = 60
x = 30
Step 3: Find other angle
90 - 30 = 60
Answer:
30 and 60
Step-by-step explanation:
Let x be one angle
x+30 is the other angle
Complementary angles add to 90
x+ x+30 = 90
2x+30 = 90
Subtract 30 from each side
2x=90-30
2x= 60
Divide by 2
2x/2 = 60/2
x = 30
The angles are 30 and 30+30 = 60
identify the reflection of the figure with vertices L(-5,15), M(-12,-36), and N(21,-11) across the y-axis. HELP ASAP please. answer choices r in photo
Answer:
The correct answer is:
L'(5,15), M'(12,-36), and N'(-21,-11)
Step-by-step explanation:
We are given the following points:
L(-5,15)
M(-12,-36) and
N(21,-11)
To find:
Reflection of the points across the y axis.
Solution:
To find the reflection of any point across y axis, we need to consider the y axis as the mirror and we need to find the location of the image in this manner.
Property of the image:
The image of point and actual point will be equidistant from the y axis.
If we find mirror image across y axis, there is change in only x coordinate value. There is no change in y axis value.
Let us take the first point:
L(-5,15)
x coordinate value -5 is on the left side of y axis.
The reflection will be 5 units on the right side of x axis
[tex]\therefore[/tex] L' (5, 15)
Let us take the second point:
M(-12,-36)
x coordinate value -12 is on the left side of y axis.
The reflection will be 12 units on the right side of x axis
[tex]\therefore[/tex] M'(12,-36)
Let us take the third point:
N(21,-11)
x coordinate value 21 is on the right side of y axis.
The reflection will be 21 units on the left side of x axis
[tex]\therefore[/tex] N'(-21,-11)
Please have a look at the attached figure for the points and their reflection.
Reflection triangles is shown as dotted line.
The correct answer is:
L'(5,15), M'(12,-36), and N'(-21,-11)
Today there are 3,431 thousand elementary and secondary teachers employed in a certain country. This number is expected to increase to 3,732 thousand teachers by the next decade. What is the percent increase?
A = old value = 3431
B = new value = 3732
C = percent change
C = [ (B-A)/A ] * 100%
C = [ (3732-3431)/3431 ] * 100%
C = (301/3431) * 100%
C = 0.0877 * 100%
C = 8.77%
Answer: Roughly an 8.77% increaseNote: if C was a negative value, then we'd have a percentage decrease
Which expressions is not polynomial
Answer: c
Step-by-step explanation:
HELPPPPPP ASAP!!!!!!!!!!!!!!!!!!!!!!! PLS DO NOT LOOK IT UP
Answer:
The constant proportionality of the table above is 16.
Step-by-step explanation:
In order to solve this problem, you must divide the weight of cat food by the number of bags. You must also continue doing this for each of the ratios shown in the table.
64 ÷ 4 = 16
80 ÷ 5 = 16
96 ÷ 6 = 16
So, the proportionality of the table is 16. As you can see, when we divided the numbers, they all had a quotient of 16, which is our proportion.
1. Which of the following sets of numbers could represent the lengths of the sides of an acute triangle?
A.4,5,8
b. 5,5,7
c. 6,6,14
d. 7,7,15
Answer:
C
Step-by-step explanation:
That would be an isosceles triangle, therefore, acute. All angles measure 60, therefore being acute. I'm not 100% sure though.
Will Give Brainliest and 5 star..... Please Help
Q. ε = {x: 2 ≤ x ≤30, x is an integer}, M = {even numbers}, P = {prime numbers}, T = {odd numbers} Find: (i) MUP (ii) M - T (iii) P∪(M∩T) (iv) P’U(M∩T’)
Answer:
(i)[tex]M \cup P=\{2,3,4,5,6,7,8,10,11,12,13,14,16,17,18,19,20,22,23,24,26,28,29,30\}[/tex]
(ii)M-T={2,4,6,8,10,12,14,16,18,20,22,24,26,28,30}
(iii)P∪(M∩T) = {2, 3, 5, 7, 11, 13, 17, 19, 23, 29}
(iv)P’U(M∩T’)={2,4,6,8,9,10,12,14,15,16,18,20,21,22,24,25,26,27,28,30}
Step-by-step explanation:
Given the sets:
ε = {x: 2 ≤ x ≤30, x is an integer}
M = {even numbers}={2,4,6,8,10,12,14,16,18,20,22,24,26,28,30}
P = {prime numbers}={2, 3, 5, 7, 11, 13, 17, 19, 23, 29}
T = {odd numbers} ={3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29}
(i)This is the union of sets M and P. (Do not repeat same elemnts)
[tex]M \cup P=\{2,3,4,5,6,7,8,10,11,12,13,14,16,17,18,19,20,22,23,24,26,28,29,30\}[/tex]
(ii)M-T: This is the set M less elements in set T.
Since [tex]M \cap T =\{\}[/tex], the set M-T=M.
M-T={2,4,6,8,10,12,14,16,18,20,22,24,26,28,30}
(iii) P∪(M∩T)
[tex]M \cap T =\{\}[/tex]
Therefore:
P∪(M∩T) = P
P∪(M∩T) = {2, 3, 5, 7, 11, 13, 17, 19, 23, 29}
(iv) P’U(M∩T’)
Since T is the set of odd numbers, its complement will be the set of even numbers.
T'=M={2,4,6,8,10,12,14,16,18,20,22,24,26,28,30}
M∩T’=M={2,4,6,8,10,12,14,16,18,20,22,24,26,28,30}
[tex]P' =\{4,6,8,9,10,12,14,15,16,18,20,21,22,24,25,26,27,28,30\}[/tex]
Therefore:
P’U(M∩T’) = {4,6,8,9,10,12,14,15,16,18,20,21,22,24,25,26,27,28,30} U {2,4,6,8,10,12,14,16,18,20,22,24,26,28,30}
={2,4,6,8,9,10,12,14,15,16,18,20,21,22,24,25,26,27,28,30}
What is the mean of: 3.7, 5, 9.2, 4, 6.1, 5, 2.6, 4, 5.2, 5?
Answer:
4.98
Step-by-step explanation:
Answer:
4.98
Step-by-step explanation:
Help me please, thanks again if you do :)
Answer: B) 6
Step-by-step explanation:
First let's distribute the left side of the equation.
k - 16 + 4k = -2(2k -1) + 6k
Then let's combine like terms on the left side of the equation.
5k - 16 = -2(2k - 1) + 6k
Then let's distribute the right side of the equation.
5k - 16 = -4k + 2 + 6k
Then let's combine like terms on the right side of the equation.
5k - 16 = 2k + 2
Then let's move all the x's to one side, and all the constants to the other.
3k = 18
Then divide both sides of the equation by 3.
k = 6
Hope it helps <3
Answer:
6
Step-by-step explanation:
k - 16 + 4k = -2(2k -1) + 6k
5k - 16 = -2(2k - 1) + 6k
5k - 16 = -4k + 2 + 6k
5k - 16 = 2k + 2
3k = 18
k = 6
I need help plz i will make u a brainllest
1.Identify the property that justifies the following statement: 31. 36.Find the value of x rounded to the nearest tenth. 38.Which statements could you use to conclude that JKLM is a parallelogram?
Answer: 1) C. Reflexive Property of Congruence
2) A. MD ≅ SG
3) C. 5.3
4) D. LK || MJ & JK ≡ LM
Step-by-step explanation:
1) An angle or side is congruent to itself by the Reflexive Property
2) TM ≡ LG Sides are congruent (given)
∠M ≡ ∠G Angles are congruent (given)
MD ≡ SG Sides are congruent
ΔTMD ≡ ΔLGS Side-Angle-Side (SAS) Theorem
Note: The angle must connect the two sides
3) Use similarity proportion
[tex]\dfrac{6}{x}=\dfrac{9}{8}\\\\\\48=9x\\\\\\\dfrac{48}{9}=x\\\\\\5.3=x[/tex]
4) In order to prove a polygon is a parallelogram, you must show
opposite sides are parallelopposite sides are congruentWhat is the total cost of troys order?
PLEASE HELP ME WITH THIS QUESTION :0
what is an slope? like in general
Answer:
A slope is a surface of which one end or side is at a higher level than another; a rising or falling surface
Step-by-step explanation: