Answer:
The answers are A. and B.
Step-by-step explanation:
Since the area of the largest square is 36. We need two numbers that equal 36. and A. had 6 and 30 so i picked it and it was right and B. is 28 and 8 which also equals 36. But, C. is 4 and 16 which is not 36. So A. and B. are the answers. Hope this helps! :)
We can use the Pythagorean theorem (a^2+b^2=c^2)(a
2
+b
2
=c
2
)left parenthesis, a, squared, plus, b, squared, equals, c, squared, right parenthesis to determine possible areas of the two smaller squares.
\text{Area of a square} =\text{side}^2Area of a square=side
2
start text, A, r, e, a, space, o, f, space, a, space, s, q, u, a, r, e, end text, equals, start text, s, i, d, e, end text, squared
So, we can substitute the areas of the squares that share side lengths with the triangle for a^2, b^2a
2
,b
2
a, squared, comma, b, squared and c^2c
2
c, squared in the Pythagorean theorem.
Hint #22 / 6
For example, in the diagram above, the area of the square that shares a side with the hypotenuse is 363636 square units. So, c^2=36c
2
=36c, squared, equals, 36.
Hint #33 / 6
Let's fill in the possible values to see if they make the equation true.
\begin{aligned} a^2 + b^2 &= c^2 \\\\ a^2 + b^2 &= 36 \\\\ 6 + 30 &\stackrel{\large?}{=}36 \\\\ 36 &\stackrel{\checkmark}{=}36\\\\ \end{aligned}
a
2
+b
2
a
2
+b
2
6+30
36
=c
2
=36
=
?
36
=
✓
36
The sum of the areas of the squares connected to the two shorter triangle sides is equal to the area of the square connected to the longest side.
So, 666 and 303030 could be the areas of the smaller squares.
Hint #44 / 6
\begin{aligned} a^2 + b^2 &= c^2 \\\\ a^2 + b^2 &= 36 \\\\ 8 + 28 &\stackrel{\large?}{=}36 \\\\ 36 &\stackrel{\checkmark}{=}36\\\\ \end{aligned}
a
2
+b
2
a
2
+b
2
8+28
36
=c
2
=36
=
?
36
=
✓
36
The sum of the areas of the squares connected to the two shorter triangle sides is equal to the area of the square connected to the longest side.
So, 888 and 282828 could be the areas of the smaller squares.
Hint #55 / 6
\begin{aligned} a^2 + b^2 &= c^2 \\\\ a^2 + b^2 &= 36 \\\\ 4 + 16 &\stackrel{\large?}{=}36 \\\\ 20 &\neq 36\\\\ \end{aligned}
a
2
+b
2
a
2
+b
2
4+16
20
=c
2
=36
=
?
36
=36
The sum of the areas of the squares connected to the two shorter triangle sides is not equal to the area of the square connected to the longest side.
So, 444 and 161616 could not be the areas of the smaller squares.
Hint #66 / 6
The area of the smaller squares could be:
666 and 303030
888 and 2828
which of the following is equivalent to the expression below? log2-log14 A. LOG(1/7) B. LOG(-12) C. LOG 12 D. LOG 7
Answer:
The answer is option A.
Step-by-step explanation:
Using the properties of logarithms
that's
[tex] log(x) - log(y) = log( \frac{x}{y} ) [/tex]
log 2 - log 14 is
[tex] log(2) - log(14) = log( \frac{2}{14} ) [/tex]
Simplify
We have the final answer as
[tex] log( \frac{1}{7} ) [/tex]
Hope this helps you
Answer:
log ( 1/7)
Step-by-step explanation:
log2-log14
We know that log ( a/b) = log a - log b
log (2 /14)
log ( 1/7)
A company manufacturing oil seals wants to establish X and R control charts on the process. There are 25 preliminary samples of size 5 on the internal diameter of the seal. The summary data (in mm) are as follows:
sigma^25_i = 1 X_t = 1, 253.75, sigma^25_i = 1 R_i = 14.08
(a) Find the control limits that should be used on the X and R control charts. For n = 5, A2 = 0.577, D4 = 2.114, D3 = 0
(b) Assume that the 25 preliminary samples plot in control on both charts. Estimate the process mean and standard deviation.
Answer:
A ) i) X control chart : upper limit = 50.475, lower limit = 49.825
ii) R control chart : upper limit = 1.191, lower limit = 0
Step-by-step explanation:
A) Finding the control limits
grand sample mean = 1253.75 / 25 = 50.15
mean range = 14.08 / 25 = 0.5632
Based on X control CHART
The upper control limit ( UCL ) =
grand sample mean + A2* mean range ) = 50.15 + 0.577(0.5632) = 50.475
The lower control limit (LCL)=
grand sample mean - A2 * mean range = 50.15 - 0.577(0.5632) = 49.825
Based on R control charts
The upper limit = D4 * mean range = 2.114 * 0.5632 = 1.191
The lower control limit = D3 * mean range = 0 * 0.5632 = 0
B) estimate the process mean and standard deviation
estimated process mean = 50.15 = grand sample mean
standard deviation = mean range / d2 = 0.5632 / 2.326 = 0.2421
note d2 is obtained from control table
Compute the least-squares regression line for predicting y from a given the following summary statistics. Round final answers to four decimal places, as needed.
xbar = 8.8 sx = 1.5 sy = 1.8 ybar = 30.3
r = -0.84
Download data
Regression line equation: y = ______ + _______ x
Answer: Regression line equation: [tex]\hat{y}=-1.008x+39.1704[/tex]
Step-by-step explanation:
Equation of least-squares regression line for predicting y :
[tex]\hat{y}=b_1x+b_o[/tex]
, where [tex]\text{Slope} (b_1)=r\dfrac{s_y}{s_x}[/tex] , [tex]\text{intercept}(b_0)=\bar{y}-b_1\bar{x}[/tex]
Given: [tex]\bar{x}=8.8,\ s_x=1.5,\ s_y=1.8,\ \bar{y}=30.3,\ r=-0.84[/tex]
Then,
[tex]b_1=(-0.84)\dfrac{ 1.8}{ 1.5}\\\\\Rightarrow\ b_1=-1.008[/tex]
Now,
[tex]b_0=30.3-(-1.008)(8.8)=30.3+8.8704\\\\\Rightarrow\ b_0=39.1704[/tex]
Then, Regression line equation: [tex]\hat{y}=-1.008x+39.1704[/tex]
Researchers recorded that a certain bacteria population declined from 800,000 to 500,000 in 6 hours after the administration of medication. At this rate of decay, how many bacteria would there have been at 24 hours? Round to the nearest whole number
Answer:
We can assume that the decline in the population is an exponential decay.
An exponential decay can be written as:
P(t) = A*b^t
Where A is the initial population, b is the base and t is the variable, in this case, number of hours.
We know that: A = 800,000.
P(t) = 800,000*b^t
And we know that after 6 hours, the popuation was 500,000:
p(6h) = 500,000 = 800,000*b^6
then we have that:
b^6 = 500,000/800,000 = 5/8
b = (5/8)^(1/6) = 0.925
Then our equation is:
P(t) = 800,000*0.925^t
Now, the population after 24 hours will be:
P(24) = 800,000*0.925^24 = 123,166
Answer:
122,070 bacteria.
Step-by-step explanation:AA0ktA=500,000=800,000=?=6hours=A0ekt
Substitute the values in the formula.
500,000=800,000ek⋅6
Solve for k. Divide each side by 800,000.
58=e6k
Take the natural log of each side.
ln58=lne6k
Use the power property.
ln58=6klne
Simplify.
ln58=6k
Divide each side by 6.
ln586=k
Approximate the answer.
k≈−0.078
We use this rate of growth to predict the number of bacteria there will be in 24 hours.
AA0ktA=?=800,000=ln586=24hours=A0ekt
Substitute in the values.
A=800,000eln586⋅24
Evaluate.
A≈122,070.31
At this rate of decay, researchers can expect 122,070 bacteria.
Determine which of the following statements is true. A: If V is a 6-dimensional vector space, then any set of exactly 6 elements in V is automatically a basis for V. B: If there exists a set that spans V, then dim V = 3. C: If H is a subspace of a finite-dimensional vector space V, then dim H ≤ dim V
Answer:
A. This statement A is false.
B. This statement A is false.
C. This statement is true .
Step-by-step explanation:
Determine which of the following statements is true.
From the statements we are being given , we are to determine if the statements are valid to be true or invalid to be false.
SO;
A: If V is a 6-dimensional vector space, then any set of exactly 6 elements in V is automatically a basis for V
This statement A is false.
This is because any set of exactly 6 elements in V is linearly independent vectors of V . Hence, it can't be automatically a basis for V
B. If there exists a set that spans V, then dim V = 3
The statement B is false.
If there exists a set , let say [tex]v_1 ...v_3[/tex], then any set of n vector (i.e number of elements forms the basis of V) spans V. ∴ dim V < 3
C. If H is a subspace of a finite-dimensional vector space V then dim H ≤ dim V is a correct option.
This statement is true .
We all know that in a given vector space there is always a basis, it is equally important to understand that there is a cardinality for every basis that exist ,hence the dimension of a vector space is uniquely defined.
SO,
If H is a subspace of a finite-dimensional vector space V then dim H ≤ dim V is a correct option.
Find the solution(s) of the system of equations: x2 + y2 = 8 y = x – 4 options: (–2,–6) (2,–2) and (–2,–6) (2,–2) No solutions
Answer: x=2 y=-2
(2,-2) one solution
Step-by-step explanation:
Solve by substitution
[tex]\begin{bmatrix}x^2+y^2=8\\ y=x-4\end{bmatrix}[/tex]
[tex]\mathrm{Subsititute\:}y=x-4[/tex]
[tex]\begin{bmatrix}x^2+\left(x-4\right)^2=8\end{bmatrix}[/tex]
[tex]2x^2-8x+16=8[/tex]
[tex]\mathrm{Isolate}\:x\:\mathrm{for}\:2x^2-8x+16=8:\quad x=2[/tex]
[tex]\mathrm{For\:}y=x-4[/tex]
[tex]\mathrm{Subsititute\:}x=2[/tex]
[tex]y=2-4[/tex] [tex]2-4=-2[/tex]
[tex]y=-2[/tex]
[tex]The\:solutions\:to\:the\:system\:of\:equations\:are[/tex]
[tex]x=2,\:y=-2[/tex]
Need Help with these (Giving brainiest if you can solve these)
Answer: try using sine for this equasion
Step-by-step explanation:
You have $50,000 in savings for retirement in an investment earning 5% annually. You aspire to have $1,000,000 in savings when you retire. Assuming you add no more to your savings, how many years will it take to reach your goal?
Answer: It will take you about 61 years for you to reach your goal.
Step-by-step explanation:
We will represent this situation by an exponential function. So if you earn 5% yearly then we could represent it by 1.05.So in exponential function we need to find the initial value and the common difference and in this case the common difference is 1.05 and the initial value or amount is 50,000 dollars.
We could represent the whole situation by the equation.
y= [tex]50,000(1.05)^{x}[/tex] where x is the number of years. so if you aspire to have 1,000,000 in some years then we will put in 1 million dollars for y and solve for x.
1,000,000 = 50,000(1.05)^x divide both sides by 50,000
20 = (1.05)^x
x= 61.40
here are the 2 questions in the 2 pics separated lol
Answer:
60 and 87
Step-by-step explanation:
Question 1: The chance of losing would be 100% - 40% = 60%.
Question 2: Again, we just have to do 100% - 13% = 87%.
Answer:
Below
Step-by-step explanation:
First question:
Jade has a 40% chance of winnig wich could be expressed as 2/5
The chance of losing is the remainning pourcentage from 100%
●100-40 =60%
60% is the chance of losing wich could be expressed as 3/5
The sum of 3/5 and 2/5 is 1 so it's true.
■■■■■■■■■■■■■■■■■■■■■■■■■
Same method for the 2nd question:
The person has a 13 % chance of winning.
The chance of losing is 87%
● 100-13 =87
The numbers of regular season wins for 10 football teams in a given season are given below. Determine the range, mean, variance, and standard deviation of the population data set.
2, 10, 15, 4, 11, 10, 15, 10, 2, 10
Answer:
a
[tex]R =13[/tex]
b
[tex]\= x =8.9[/tex]
c
[tex]var(x) = 16.57[/tex]
d
[tex]\sigma = 4.1[/tex]
Step-by-step explanation:
From the question we are given a data set
2, 10, 15, 4, 11, 10, 15, 10, 2, 10
The sample size is n = 10
The range is
[tex]R = maxNum - MinNum[/tex]
Where maxNum is the maximum number on the data set which is 15
and MinNum is the minimum number on the data set which is 2
So
[tex]R = 15 - 2[/tex]
[tex]R =13[/tex]
The mean is mathematically represented as
[tex]\= x = \frac{\sum x_i}{N}[/tex]
substituting values
[tex]\= x = \frac{2 + 10 + 15 + 4 + 11 + 10 + 15 + 10 + 2 + 10 }{10}[/tex]
[tex]\= x =8.9[/tex]
The variance is mathematically evaluated as
[tex]var(x) = \frac{\sum (x - \= x)^2}{N}[/tex]
substituting values
[tex]var(x) = \frac{(2 - 8.9 )^2 + (10 - 8.9 )^2 + (15 - 8.9 )^2 +(4 - 8.9 )^2 +(11 - 8.9 )^2 +(10 - 8.9 )^2 +(15 - 8.9 )^2 +(10 - 8.9 )^2 +} {10}[/tex] [tex]\frac{(2 - 8.9 )^2 +(10 - 8.9 )^2 }{10}[/tex]
[tex]var(x) = 16.57[/tex]
The standard deviation is [tex]\sigma = \sqrt{var(x)}[/tex]
substituting values
[tex]\sigma = \sqrt{16.57}[/tex]
[tex]\sigma = 4.1[/tex]
4km in the ratio 9:4:7
Answer:
500km
Step-by-step explanation:
add all the proportions and then divide by 3. with conversion.
Section 8
Find the mean of these numbers:
24 18
37
82 17
26
Answer:
[tex]\boxed{Mean = 34.33}[/tex]
Step-by-step explanation:
Mean = Sum of Observations / No. Of Observations
Mean = (24+18+37+82+17+26)/6
Mean = 206 / 6
Mean = 34.33
what is the length of bc in the right triangle below?
Answer: A) 15
Step-by-step explanation:
Because of Pythagorean Theorem, 9^2+12^2=BC^2. Thus, 81+144=BC^2. Thus, 225=BC^2. Thus, 15=BC.
Hope it helps, and ask if you want further clarification <3
what is the sum of 1 2/5 and 5 3/4
Answer:
[tex]7\frac{3}{20}[/tex]
Step-by-step explanation:
Hey there!
Well to add this we need to pu it in improper form.
7/5 + 23/4
Now we need to find the LCM.
5 - 5, 10, 15, 20, 25, 30
4 - 4, 8, 12, 16, 20, 24, 28
So the LCD is 20.
Now we need to change the 5 and 4 to 20.
5*4 = 20
7*4 = 28
28/20
4*5=20
23*5=115
115/20
Now we can add 28 and 115,
= 143/20
Simplified
7 3/20
Hope this helps :)
Answer:
[tex] \boxed{7 \frac{3}{20} }[/tex]Step-by-step explanation:
[tex] \mathrm{1 \frac{2}{5} + 5 \frac{3}{4} }[/tex]
Add the whole numbers and fractional parts of the mixed numbers separately
[tex] \mathrm{ = (1 + 5) + ( \frac{2}{5} + \frac{3}{4} })[/tex]
Add the numbers
[tex] \mathrm{=6 + ( \frac{2}{5} + \frac{3}{4} )}[/tex]
Add the fractions
[tex] \mathrm{=6 + (\frac{2 \times 4 + 3 - 5}{20} )}[/tex]
[tex] \mathrm{=6 + \frac{23}{20} }[/tex]
Convert the improper fractions into a mixed number
[tex] \mathrm{=6 + 1 \frac{3}{20} }[/tex]
Write the mixed number as a sum of the whole number and the fractional part
[tex] \mathrm {= 6 + 1 + \frac{3}{20} }[/tex]
Add the numbers
[tex] \mathrm{ = 7 + \frac{3}{20} }[/tex]
Write the sum of the whole number and the fraction as a mixed number
[tex] \mathrm{ = 7 \frac{3}{20} }[/tex]
Hope I helped
Best regards!
URGENT!!!!!! A 5 inch × 7 inch photograph is placed inside a picture frame. Both the length and width of the frame are 2x inches larger than the width and length of the photograph. Which expression represents the perimeter of the frame? REPLY IN COMMENTS PLEASE IM GLITCHING AND CANT SEE ANSWERS
Answer:
the perimeter of the square is just "(5+2x)(2)+(7+2x)(2)
Step-by-step explanation:
Answer:
2 × 10 + 2 × 14
Step-by-step explanation:
The frame is given to have measurements 2 times that of the photograph's measurements. We also know that the photograph is given by dimensions being 5 inch by 7 inch. Therefore the measurements of the frame should be 5 [tex]*[/tex] 2, which = 10 inches, by 7 [tex]*[/tex] 2 = 14 inches.
So the dimensions of the frame are 10 inch × 14 inch. As the frame is present as a rectangle, the perimeter is given by two times both dimensions together. That would be represented by the expression " 2 × 10 inch + 2 × 14 inch. " In other words you can say that the expression is 2 × 10 + 2 × 14 - the expression that represents the perimeter of the frame.
Using Pascal’s Theorem, expand the expression 〖(2x-y)〗^3
Answer:
(2x - y)³ = 8x³ - 12x²y + 6xy² - y³
Step-by-step explanation:
Pascal's Theorem uses a set of already known and easily obtainable numbers in the expansion of expressions. The numbers serve as the coefficients of the terms in the expanded expression.
For the expansion of
(a + b)ⁿ
As long as n is positive real integer, we can obtain the coefficients of the terms of the expansion using the Pascal's triangle.
The coefficient of terms are obtained starting from 1 for n = 0.
- For the next coefficients of terms are 1, 1 for n = 1.
- For n = 2, it is 1, 2, 1
- For n = 3, it is 1, 3, 3, 1
The next terms are obtained from the previous one by writing 1 and summing the terms one by one and ending with 1.
So, for n = 4, we have 1, 1+3, 3+3, 3+1, 1 = 1, 4, 6, 4, 1.
The Pascal's triangle is
1
1 1
1 2 1
1 3 3 1
1 4 6 4 1
1 5 10 10 5 1
1 6 15 20 15 6 1
1 7 21 35 35 21 7 1
1 8 28 56 70 56 28 8 1
1 9 36 84 126 126 84 36 9 1
The terms can also be obtained from using the binomial theorem and writing the terms from ⁿC₀ all through to ⁿCₙ
So, for n = 3, the coefficients are 1, 3, 3, 1
Then the terms are written such that the sum of the powers of the terms is 3 with one of the terms having the powers reducing from n all through to 0, and the other having its powers go from 0 all through to n
So,
(2x - y)³ = [(1)(2x)³(-y)⁰] + [(3)(2x)²(-y)¹] + [(3)(2x)¹(-y)²] + [(1)(2x)⁰(-y)³]
= (1×8x³×1) + (3×4x²×-y) + (3×2x×y²) + (1×1×-y³)
= 8x³ - 12x²y + 6xy² - y³
Hope this Helps!!!
What is the complete factorization of 36y2 − 1?
Answer:
36y² - 1
Factorize
We have the final answer as
[tex](y - \frac{1}{6} )(36y + 6)[/tex]
Hope this helps you
If one termite can destroy 1.2mg of wood per day, how many kilograms of wood can 10 termites destroy in 1 week? *Can someone please explain how to do this*
Answer:
10 termites will destroy 0.000084kg of wood per week
Step-by-step explanation:
Convert milligram to kilogram
1.2mg=(1.2 / 1,000,000)kg
1.2mg=0.0000012kg
1 termite destroys=0.0000012kg per day
10 termites will destroy (per day) =0.0000012×10 termites per day
10 termites in one day will destroy=0.000012kg
There are 7 days in a week
Therefore,
10 termites will destroy=destruction per day × 7 days
=0.000012×7
=0.000084kg per week
In triangle abc what is the value of cos b A 5/13 B 12/13 C 5/12 D 13/12
Answer:
[tex]\boxed{Option \ B}[/tex]
Step-by-step explanation:
In the triangle,
Hypotenuse = 13
Opposite = Perpendicular = 5
Adjacent = Base = 12
Now,
Cos B = [tex]\frac{Adjacent}{Hypotenuse}[/tex]
Cos B = 12/13
If the triangle is just like in the attached file!
Answer:
B) 12/13
Step-by-step explanation:
x(x+3)(x+3)=0 Please I NEED HELP FAST! PLLLLLLLLLLLLLLLLLLLLLLLLLLEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEAAAAAAAAAAAAAAAAAAAAAAAAAAAAASSSSSSSSSSSSSSSSSSSSSSSSSSEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEE!
Answer:
[tex]\boxed{x^3+6x^2+9x}[/tex]
Step-by-step explanation:
[tex]x(x+3)(x+3)[/tex]
Resolving the first parenthesis
[tex](x^2+3x) (x+3)[/tex]
Using FOIL
[tex]x^3+3x^2+3x^2+9x[/tex]
Adding like terms
[tex]x^3+6x^2+9x[/tex]
[tex]\text{If } \: a\cdot b \cdot c = 0 \text{ then } a=0 \text{ or } b =0 \text{ or } c=0 \text{ or all of them are equal to zero.}[/tex]
[tex]x(x+3)(x+3) =0[/tex]
[tex]\boxed{x_1 =0}[/tex]
[tex]x_2+3 =0[/tex]
[tex]\boxed{x_2 = -3}[/tex]
[tex]x_3+3 =0[/tex]
[tex]\boxed{x_3 = -3}[/tex]
What is the value of x in the diagram below?
A.
6
B.
4
C.
5
D.
3
Answer:
[tex]\boxed{3}[/tex]
Step-by-step explanation:
We can use ratios to solve since the sides are proportional.
[tex]\frac{18}{x} =\frac{48}{8}[/tex]
Cross multiply.
[tex]48x=18 \times 8[/tex]
Divide both sides by 48.
[tex]\frac{48x}{48} = \frac{18 \times 8}{48}[/tex]
[tex]x=3[/tex]
The value of x in the given triangle is 3.
What are similar triangles?Two triangles are similar if they have the same ratio of corresponding sides and equal pair of corresponding angles.
Given are two similar triangles,
Therefore, they have the same ratio of corresponding sides
18/48 = x/8
x = 3
Hence, The value of x in the given triangle is 3.
For more references on similar triangles, click;
https://brainly.com/question/25882965
#SPJ2
Find the probability of each of the following, if Z~N(μ = 0,σ = 1).
(please round any numerical answers to 4 decimal places)
a) P(Z > -1.13) =
b) P(Z < 0.18) =
c) P(Z > 8) =
d) P(| Z | < 0.5) =
Answer: a) 0.8708, b) 5714, c) 0.000, d) 0.3830
Step-by-step explanation:
(a)
To find P(Z>-1.13):
Since Z is negative, it lies on left hand side of mid value.
Table of Area Under the Standard Normal Curve gives area = 0.3708
So,
P(Z>-1.13) = 0.5 + 0.3708 = 0.8708
(b)
To find P(Z<0.18):
Since Z is positive, it lies on right hand side of mid value.
Table of Area Under the Standard Normal Curve gives area = 0.0714
So,
P(Z<0.18) = 0.5 + 0.0714 = 0.5714
(c)
To find P(Z>8):
Since Z is positive, it lies on right hand side of mid value.
Table of Area Under the Standard Normal Curve gives area = 0.5 nearly
So,
P(Z>8) = 0.5 - 0.5 nearly = 0.0000
(d)
To find P(| Z | < 0.5)
that is
To find P(-0.5 < Z < 0.5):
Case 1: For Z from - 0.5 to mid value:
Table of Area Under the Standard Normal Curve gives area = 0.1915
Case 2: For Z from mid value to 0.5:
Table of Area Under the Standard Normal Curve gives area = 0.1915
So,
P(| Z | < 0.5) = 2 * 0.1915 = 0.3830
The Probability can be determine using z-Table. The z- table use to determine the area under the standard normal curve for any value between the mean (zero) and any z-score.
(a) The value of [tex]P(z>-1.13)=0.8708[/tex].
(b) The value of [tex]P(Z < 0.18) = 0.5714[/tex].
(c) The value of [tex]P(Z > 8) = 0.0000[/tex].
(d) The value of [tex]P(| Z | < 0.5) =0.3830[/tex].
Given:
The given condition is [tex]Z\sim N(\mu= 0,\sigma = 1).[/tex]
(a)
Find the value for [tex]P(Z > -1.13)[/tex].
Here Z is less than 1 that means Z is negative. So it will lies it lies on left hand side of mid value.
Refer the table of Area Under the Standard Normal Curve.
[tex]\rm Area = 0.3708[/tex].
Now,
[tex]P(Z > -1.13)=0.5 + 0.3708 = 0.8708[/tex]
Thus, the value of [tex]P(z>-1.13)=0.8708[/tex].
(b)
Find the value for [tex]P(Z < 0.18)[/tex].
Here Z is positive. So it will lies it lies on right hand side of mid value.
Refer the table of Area Under the Standard Normal Curve.
[tex]\rm Area = 0.0714[/tex].
Now,
[tex]P(Z <0.18)=0.5 + 0.0714 = 0.5714[/tex]
Thus, the value of [tex]P(Z < 0.18) = 0.5714[/tex].
(c)
Find the value for [tex]P(Z >8)[/tex].
Here Z is positive. So it will lies it lies on right hand side of mid value.
Refer the table of Area Under the Standard Normal Curve.
[tex]\rm Area \approx 0.5[/tex].
Now,
[tex]P(Z >8)\approx0.5 - 0.5 = 0.0000[/tex]
Thus, the value of [tex]P(Z > 8) = 0.0000[/tex].
(d)
Find the value for [tex]P(|Z| <0.05)[/tex].
Here Z is mod of Z, it may be positive or negative. Consider the negative value of Z.
Refer the table of Area Under the Standard Normal Curve.
[tex]\rm Area =0.1915[/tex].
Consider the positive value of Z.
Refer the table of Area Under the Standard Normal Curve.
[tex]\rm Area =0.1915[/tex].
Now,
[tex]P(|Z| <0.5)=2\times 0.1915 = 0.3830[/tex]
Thus, the value of [tex]P(| Z | < 0.5) =0.3830[/tex].
Learn more about z-table here:
https://brainly.com/question/16051105
a box contains 20 blue marbes, 16 green marbles, and 14 red marbles. two marbles are selected at random. let 3 be the event that first marbke selected is green. find p(fe) g
Answer:
Let E be the event that the first marble selected is green. Let F be the event that the second marble selected is green. A box contains 20 blue marbles, 16 green marbles and 14 red marbles P(F/E)=15/49 because if the first marble selected is green there are 49 in total and 15 are green. I think this is it.
Step-by-step explanation:
An estimator is said to be consistent if: the difference between the estimator and the population parameter grows smaller as the sample size grows larger. it is an unbiased estimator. the variance of the estimator is zero. the difference between the estimator and the population parameter stays the same as the sample size grows larger.
Answer:
the difference between the estimator and the population parameter grows smaller as the sample size grows larger.
Step-by-step explanation:
In Statistics, an estimator is a statistical value or quantity, which is used to estimate a parameter.
Generally, parameters are the determinants of the probability distribution. Thus, to determine a normal distribution we would use the parameters, mean and variance of the population.
An estimator is said to be consistent if the difference between the estimator and the population parameter grows smaller as the sample size grows larger. This simply means that, for an estimator to be consistent it must have both a small bias and small variance.
Also, note that the bias of an estimator (b) that estimates a parameter (p) is given by; [tex]E(b) - p[\tex]
Hence, an unbiased estimator is an estimator that has an expected value that is equal to the parameter i.e the value of its bias is equal to zero (0).
A sample variance is an unbiased estimator of the population variance while the sample mean is an unbiased estimator of the population mean.
Generally, a consistent estimator in statistics is one which gives values that are close enough to the exact value in a population.
22,403 Check:
- 8,675
how i do this
Answer:
Hello!! :) The answer to your question is 13,728
Steps will be below.
Step-by-step explanation:
So we will subtract 22,403 and 8,675.
When we do that we will get 13,728
To check your answer we have to do the opposite of subtracting which will be adding.
This is how we check our work: the answer we got was 13,728...we have to take that answer and add it to 8,675 which will give us 22,403
(Both of the numbers are from the question)
At the bottom I attached a picture of how I did the subtracting and how I checked my work.
Sorry for my handwriting......if you can’t understand my handwriting, I attached another picture which is more clearer.
ANSWER TO YOUR QUESTION: 13,728
Brainliest would be appreciated! Thank you :3
Hope this helps! :)
Answer:
The answer is 13,728
Step-by-step explanation:
Check your work with addition.
solve for inequality
ᶜ⁄₋₃ ≥ 3
Answer:
c ≤ -9
Step-by-step explanation:
c / -3 ≥ 3
c ≤ -9
Remember, we flip the sign of the inequality by multiplying / dividing by a negative number.
Answer:
c ≤ -9
Step-by-step explanation:
c / -3 ≥ 3
c ≤ -9
Find the volume V of the solid obtained by rotating the region bounded by the given curves about the specified line.? y = 2 + sec(x), −π/3 ≤ x ≤ π/3, y = 4; about y = 2
Answer:
The volume of the solid is: [tex]\mathbf{V = \pi [ \dfrac{8 \pi}{3} - 2\sqrt{3}]}[/tex]
Step-by-step explanation:
GIven that :
[tex]y = 2 + sec \ x , -\dfrac{\pi}{3} \leq x \leq \dfrac{\pi}{3} \\ \\ y = 4\\ \\ about \ y \ = 2[/tex]
This implies that the distance between the x-axis and the axis of the rotation = 2 units
The distance between the x-axis and the inner ring is r = (2+sec x) -2
Let R be the outer radius and r be the inner radius
By integration; the volume of the of the solid can be calculated as follows:
[tex]V = \pi \int\limits^{\dfrac{\pi}{3}}_{\dfrac{-\pi}{3}} [(4-2)^2 - (2+ sec \ x -2)^2]dx \\ \\ \\ V = \pi \int\limits^{\dfrac{\pi}{3}}_{\dfrac{-\pi}{3}} [(2)^2 - (sec \ x )^2]dx \\ \\ \\ V = \pi \int\limits^{\dfrac{\pi}{3}}_{\dfrac{-\pi}{3}} [4 - sec^2 \ x ]dx[/tex]
[tex]V = \pi [4x - tan \ x]^{\dfrac{\pi}{3}}_{\dfrac{-\pi}{3}} \\ \\ \\ V = \pi [4(\dfrac{\pi}{3}) - tan (\dfrac{\pi}{3}) - 4(-\dfrac{\pi}{3})+ tan (-\dfrac{\pi}{3})] \\ \\ \\ V = \pi [4(\dfrac{\pi}{3}) - tan (\dfrac{\pi}{3}) + 4(\dfrac{\pi}{3})- tan (\dfrac{\pi}{3})] \\ \\ \\ V = \pi [8(\dfrac{\pi}{3}) - 2 \ tan (\dfrac{\pi}{3}) ][/tex]
[tex]\mathbf{V = \pi [ \dfrac{8 \pi}{3} - 2\sqrt{3}]}[/tex]
A magazine article states that the mean weight of one-year-old boys is the same as that of one-year-old girls. Does the confidence interval contradict this statement? The confidence interval this statement
Answer:
Yes, the confidence interval contradict this statement.
Step-by-step explanation:
The complete question is attached below.
The data provided is:
[tex]n_{1}=318\\n_{2}=297\\\bar x_{1}=25\\\bar x_{2}=24.1\\s_{1}=3.6\\s_{2}=3.8[/tex]
Since the population standard deviations are not provided, we will use the t-confidence interval,
[tex]CI=(\bar x_{1}-\bar x_{2})\pm t_{\alpha/2, (n_{1}+n_{2}-2)}\cdot s_{p}\cdot\sqrt{\frac{1}{n_{1}}+\frac{1}{n_{2}}}[/tex]
Compute the pooled standard deviation as follows:
[tex]s_{p}=\sqrt{\frac{(n_{1}-1)s_{1}^{2}+(n_{2}-1)s_{2}^{2}}{n_{1}+n_{2}-2}}=\sqrt{\frac{(318-1)(3.6)^{2}+(297-1)(3.8)^{2}}{318+297-2}}=2.9723[/tex]
The critical value is:
[tex]t_{\alpha/2, (n_{1}+n_{2}-2)}=t_{0.05/2, (318+297-2)}=t_{0.025, 613}=1.962[/tex]
*Use a t-table.
The 95% confidence interval is:
[tex]CI=(\bar x_{1}-\bar x_{2})\pm t_{\alpha/2, (n_{1}+n_{2}-2)}\cdot s_{p}\cdot\sqrt{\frac{1}{n_{1}}+\frac{1}{n_{2}}}[/tex]
[tex]=(25-24.1)\pm 1.962\times 2.9723\times \sqrt{\frac{1}{318}+\frac{1}{297}}\\\\=0.90\pm 0.471\\\\=(0.429, 1.371)\\\\\approx (0.43, 1.37)[/tex]
The 95% confidence interval for the difference between the mean weights is (0.43, 1.37).
To test the magazine's claim the hypothesis can be defined as follows:
H₀: There is no difference between the mean weight of 1-year old boys and girls, i.e. [tex]\mu_{1}-\mu_{2}=0[/tex].
Hₐ: There is a significant difference between the mean weight of 1-year old boys and girls, i.e. [tex]\mu_{1}-\mu_{2}\neq 0[/tex].
Decision rule:
If the confidence interval does not consists of the null value, i.e. 0, the null hypothesis will be rejected.
The 95% confidence interval for the difference between the mean weights does not consists the value 0.
Thus, the null hypothesis will be rejected.
Conclusion:
There is a significant difference between the mean weight of 1-year old boys and 1-year old girls.
Solve the equation using the distributive property and properties of equality.
1/2(x+6) = 18
What is the value of x?
O 6
O7 1/2
O 14 1/2
0 30
Answer:
x = 30
Step-by-step explanation:
1/2(x+6) = 18
Expand brackets or use distributive law.
1/2(x) + 1/2(6) = 18
1/2x + 6/2 = 18
1/2x + 3 = 18
Subtract 3 on both sides.
1/2x + 3 - 3 = 18 - 3
1/2x = 15
Multiply both sides by 2.
(2)1/2x = (2)15
x = 30
Answer:
30
Step-by-step explanation:
State the degrees of freedom error in each of the following tests. (a) A consultant measures job satisfaction in a sample of 14 supervisors, 14 managers, and 14 executives at a local firm. (b) A researcher tests how nervous public speakers get in front of a small, medium, or large audience. Ten participants are randomly assigned to each group. (c) A high school counselor has 8 students in each of five classes rate how much they like their teacher.
Answer:
.
Step-by-step explanation: