Answer:
[tex]74.8m[/tex]
Step-by-step explanation:
[tex]A=a^2\\P=4a\\P=4\sqrt{A} \\=4*\sqrt{349.69} \\=74.8m[/tex]
4. The average annual income of 100 randomly chosen residents of Santa Cruz is $30,755 with a standard deviation of $20,450. a) What is the standard deviation of the annual income? b) Test the hypothesis that the average annual income is $32,000 against the alternative that it is less than $32,000 at the 10% level. c) Test the hypothesis that the average annual income is equal to $33,000 against the alternative that it is not at the 5% level. d) What is the 95% confidence interval of the average annual income?
Answer:
a) The standard deviation of the annual income σₓ = 2045
b)
The calculated value Z = 0.608 < 1.645 at 10 % level of significance
Null hypothesis is accepted
The average annual income is greater than $32,000
c)
The calculated value Z = 1.0977 < 1.96 at 5 % level of significance
Null hypothesis is accepted
The average annual income is equal to $33,000
d)
95% of confidence intervals of the Average annual income
(26 ,746.8 ,34, 763.2)
Step-by-step explanation:
Given size of the sample 'n' =100
mean of the sample x⁻ = $30,755
The Standard deviation = $20,450
a)
The standard deviation of the annual income σₓ = [tex]\frac{S.D}{\sqrt{n} }[/tex]
= [tex]\frac{20,450}{\sqrt{100} }= 2045[/tex]
b)
Given mean of the Population μ = $32,000
Given size of the sample 'n' =100
mean of the sample x⁻ = $30,755
The Standard deviation ( σ)= $20,450
Null Hypothesis:- H₀: μ > $32,000
Alternative Hypothesis:H₁: μ < $32,000
Level of significance α = 0.10
[tex]Z = \frac{x^{-}-mean }{\frac{S.D}{\sqrt{n} } }[/tex]
[tex]Z = \frac{30755-32000 }{\frac{20450}{\sqrt{100} } }[/tex]
Z= |-0.608| = 0.608
The calculated value Z = 0.608 < 1.645 at 10 % level of significance
Null hypothesis is accepted
The average annual income is greater than $32,000
c)
Given mean of the Population μ = $33,000
Given size of the sample 'n' =100
mean of the sample x⁻ = $30,755
The Standard deviation ( σ)= $20,450
Null Hypothesis:- H₀: μ = $33,000
Alternative Hypothesis:H₁: μ ≠ $33,000
Level of significance α = 0.05
[tex]Z = \frac{x^{-}-mean }{\frac{S.D}{\sqrt{n} } }[/tex]
[tex]Z = \frac{30755-33000 }{\frac{20450}{\sqrt{100} } }[/tex]
Z = -1.0977
|Z|= |-1.0977| = 1.0977
The 95% of z -value = 1.96
The calculated value Z = 1.0977 < 1.96 at 5 % level of significance
Null hypothesis is accepted
The average annual income is equal to $33,000
d)
95% of confidence intervals is determined by
[tex](x^{-} - 1.96 \frac{S.D}{\sqrt{n} } , x^{-} + 1.96 \frac{S.D}{\sqrt{n} })[/tex]
[tex](30755 - 1.96 \frac{20450}{\sqrt{100} } , 30755 +1.96 \frac{20450}{\sqrt{100} })[/tex]
( 30 755 - 4008.2 , 30 755 +4008.2)
95% of confidence intervals of the Average annual income
(26 ,746.8 ,34, 763.2)
Let f(x) = -2x + 7 and g(x) = -6x + 3. Find fg and state its domain.
Answer:
f(g(x))=12x+1
Step-by-step explanation:
f(g(x)) = -2(-6x+3)+7
f(g(x))= 12x-6+7
f(g(x))=12x+1
Domain: All real numbers
Find the amount to which $2,500 will grow if interest of 6.75% is compounded quarterly for 10
years.
Find the amount to which $2,500 will grow if interest of 6.75% is compounded daily for 10
years.
Answer:
Part a
For this case n = 4. If we use the future value formula we got:
[tex] A= 2500 (1+ \frac{0.0675}{4})^{4*10}= 4882.506[/tex]
Part b
For this case n = 365. If we use the future value formula we got:
[tex] A= 2500 (1+ \frac{0.0675}{365})^{365*10}= 4909.776[/tex]
Step-by-step explanation:
We can use the future vaue formula for compound interest given by:
[tex] A= P(1+ \frac{r}{n})^{nt}[/tex]
Where P represent the present value, r=0.0675 , n is the number of times that the interest is compounded in a year and t the number of years.
Part a
For this case n = 4. If we use the future value formula we got:
[tex] A= 2500 (1+ \frac{0.0675}{4})^{4*10}= 4882.506[/tex]
Part b
For this case n = 365. If we use the future value formula we got:
[tex] A= 2500 (1+ \frac{0.0675}{365})^{365*10}= 4909.776[/tex]
A farmer was interest in determining how many grasshoppers were in his field. He knows that the distribution of grasshoppers may not be normally distributed in his field due to growing conditions. As he drives his tractor down each row he counts how many grasshoppers he sees flying away. After several rows he figures the mean number of flights to be 57 with a standard deviation of 12. What is the probability of the farmer will count 52 or fewer flights on average in the next 40 rows down which he drives his tractor
Answer:
= 0.0041
Step-by-step explanation:
Given that:
A farmer was interest in determining how many grasshoppers were in his field. He knows that the distribution of grasshoppers may not be normally distributed in his field due to growing conditions. As he drives his tractor down each row he counts how many grasshoppers he sees flying away
mean number of flights to be 57
a standard deviation of 12
fewer flights on average in the next 40 rows
[tex]\mu = 57\\\\\sigma=12\\\\n=40[/tex]
so,
[tex]P(x<52)[/tex]
[tex]=P(\frac{x-\mu}{\sigma/\sqrt{n} } <\frac{52-57}{12/\sqrt{40} } )\\\\=P(z<\frac{-5\times6.325}{12} )\\\\=P(z<\frac{-31.625}{12})\\\\=P(z<-2.64)[/tex]
using z table
= 0.0041
The probability of the farmer will count 52 or fewer flights on average in the next 40 rows down which he drives his tractor is 0.0041 and this can be determined by using the properties of probability.
Given :
The distribution of grasshoppers may not be normally distributed in his field due to growing conditions.The mean number of flights to be 57 with a standard deviation of 12.The probability of the farmer will count 52 or fewer flights on average in the next 40 rows down which he drives his tractor, can be determined by using the following calculations:
[tex]\rm P(x<52)=P\left (\dfrac{x-\mu}{\dfrac{\sigma}{\sqrt{n} }}<\dfrac{52-57}{\dfrac{12}{\sqrt{40} }}\right)[/tex]
[tex]\rm P(x<52)=P\left (z<\dfrac{-5\times 6.325}{12 }}\right)[/tex]
[tex]\rm P(x<52)=P\left (z<\dfrac{-31.625}{12 }}\right)[/tex]
[tex]\rm P(x<52)=P\left (z<-2.64\right)[/tex]
Now, using z-table:
P(x < 52) = 0.0041
For more information, refer to the link given below:
https://brainly.com/question/21586810
2. {5.0A.A.1, 5.0A.A.2} Write an expression to show....the product of eight
and two, minus the product of three and four. *
Answer:
[tex]\left ( 8\times 2 \right )-\left ( 3\times 4 \right )[/tex]
Step-by-step explanation:
Given: The statement is ' the product of eight and two, minus the product of three and four'
To find: expression for the given statement
Solution:
An algebraic expression is an expression consists of coefficients, variables, and the arithmetic operations.
Product of eight and two = [tex]\left ( 8\times 2 \right )[/tex]
Product of three and four = [tex]\left ( 3\times 4 \right )[/tex]
Therefore,
Product of eight and two, minus the product of three and four = [tex]\left ( 8\times 2 \right )-\left ( 3\times 4 \right )[/tex]
Aakash has a liability of 6000 due in four years. This liability will be met with payments of A in two years and B in six years. Aakash is employing a full immunization strategy using an annual effective interest rate of 5%.Calculate |A-B|
Answer:
|A-B|= 586.411565Step-by-step explanation:
We know that = Liability
[tex]PLiability= \frac{6000}{1.05^{4} }[/tex]
[tex]\frac{6000}{1.05^{4} }=\frac{A}{1.05^{2} }+\frac{B}{1.05^{6} }\\\\6000(1.05^{2} ) = (1.05^{4} ) +B\\B= 6000(1.05^{2} )-(1.05^{4} )----------(1)\\\\[/tex]
dAssets =dLiability
[tex]4=2*\frac{\frac{A}{1.05^2} }{\frac{6000}{1.05^4} } +6*\frac{\frac{B}{1.05^6} }{\frac{6000}{1.05^4} } \\4={\frac{6000}{1.05^4}= 2*\frac{A}{1.05^2} +6*\frac{B}{1.05^6}\\\\4[6000(1.05^2)]= 2*A(1.05^4)+6*B[/tex]
From equation 1 we have
[tex]4[6000(1.05^2)]= 2*A(1.05^4)+6*6000(1.05^2)-6*A(1.05^4)\\4*A(1.05^4)=2*6000(1.05^2)\\A=\frac{2*6000(1.05^2)}{4*(1.05^4)} \\A=272.088435\\[/tex]
Going back to equation 1 we have
[tex]B= 6000(1.05^2)-A(1.05^4)\\B= 3307.5\\|A-B|= |2721.088435-3307.5|= 586.411565[/tex]
For a long-distance person-to-person telephone call, a telephone company charges $ 0.72 for the first minute, $ 0.42 for each additional minute, and a $ 1.85 service charge. If the cost of a call is $ 8.03 comma how long did the person talk?
Answer:
13 mins
Step-by-step explanation:
8.03- 1.85= 6.18
-.72=5.46
/.42=13
The tallest church tower in the Netherlands is the Dom Tower in Utrecht. If the angle of elevation to the top of the tower is 77° when 25.9 m from the base, what is the height of the Dom Tower to the nearest metre.
Answer:
Height of the Dom is 112.18 m.
Step-by-step explanation:
The tallest church tower in the Netherlands is the Dom Tower in Utrecht. The angle of elevation to the top of the tower is 77° when 25.9 m from the base. It is required to find the height of the Dom Tower. Let its height is h. So, using trigonometric formula to find it as :
[tex]\tan\theta=\dfrac{h}{b}\\\\\tan(77)=\dfrac{h}{25.9}\\\\h=\tan(77)\times 25.9\\\\h=112.18\ m[/tex]
So, the height of the Dom is 112.18 m.
An insurance policy pays a total medical benefit consisting of two parts for each claim. Let X represent the part of the benefit that is paid to the surgeon, and let Y represent the part that is paid to the hospital. The variance of X is 5000, the variance of Y is 10,000, and the variance of the total benefit, X + Y, is 17,000. Due to increasing medical costs, the company that issues the policy decides to increase X by a flat amount of 100 per claim and to increase Y by 10% per claim. Calculate the variance of the total benefit after these revisions have been made
Answer:
= 19300
Step-by-step explanation:
Each claim consists of two parts = X + Y
where
X = the benefit that is paid to the surgeon and
Y = benefit that is paid to the hospital
V(X) = 5000, V(Y) = 10000 and V(X+Y) = 17000
So V(X+Y) = V(X) + V(Y) + 2cov(X,Y)
17000 = 5000 + 10000 +2 cov(X,Y)
17000 -15000 = 2cov(X,Y)
2000 = 2cov(X,Y)
cov(X,Y) = 1000
Now X is increased by flat Rs. 100 per claim and Y by 10% per claim
total benefit = X+100+Y+0.1Y = X+100 + 1.1Y
V(total benefit) = V(X) + 1.1²V(Y) +2(1.1)cov(X,Y) [ V(aX+bY)
= a²V(X) +b²V(Y) +2abcov(X,Y) and V(X+c) = V(X)]
= 5000 + (1.21*10000) + (2.2*1000)
= 5000 + 12100 + 2200
= 19300
Which of the following sets would have a graph with an open circle on 5 and a ray pointing right on the number line?
The open circle means we do not include the endpoint, hence the use of a greater than symbol. If we were to include the endpoint, then we'd have greater than or equal to. We can rule out choice B due to this reasoning.
The ray pointing to the right indicates we are talking about x values larger than 5, so we can rule out choice A and conclude the answer is C.
Side note: The notation [tex]x \in \mathbb{R}[/tex] is saying "x is a real number"
2 Points
Which is a kingdom?
O A. Prokarya
B. Protista
C. Mammalia
O D. Chordata
Answer:
Protista
Step-by-step explanation:
Archaebacteria.
Eubacteria.
Protista.
Fungi.
Plantae.
Animalia.
These are the 6 kingdoms
What is the value of d21+d22+d23 given the matrix equation below?
Answer:
B. 8
Step-by-step explanation:
The question lacks the required diagram. Find the diagram in the attachment.
Before we can find d21, d22 and d23, we need to get the matrix D first as shown in the attached solution.
On comparison as shown in the attachment, d21 = 11, d22 = -10 and d23 = 7
Note that d21 refers to element in the second row and first column of the matrix
d22 is the element in the second row and second column of the matrix
d23 is the element in the second row and third column of the matrix
d21+d22+d23 = 11-10+7
d21+d22+d23 = 8
The second option is correct.
Write the value of the digit 5 in this number:178.25
I
Step-by-step explanation:
178.25
The number 5 is in the place of one's so the value of 5 is 5
3/5 of a juice drink is made of real juice. What percent of the drink is
real juice?
Answer:
60%
Step-by-step explanation:
Percent means out of 100
Changing 3/5 to a denominator of 100
3/5*20/20
60/100
The percent is 60 %
Help me which answer is it
Answer:
C.
Step-by-step explanation:
[tex]\frac{1}{5} +\frac{5}{6}[/tex] ≈ 1
5 + 8 + 1 = 14
What’s the correct answer for this?
Answer:
The capital B refers to the base of the area
Step-by-step explanation:
Answer:
A
Step-by-step explanation:
The capital B means the area of the base
what function is increasing? will give brainlist !
Answer:
Option B.
Step-by-step explanation:
Option A.
f(x) = [tex](0.5)^{x}[/tex]
Derivative of the given function,
f'(x) = [tex]\frac{d}{dx}(0.5)^x[/tex]
= [tex](0.5)^x[\text{ln}(0.5)][/tex]
= [tex]-(0.693)(0.5)^{x}[/tex]
Since derivative of the function is negative, the given function is decreasing.
Option B. f(x) = [tex]5^x[/tex]
f'(x) = [tex]\frac{d}{dx}(5)^x[/tex]
= [tex](5)^x[\text{ln}(5)][/tex]
= [tex]1.609(5)^x[/tex]
Since derivative is positive, given function is increasing.
Option C. f(x) = [tex](\frac{1}{5})^x[/tex]
f'(x) = [tex]\frac{d}{dx}(\frac{1}{5})^x[/tex]
= [tex]\frac{d}{dx}(5)^{(-x)}[/tex]
= [tex]-5^{-x}.\text{ln}(5)[/tex]
Since derivative is negative, given function is decreasing.
Option D. f(x) = [tex](\frac{1}{15})^x[/tex]
f'(x) = [tex]-15^{-x}[\text{ln}(15)][/tex]
= [tex]-2.708(15)^{-x}[/tex]
Since derivative is negative, given function is decreasing.
Option (B) is the answer.
Ares is making 14 jars of honey peanut butter. He wants to use 45 milliliter (ML) of honey in each jar. How much honey (in ML) will ares use in all?
Answer:
630 milliliters.
Step-by-step explanation:
The statement tells us that the final product is 14 jars of honey peanut butter and that in each jar use 45 mliliters of honey. This means that to know the total honey to be used, the required quantity for each jar must be multiplied by the total number of jars, that is:
14 * 45 = 630
Which means that he would spend a total of 630 milliliters.
Step-by-step explanation:
Ares uses 630 ml of honey, because 14×45=630
Jose predicted that he would sell 48 umbrellas. He actually sold 72 umbrellas.What are the values of a and b in the table below. Round to the nearest tenth if necessary
Answer:
The answer is A
Step-by-step explanation:
The hypotenuse of a right triangle is 95 inches long. One leg is 4 inch(es) longer than the other. Find the lengths of the legs of the triangle. Round your answers to the nearest tenth of an inch.
Answer:
65.1 and 69.1
Step-by-step explanation:
a^2+b^2=c^2
c=95
b=a+4
Solve for a^2+(a+4)^2=95^2
a=65.1
b=a+4=69.1
Answer:
65.1 and 69.1
Step-by-step explanation:
c² = a² + b²
c= 95
a - one leg
b= (a + 4) - second leg
95² = a² + (a + 4)²
9025 = a² + a² + 2*4a + 16
2a² + 8a - 9009 = 0
[tex]a= \frac{-b +/-\sqrt{b^2 - 4ac} }{2a} \\\\a = \frac{-8 +/-\sqrt{8^2 - 4*2*9009} }{2*2} \\\\a=65.1 \ and \ a=- 69.1[/tex]
A leg length can be only positive. a = 65.1
b = 65.1 + 4 = 69.1
URGERNT!!!PLS AT LEAST TAKE A LOOK!!! SHARE YO SMARTNESSS!! AND BLESS YOUR GRADES!
Which sign explains the relationship between m∠1 and m∠2 in the diagram?
A) not equal to
B) >
C) <
D) =
Answer:
Dear Laura Ramirez
Answer to your query is provided below
Option D is correct.
Reason - Because of Hinge and Converse of Hinge theorem
2. Students who wish to represent the school at a school board meeting are asked to stop
by the office after lunch. After lunch, 5 students wish to represent the school.
Answer: Biased sample
Step-by-step explanation:
This is a biased sample because only students with strong opinions are likely going to volunteer or show interest in representing the school at the board meeting. This sample is a voluntary type sample, and at such the conclusion is not valid. This sample is biased because a group or population of students have a higher or lower sampling probability.
What’s the correct answer for this?
Answer:
B.
Step-by-step explanation:
Since two diameters are intersecting eachother, the angles inside them would be vertical angles so they'll be congruent.
So
m<LYM = m<JYM
Also their arcs would be equal to their angles measures so,
Arc JK = 52°
What is the result of converting 81 inches to feet ? Remember, there are 12 inches in a foot.
A) 69 feet
B) 8.1 feet
C) 7.25 feet
D) 6.75 feet
Answer:
6.75 ft
Step-by-step explanation:
81 inches
We know there are 12 inches in 1 ft
81 inches * 1 ft/ 12 inches = 81/12 ft =6.75 ft
Express the following ratio in it’s simplest form.
25:30
Answer:
5/6
Step-by-step explanation:
Find the factor that divides both numbers...
25/5=5
30/5=6
5/6 is the simplified ratio
P.S. Please give me brainliest, i have only have two!
Answer:
1/3:1/4
Step-by-step explanation:
203/259
write in simplest form
2 hours to 45 seconds
Express ratio
15:1
simplest form
1/3:1/4
Scientists think that robots will play a crucial role in factories in the next several decades. Suppose that in an experiment to determine whether the use of robots to weave computer cables is feasible, a robot was used to assemble 507 cables. The cables were examined and there were 9 defectives. If human assemblers have a defect rate of 0.035 (3.5%), does this data support the hypothesis that the proportion of defectives is lower for robots than humans
Answer:
The data support the hypothesis that the proportion of defectives is lower for robots than humans.
Step-by-step explanation:
To know if the proportion of defectives is lower for robots than humans so as to prove if the hypothesis is true.
From the data given:
Total number of cables a robot assembled = 507
Defectives = 9
To get the defect rate = the number of defects divided by the total number of cables, multiplied by 100.
Defect rate = (9 / 507) x 100 = 0.01775 x 100
Defect rate for the robot = 1.775%
From the question, a robot was used and the defect rate after the calculation is 1.775%. While for humans, the defect rate is 3.5%. This implies, if humans were used to assembling the same 507 cables, there will be 17.745 defectives.
x / 507 = 3.5%
x (defectives) = 17.745
Therefore, the data support the hypothesis that the proportion of defectives is lower for robots than humans.
A woman forgot her bank ATM PIN but she was able to recall some of the pin.
1)the 1st digit is half of the 2nd pin
2)the sum of 2nd and 3rd is equal to 10
3)the 4th is equal to the 2nd plus 1
4)the sum of all digits is 23
show workings please
what is the ATM digit?
The PIN is 4829
Step-by-step explanation:
let s take 4 numbers a b c and d
the PIN is abcd
we know that
(1) a = b/2
(2) b+c=10
(3) d=b+1
(4) a+b+c+d=23
from (2) c = 10 - b
from (3) d = b + 1
so (4) gives
b/2 + b + 10 - b + b +1 = 23
so
3/2 b = 23 -11 = 12
b = 12*2/3 = 8
so d = 9
c = 10-8=2
and a = 4
so the PIN is 4829
thank you
Order the numbers from least to greatest based on their absolute values.
|23|, |−37|, |−6|, |18|, |−24|, |2|
Answer:
/-37/, /-24/, /-6/, /2/, /18/, /23/
The top and bottom margins of a poster are each 15 cm and the side margins are each 10 cm. If the area of printed material on the poster is fixed at 2400 cm2, find the dimensions of the poster with the smallest area.
Answer:
the dimension of the poster = 90 cm length and 60 cm width i.e 90 cm by 60 cm.
Step-by-step explanation:
From the given question.
Let p be the length of the of the printed material
Let q be the width of the of the printed material
Therefore pq = 2400 cm ²
q = [tex]\dfrac{2400 \ cm^2}{p}[/tex]
To find the dimensions of the poster; we have:
the length of the poster to be p+30 and the width to be [tex]\dfrac{2400 \ cm^2}{p} + 20[/tex]
The area of the printed material can now be: [tex]A = (p+30)(\dfrac{2400 }{p} + 20)[/tex]
=[tex]2400 +20 p +\dfrac{72000}{p}+600[/tex]
Let differentiate with respect to p; we have
[tex]\dfrac{dA}{dp}= 20 - \dfrac{72000}{p^3}[/tex]
Also;
[tex]\dfrac{d^2A}{dp^2}= \dfrac{144000}{p^3}[/tex]
For the smallest area [tex]\dfrac{dA}{dp }=0[/tex]
[tex]20 - \dfrac{72000}{p^2}=0[/tex]
[tex]p^2 = \dfrac{72000}{20}[/tex]
p² = 3600
p =√3600
p = 60
Since p = 60 ; replace p = 60 in the expression q = [tex]\dfrac{2400 \ cm^2}{p}[/tex] to solve for q;
q = [tex]\dfrac{2400 \ cm^2}{p}[/tex]
q = [tex]\dfrac{2400 \ cm^2}{60}[/tex]
q = 40
Thus; the printed material has the length of 60 cm and the width of 40cm
the length of the poster = p+30 = 60 +30 = 90 cm
the width of the poster = [tex]\dfrac{2400 \ cm^2}{p} + 20[/tex] = [tex]\dfrac{2400 \ cm^2}{60} + 20[/tex] = 40 + 20 = 60
Hence; the dimension of the poster = 90 cm length and 60 cm width i.e 90 cm by 60 cm.
Factorize (3x-2y)2 + 3(3x-2y)-10
Answer:
[tex]5(3x-2y-2)[/tex] i think. i am sorry if i am wrong
Step-by-step explanation:
