Answer:
Step-by-step explanation:
Mean = (29.7 + 29.4 + 31.7 + 29.0 + 29.1 + 30.5 + 29.1 + 29.8)/8 = 29.7875
Mean = 29.7875 × 1000 = $29787.5
Standard deviation = √(summation(x - mean)²/n
n = 8
Summation(x - mean)² = (29.7 - 29.7875)^2 + (29.4 - 29.7875)^2 + (31.7 - 29.7875)^2 + (29.0 - 29.7875)^2 + (29.1 - 29.7875)^2 + (30.5 - 29.7875)^2 + (29.1 - 29.7875)^2 + (29.8 - 29.7875)^2 = 5.88875
Standard deviation = √(5.88875/8
s = 0.88
s = 0.88 × 1000 = $880
a) We would set up the hypothesis test. This is a test of a single population mean since we are dealing with mean
For the null hypothesis,
H0:µ ≤ 30000
For the alternative hypothesis,
H1:µ > 30000
This is a right tailed test.
b) The decision rule is to reject the null hypothesis if the significance level of 0.05 is greater than the probability value. If it is otherwise, we would fail to reject the null hypothesis.
c) Since the number of samples is small and no population standard deviation is given, the distribution is a student's t.
Since n = 8
Degrees of freedom, df = n - 1 = 8 - 1 = 7
t = (x - µ)/(s/√n)
Where
x = sample mean = 29787.5
µ = population mean = 30000
s = samples standard deviation = 880
t = (29787.5 - 30000)/(880/√8) = - 0.68
We would determine the p value using the t test calculator. It becomes
p = 0.26
d) Since alpha, 0.1 < the p value, 0.26, then we would fail to reject the null hypothesis.
If a person invests $190 at 8% annual interest, find the approximate value of the investment at the end of 10 years.
Answer:
$420
Step-by-step explanation:
This the problem of compound interest
If any amount P is invested at rate of r% per year then its value after n years is given by
amount = [tex]p( 1+ r/100)^n[/tex]
______________________________
Given
p = $190
r =8%
n = 10 year then
[tex]amount = p( 1+ r/100)^n\\=> amount = 190( 1+ 8/100)^10\\=> amount = 190( 108/100)^10\\=> amount = 410.20[/tex]
Thus, value of the investment at the end of 10 years is $420.
Answer: 342
Step-by-step explanation:
This is a SIMPLE INTEREST question:
SI = prt
SI = 190 x 0.08 x 10
SI = 152
Amount = 190 + 152 = 342
Please answer this correctly
Answer:
3/4
Step-by-step explanation:
The numbers odd or less than 3 are 2, 3, and 5.
3 numbers out of 4.
P(odd or less than 3) = 3/4
Select the correct answer. Which graph represents this equation? y − 4 = -3(x + 5)
Answer:
I graphed the equation on the graph below.
Step-by-step explanation:
y − 4 = -3(x + 5) Distribute
y - 4 = -3x - 15
+ 4 + 4 Add 4 to both sides
y = -3x - 11 This is the equation in slope-intercept form, which is easier to graph
A line is a one-dimensional shape that is straight. The equation y-4 = -3(x + 5) can be represented on a graph as shown below.
What is the equation of a line?A line is a one-dimensional shape that is straight, has no thickness, and extends in both directions indefinitely. The equation of the line is given by,
y =mx + c
where,
x is the coordinate of the x-axis,
y is the coordinate of the y-axis,
m is the slope of the line, and
c is constant.
If we solve the given equation, the equation will reduce in the form of an equation of a line, therefore, the equation can be written as,
y − 4 = -3(x + 5)
y - 4 = -3x - 15
y = -3x - 15 + 4
y = -3x - 11
Hence, the equation y-4 = -3(x + 5) can be represented on a graph as shown below.
Learn more about Equation of Line:
https://brainly.com/question/21511618
#SPJ2
Select the correct answer from each drop-down menu.
Answer:
AB = 14AC = 19.8 ≈ 20Step-by-step explanation:
The Pythagorean theorem can be used to find the lengths of the segments at the top of the square. The left one is found from ...
FA² = FE² +EA²
13² -12² = EA² = 169 -144 = 25
EA = √25 = 5
The right one is found from ...
FB² = FE² +EB²
15² -12² = EB² = 225 -144 = 81
EB = √81 = 9
Then the length of the side of the square is ...
AB = AE +EB = 5 +9
AB = 14
__
The length of the diagonal can also be found using the Pythagorean theorem.
AC² = AB² +BC² = 14² +14²
AC = √(196 +196) = 14√2 ≈ 19.7990
Rounded to the nearest integer, AC ≈ 20.
please help me out asap
Answer:
SOLUTION SET={x<-3/2 or x≥48/5} option A
Step-by-step explanation:
12x+7<-11 and 5x-8≥40
solving the both inequalities
12x+7-7<-11-7 and 5x-8+8≥40+8
12x<-18 and 5x≥48
12x/12<-18/12 and 5x/5≥48/5
x<-3/2 and x≥48/5
SOLUTION SET={x<-3/2 or x≥48/5}
i hope this will help you :)
Find the perimeter and total area ? Use 3.14 in
Answer:
Perimeter is when you add up all of the sides, and the area is when you multiply length times width.
Rick is thinking of a positive factor of $14$ and Steve is thinking of a positive factor of $42$. If Rick and Steve are thinking of the same number, how many possible numbers could they be thinking of?
Answer:
Step-by-step explanation:
Hello,
14 = 7 * 2 * 1
42 = 7 * 3 * 2 * 1
It can be 14, 7, 2 or 1
So there are 4 different positive numbers which meet the criteria
Hope this helps
Answer
14 = 7 * 2 * 1
42 = 7 * 3 * 2 * 1
It can be 14, 7, 2 or 1
Step-by-step explanation:
-4(-11+4n)-3(-2n+9) simplify to create an equivalent expression
chose 1 answer
-10n-35, -18n+17, -10n-17, or -10n+17
Answer:
the last one is correct
Step-by-step explanation:
hello,
-4(-11+4n)-3(-2n+9) = 44 - 16n + 6n - 27 = -10n + 17
hope this helps
Please answer this correctly
Answer:
1/6
Step-by-step explanation:
Since the die has 6 sides that are all equally likely to be landed on, the probability of landing on 2 is 1/6, as there is one "favorable" outcome and 6 total outcomes. Hope this helps!
Answer:
1/6
Step-by-step explanation:
Sides of dice = 6
Number 2 in dice = 1
P(2) = 1/6
All boxes with a square base, an open top, and a volume of 220 ft cubed have a surface area given by S(x)equalsx squared plus StartFraction 880 Over x EndFraction , where x is the length of the sides of the base. Find the absolute minimum of the surface area function on the interval (0,infinity). What are the dimensions of the box with minimum surface area?
Answer:
Length of the sides of the base (x) = 7.606 ft
Height (h) = 3.802 ft
The minimum surface area is 173.55 ft²
Step-by-step explanation:
Surface area is given by:
[tex]S(x) = x^2+\frac{880}{x}[/tex]
The value of x for which the derivate of the surface area function is zero, is the length of the sides of the base that minimizes surface area:
[tex]S(x) = x^2+\frac{880}{x} \\\frac{dS(x)}{dx}=0=2x-\frac{880}{x^2}\\x^3=440\\x=7.606\ ft[/tex]
The height of the box is given by:
[tex]V=hx^2\\220 =h*7.606^2\\h=3.802\ ft[/tex]
The dimensions of the box with minimum surface area are:
Length of the sides of the base (x) = 7.606 ft
Height (h) = 3.802 ft
The absolute minimum is:
[tex]S(x) = 7.606^2+\frac{880}{7.606}\\S_{min}=173.55\ ft^2[/tex]
The minimum surface area is 173.55 ft²
Answer:
The absolute minimum of the surface area[tex]=173.55$ ft^2[/tex]
At the minimum surface area,
Base length=7.61 feetHeight of 3.8 feet.Step-by-step explanation:
Volume of the box =220 cubic feet.
[tex]\text{Surface Area, } S(x)=x^2+\dfrac{880}{x}[/tex]
To find the absolute minimum of the surface area function on the interval [tex](0,\infty)[/tex], we take the derivative of S(x) and solve for its critical points.
[tex]S(x)=\dfrac{x^3+880}{x}\\S'(x)=\dfrac{2x^3-880}{x^2}\\$Setting the derivative equal to 0\\S'(x)=\dfrac{2x^3-880}{x^2}=0\\2x^3-880=0\\2x^3=880\\$Divide both sides by 2\\x^3=440[/tex]
Take the cube root of both sides
[tex]x=\sqrt[3]{440}\\ x=7.61$ ft[/tex]
Therefore, the absolute minimum of the surface area function on the interval [tex](0,\infty)[/tex], is:
[tex]S(x)=\dfrac{7.61^3+880}{7.61}\\\\=173.55$ ft^2[/tex]
Since the volume of the box =220 cubic feet
[tex]V=x^2h\\220=7.61^2 \times h\\h=220 \div 7.61^2\\h=3.80 ft[/tex]
The dimensions of the box with the minimum surface area are base length of 7.61 feet and height of 3.8 feet.
Which statement best interprets the factor (r+7) in this context?
Answer:
the height of the cylinder is 7 units greater than the radius
Step-by-step explanation:
When you match the forms of the equations ...
[tex]V=\pi r^2(r+7)\\V=\pi r^2h[/tex]
you see that the factor (r+7) corresponds to the height (h) of the cylinder. That is ...
the height of the cylinder is 7 units greater than the radius.
Select all the correct answers.
Which three pieces of information contribute the most to your credit score?
the number of bank accounts you have
the amount of debt you have
your payment history
your ability to make a down payment on a credit purchase
the number of loans you have
W
Answer:
B) the amount of debt you have
C) your payment history
E) the number of loans you have
Step-by-step explanation:
To determine the three pieces of information that contribute the most to your credit score, we have to find the factors that affect credit score calculation.
The major factors that affect a person's credit score calculation include : Payment history:
This is the most important factor that affect your credit score. Lenders want to be sure that you have a reputation back your debt and on time when you apply for new credit.
Amount of Debt :
This is the amount of overall debt you carry. It is the ratio of your credit card balances to your credit limit. Too much debt can hurt your credit score
Credit History:
This is a borrower's track record for repaying debts and how old it is. Opening new accounts within a short time will affect your credit score.
Account Mix: having a diverse portfolio of credit accounts could tell how well you manage different credits.
Credit Inquiries:
Several applications involving inquiries into your credit check within a short duration can affect your credit score.
Therefore the three pieces of information that would contribute the most to your credit score:
B) the amount of debt you have
C) your payment history
E) the number of loans you have
(03.01 MC)
If AXYZ is dilated by a scale factor of 2 about point X, which of the following is true about A'Y'?
Answer:
A'Y' is parallel to AY
Step-by-step explanation:
If X is the center of dilation, the only lines that go through X after the dilation are the ones that go through X before the dilation: XY (and XY'), XZ (and XZ').
Line AY does not go through X, so A'Y' will not go through X. Rather, the line will be moved a distance from X according to the dilation factor. The line A'Y' will be parallel to AY.
Find [g ° h](x) and [h ° g](x) , if they exist. g(x)=x+6 and h(x)=3x2 YALL PLEASE I NEED HELP :((
Answer:
a) [g ° h](x) = 3x² +6
b) [h ° g](x) =3 x²+36x+108
Step-by-step explanation:
Explanation:-
a)
Given g(x) = x+6 and h(x) = 3x²
Given [g ° h](x) = g(h(x))
= g(3x²) (∵ h(x) =3x²)
= (3x²)+6 (∵ g(x) =x+6)
∴ [g ° h](x) = 3x² +6
b)
Given [h ° g](x) = h (g(x))
= h(x+6) (∵ g(x) =x+6)
= 3 (x+6)² (∵ h(x) =3x²)
= 3 (x²+2(6)x+36) (∵ (a + b)² = a²+2ab+b²)
= 3 (x²+12x+36)
= 3 x²+36x+108)
∴ [h ° g](x) =3 x²+36x+108
Need Help ASAP!!!
Which of the following is a key property of the linear parent function?
O A. It is in quadrants I and III.
B. It does not go through the origin.
C. It has a slope of zero.
O D. It is a curved line.
Answer:
The answer is:
A. It is in the quadrants I and III.
Step-by-step explanation:
I am not sure if this is correct, but I tried my best :)
I hope this helped~
Carlos biked miles on Saturday and miles on Sunday. On which day did he ride further and by how much? Carlos rode further on Saturday by miles. Carlos rode further on Saturday by miles. Carlos rode further on Sunday by miles. Carlos rode further on Sunday by miles.
Answer:
He rode farther on Sunday
135/7 - 139/8 = 107/56 or 1 51/56 miles farther
Answer:D
Step-by-step explanation: I got a hundred on my test.
A civil engineer is mapping the overhead clearance of his family’s property on a coordinate grid. The ground is represented by the x-axis and the base of the house is at the origin. There are two trees on the property. One tree is 8 feet from the base of the house and is 14 feet tall. The other tree is 16 feet from the base of the house and is 9 feet tall. What is the distance from the base of the house to the closest treetop? Round your answer to the nearest tenth.
Answer:
15.81
Step-by-step explanation:
Sorry for the delay
this circle is centered at the origin (0,0) the radius is 4, what is the equation?
Answer:
x^2 +y^2 = 16
Step-by-step explanation:
The equation of a circle is given by
(x-h) ^2 + (y-k)^2 = r^2 where (h,k) is the center and r is the radius
(x-0) ^2 + (y-0)^2 = 4^2
x^2 +y^2 = 16
if a=2 and b=3 then find the value of 4a^2-4ab+b^2
Answer:
1
Step-by-step explanation:
=> [tex]4a^2-4ab+b^2[/tex]
Where a = 2, b = 3
=> [tex]4(2)^2-4(2)(3)+(3)^2[/tex]
=> 4(4) - 4(6) + 9
=> 16 - 24 + 9
=> -8 + 9
=> 1
Answer:
1.
Step-by-step explanation:
Substituting for a and b we have
4(2)^2 - 4*2*3 + (3)^2
= 16 - 24 + 9
= -8 + 9
= 1.
The table shown lists the atomic weight of the elements that begin with the letter c. What's the range of these
atomic weights?
Review My Answers
Save & EVE
No. Atomic Weight Name 48112411 2040078 98251000
Cadmium cd Calcium Ca Californium Cf Carbon Cerium Ce Cesium Cs Chlorine C Chromium Cr Cobalt Co Copper Cu Curium Cm
6 12.011 58140116 55132906 1735453 2451996 2758933 2963546 96 *247.00
A. 215.547
B. 238.989
C. 234.989
D. 134.589
A certain medicine is given in an amount proportional to a patients body weight. Suppose a person weighted 104 pounds requires 156 milligrams of medicine. What is the weight of a patient who requires 207 milligrams of medicine?
Answer:
138 pound
Step-by-step explanation:
Given
A certain medicine is given in an amount proportional to a patients body weight.
thus,
ratio will be
amount of medicine: weight of patient
Given
Suppose a person weighted 104 pounds requires 156 milligrams of medicine.
amount of medicine = 156 milligram
weight of patient = 104 pound
Thus, ratio will be = 156/104
___________________________
What is the weight of a patient who requires 207 milligrams of medicine
Let the weight of weight of patient here be x
thus, ratio in this case will be
207/x
we also know in ratio and proportion that
if two ratio a:b and c:d are equal then a:c = c:d
here also the ratio will be same
Thus,
156/104 = 207/x
=> 156x = 207*104 = 21,528
=> x = 21,528/156 = 138
Thus, weight of patient is 138 pound.
Please help!! Will give 20 points!
Answer:
B. .32
Step-by-step explanation:
I think its B .32
Answer:
A
Step-by-step explanation:
Value of the digit 5 in 75 389
Answer:
The value of digit 5 is thousand
Step-by-step explanation:
Digit 5 has thousand value in 75 389
find P (3) if p(x)=-×^3-2x^2+7
Answer:
-38.
Step-by-step explanation:
p(x) = -x^3 - 2x^2 + 7
p(3) = -(3^3) - 2(3^2) + 7
p(3) = -27 - 2(9) + 7
p(3) = -27 - 18 + 7
p(3) = -45 + 7
p(3) = -38
Hope this helps!
Answer:
p(3) = -38
Step-by-step explanation:
p(x) = -x³ - 2x² + 7
p(3) = -3³ - 2(3)² + 7
p(3) = -27 - 2(9) + 7
p(3) = - 27 - 18 + 7
p(3) = -38
Use the addition method to solve the system of linear equations for x. (Enter an exact number.)
3x - 2y = 8
2x + y = 3
Answer:
work is shown and pictured
Solve for x in the equation x squared + 11 x + StartFraction 121 Over 4 EndFraction = StartFraction 125 Over 4 EndFraction.
Answer:
x = -13 or 2
Step-by-step explanation:
x² + 11x + ¹²¹/₄ = ¹²⁵/₄
(x + ¹¹/₂)² = ¹²⁵/₄
x + ¹¹/₂ = ±¹⁵/₂
x = -¹¹/₂ ± ¹⁵/₂
x = -13 or 2
Answer: D is the correct answer.
Step-by-step explanation: I took the test :)
Which rational function does this graph represent?
Answer:
A. F(x) = 1/(x +2)²
Step-by-step explanation:
The asymptote at x = -2 tells you that x -(-2) = x +2 is a denominator factor. The fact that the function has the same sign on both sides of the asymptote tells you that factor has even degree.
Of the choices listed, the appropriate one is ...
F(x) = 1/(x +2)²
x = 16 18 34 can someone explain please?
Answer:
x = 16
Step-by-step explanation:
(whole secant) x (external part) = (tangent)^2
(x+2) * 2 = 6^2
2(x+2) = 36
Divide each side by 2
x+2 = 18
Subtract 2
x+2-2 = 18-2
x = 16
Answer:
x = 16
Step-by-step explanation:
According to tangent-secant Theorem:
(Tangent)² = (External Part of the secant)(Whole Secant)
(6)² = (2)(2+x)
36 = 4+2x
Subtracting 4 from both sides
36-4 = 2x
=> 2x = 32
Dividing both sides by 2
=> x = 16A three-person jury has two members who each have a probability p of making the correct decision in a case. The third member doesnt care and flips a coin for each decision. The ruling is based on a majority vote amongst the jurors
(a) What is the probability that the jury will correctly decide the case?
(b) Suppose two of the jurors quit, one of whom is the juror that doesnt care. Does the rrectly deciding the case i ncrease, decrease, or no at all?
Answer:
(a) p
(b) the probability does not change at all
Step-by-step explanation:
(a) Let A and B be the jurors with probability 'p' of making the correct decision, and C be the juror that doesn't care. The case will be correctly decided if any of the following combinations of jurors decide the case correctly:
AB, AC, BC, ABC.
The probability of one of those outcomes occurring is:
[tex]P=(p*p*0.5)+(p*(1-p)*0.5)+(p*(1-p)*0.5)+(p*p*0.5)\\P=p^2+p-p^2\\P=p[/tex]
The probability is p.
(b) If two of the juros quit, the probability of correctly deciding the case lies on just one juror that correctly decides with probability 'p'. Therefore, the probability of deciding the case does not change at all
The prefix kilo means?
Answer:
one thousand
Step-by-step explanation: