Answer:
The probability that the insurer pays at least 1.44 on a random loss is 0.18.
Step-by-step explanation:
Let the random variable X represent the losses covered by a flood insurance policy.
The random variable X follows a Uniform distribution with parameters a = 0 and b = 2.
The probability density function of X is:
[tex]f_{X}(x)=\frac{1}{b-a};\ a<X<b\\\\\Rightarrow f_{X}(x)=\frac{1}{2}[/tex]
It is provided, the probability that the insurer pays at least 1.20 on a random loss is 0.30.
That is:
[tex]P(X\geq 1.2+d)=0.30\\[/tex]
⇒
[tex]P(X\geq 1.2+d)=\int\limits^{2}_{1.2+d}{\frac{1}{2}}\, dx[/tex]
[tex]0.30=\frac{2-1.2-d}{2}\\\\0.60=0.80-d\\\\d=0.80-0.60\\\\d=0.20[/tex]
The deductible d is 0.20.
Compute the probability that the insurer pays at least 1.44 on a random loss as follows:
[tex]P(X\geq 1.44+d)=P(X\geq 1.64)[/tex]
[tex]=\int\limits^{2}_{1.64}{\frac{1}{2}}\, dx\\\\=|\frac{x}{2}|\limits^{2}_{1.64}\\\\=\frac{2-1.64}{2}\\\\=0.18[/tex]
Thus, the probability that the insurer pays at least 1.44 on a random loss is 0.18.
Conduct the hypothesis test and provide the test statistic and the critical value, and state the conclusion. A person drilled a hole in a die and filled it with a lead weight, then proceeded to roll it times. Here are the observed frequencies for the outcomes of 1, 2, 3, 4, 5, and 6, respectively: , , , , , . Use a significance level to test the claim that the outcomes are not equally likely. Does it appear that the loaded die behaves differently than a fair die?
Answer: There is no sufficient evidence to support the claim that loaded die behaves differently than a fair die
Step-by-step explanation:
Find explanations in the attached file
Find the measure of y. Polygon Angle-Sum theorems
Answer:
z = 70°
y = 103°
Step-by-step explanation:
From the picture attached,
110° + z° = 180° [Supplementary angles]
z = 180 - 110
z = 70°
Since sum of interior angles of a polygon = (n - 2)×180°
where n = number of sides of the polygon
For a quadrilateral (n = 4),
Sum of interior angles = (4 - 2) × 180°
= 360°
z° + y° + 100° + 87° = 360°
70° + y° + 187° = 360°
y = 103°
Therefore, measure of the angles x = 70° and y = 103°.
Chapter Reference
b
A board 65 inches long is sawed into two pieces, so that one piece is 7 inches shorter than twice the length of the other piece ? Find the length of the two pieces .
Step-by-step explanation:
It is given that,
Total length of a board is 65 inches
It is sawed into two pieces such that one piece is 7 inches shorter than twice the length of the other piece.
Let x is the length of other piece and y is the length of first piece such that,
y = 2x-7 ....(1)
Also,
x+y = 65 .....(2)
Put the value of y from equation (1) to equation (2) such that,
x+2x-7 = 65
3x=65+7
3x=72
x = 24 inches
Put the value of x in equation (1)
y = 2(24)-7
y = 41 inches
So, the length of first piece is 41 inches while the length of other piece is 24 inches.
Construct a 90% confidence interval for the true mean using the FPCF. (Round your answers to 4 decimal places.) The 90% confidence interval is from to
Answer:
The answer is below
Step-by-step explanation:
Twenty-five blood samples were selected by taking every seventh blood sample from racks holding 187 blood samples from the morning draw at a medical center. The white blood count (WBC) was measured using a Coulter Counter Model S. The mean WBC was 8.636 with a standard deviation of 3.9265. (a) Construct a 90% confidence interval for the true mean using the FPCF. (Round your answers to 4 decimal places.) The 90% confidence interval is from to
Answer:
Given:
Mean (μ) = 8.636, standard deviation (σ) = 3.9265, Confidence (C) = 90% = 0.9, sample size (n) = 25
α = 1 - C = 1 - 0.9 = 0.1
α/2 = 0.1/2 = 0.05
From the normal distribution table, The z score of α/2 (0.05) corresponds to the z score of 0.45 (0.5 - 0.05) which is 1.645
The margin of error (E) is given by:
[tex]E=z_{\frac{\alpha}{2} }*\frac{\sigma}{\sqrt{n} }\\ \\E=1.645*\frac{3.9265}{\sqrt{25} }=1.2918[/tex]
The confidence interval = μ ± E = 8.636 ± 1.2918 = (7.3442, 9.9278)
The 90% confidence interval is from 7.3442 to 9.9278
Determine whether the function below is an even function, an odd function, both, or neither.
f(x)=x^6 + 10x^4-11x^2+19
ОА.
neither even nor odd
OB.
odd function
Ос.
both even and odd
OD.
even function
Reset
Next
Answer:
Step-by-step explanation:
even function are symmetrical about the y axis or f(-x)=f(x)
odd function are symmetrical about the origin -f(-x)=f(x)
f(x)=x^6 + 10x^4-11x^2+19
f(-x)=(-x)^6+10(-x)^4+11(-x)^2+19=x^6 + 10x^4-11x^2+19
the function is even
A firm has the marginal-demand function Upper D prime (x )equalsStartFraction negative 1200 x Over StartRoot 25 minus x squared EndRoot EndFraction . Find the demand function given that Dequals16 comma 000 when x equals $ 4 per unit.
Answer:
The demand function is [tex]\mathbf{D(x) = 1200(\sqrt{25-x^2})+ 124000}[/tex]
Step-by-step explanation:
A firm has the marginal-demand function [tex]D' x = \dfrac{-1200}{\sqrt{25-x^2 } }[/tex].
Find the demand function given that D = 16,000 when x = $4 per unit.
What we are required to do is to find the demand function D(x);
If we integrate D'(x) with respect to x ; we have :
[tex]\int\limits \ D'(x) \, dx = \int\limits{\dfrac{-1200 x}{\sqrt{25-x^2}} } \, dx[/tex]
[tex]D(x) = \int\limits{\dfrac{-1200 x}{\sqrt{25-x^2}} } \, dx[/tex]
Let represent t with [tex]\sqrt{25-x^2}}[/tex]
The differential of t with respect to x is :
[tex]\dfrac{dt}{dx}= \dfrac{1}{2 \sqrt{25-x^2}}}(-2x)[/tex]
[tex]\dfrac{dt}{dx}= \dfrac{-x}{ \sqrt{25-x^2}}}[/tex]
[tex]{dt}= \dfrac{-xdx}{ \sqrt{25-x^2}}}[/tex]
replacing the value of [tex]\dfrac{-xdx}{ \sqrt{25-x^2}}}[/tex] for dt in [tex]D(x) = \int\limits{\dfrac{-1200 x}{\sqrt{25-x^2}} } \, dx[/tex]
So; we can say :
[tex]D(x) = \int\limits{\dfrac{-1200 x}{\sqrt{25-x^2}} } \, dx[/tex]
[tex]D(x) = 1200\int\limits{\dfrac{- x}{\sqrt{25-x^2}} } \, dx[/tex]
[tex]D(x) = 1200\int\limits \ dt[/tex]
[tex]D(x) = 1200t+ C[/tex]
Let's Recall that :
t = [tex]\sqrt{25-x^2}}[/tex]
Now;
[tex]\mathbf{D(x) = 1200(\sqrt{25-x^2}})+ C}[/tex]
GIven that:
D = 16,000 when x = $4 per unit.
i.e
D(4) = 16000
SO;
[tex]D(x) = 1200(\sqrt{25-x^2}})+ C[/tex]
[tex]D(4) = 1200(\sqrt{25-4^2}})+ C[/tex]
[tex]D(4) = 1200(\sqrt{25-16}})+ C[/tex]
[tex]D(4) = 1200(\sqrt{9}})+ C[/tex]
[tex]D(4) = 1200(3}})+ C[/tex]
16000 = 1200 (3) + C
16000 = 3600 + C
16000 - 3600 = C
C = 12400
replacing the value of C = 12400 into [tex]\mathbf{D(x) = 1200(\sqrt{25-x^2}})+ C}[/tex], we have:
[tex]\mathbf{D(x) = 1200(\sqrt{25-x^2})+ 124000}[/tex]
∴ The demand function is [tex]\mathbf{D(x) = 1200(\sqrt{25-x^2})+ 124000}[/tex]
NEED URGENT HELP ON 5 QUESTIONS SIMILAR TO THIS!!!!! WILL GIBE BRAINLIEST AND 5 STARS IF CORRECT QUICKLY! - 50 POINT - also, no wrong answers just for the points please.
Answer:
As X → - ∞ , y → ∞ and as x→ ∞ , y → ∞
option c is the correct option.Step-by-step explanation:
let f(x) = y = 3x² - 5x + 2
y = 3x² - 5x + 2
= x ( 3x - 5 ) + 2
y = ∞ ( 3 ( ∞ - 5 ) ) + 2
= ∞ (∞ ) + 2
y = ∞
y → ∞ as x → ∞
Now,
as x → - ∞
y = x ( 3x - 5 ) + 2
= ∞ ( 3 ( - ∞ ) - 5 ) + 2
= - ∞ ( - ∞ ) + 2
∞² + 2 = ∞
Hence , Option C is the correct answer.
Answer:
Mathematically you can use the following V = ⁴⁄₃πr³
π = pi
r = radius
To do this you would need a set of scales, a jug, some water, a pen, a ruler and some paper.
ωα√
bh. Find the area of the shape with the given
The area of a triangle can be found by the formula A
base (b) and height (h).
h
b
b = 5 cm and h = 3 cm
Answer:
[tex]7.5cm^2[/tex]
Step-by-step explanation:
Well using the following formula,
[tex]\frac{b*h}{2}[/tex]
5*3 = 15
15 / 2
7.5cm^2
Answer:[tex]7.5cm^{2}[/tex]
Step-by-step explanation:
h=3
b=5
area=1/2 x b x h
1/2 x 5 x 3
area=7.5
Raven has a bag of 33 red and black marbles. The number of red marbles is 6 more than double the number of black marbles. Let r represent the number of red marbles and b represent the number of black marbles. Which statements about the marbles are true? Check all that apply. The equation r + b = 33 represents the total number of marbles. The equation r = 2 b + 6 can be used to find the number of red marbles. The equation r = 2 b + 6 represents the total number of marbles. The equation r + b = 33 can be used to find the number of red marbles. There are 9 red marbles in the bag. There are 9 black marbles in the bag. There are 24 black marbles in the bag. There are 24 red marbles in the bag.
Hey there! I'm happy to help!
If the number of red marbles is 6 more than double the number of black marbles, we can create this equation, with r representing the red marbles and b representing the black marbles.
r=2b+6
We also know that r+b=33, and if we know that r is equal to 2b+6, we can just replace r with that and then solve for b.
2b+6+b=33
We combine like terms.
3b+6=33
We subtract six from both sides.
3b=27
We divide both sides by 3.
b=9
Now we just subtract 9 from 33 to see how many red ones there are.
33-9=24
So, there are 24 red marbles and 9 black marbles.
Now, let's see which of these options are correct.
The equation r+b=33 represents the total number of marbles.
This is true because r plus b is equal to the total, which is 33.
The equation r=2b+6 can be used to find the number of red marbles.
This is true because it we used this r-value to find how many black marbles there were.
The equation r=2b+6 represents the total number of marbles.
This is false because it does not have the total number, which is 33.
The equation r=b=33 can be used to find the number of red marbles.
This is true because we plugged in the r-value to solve for b with this equation.
There are 9 red marbles in the bag.
This is false. There are 24 red marbles.
There are 9 black marbles in the bag.
This is true.
There are 24 black marbles in the bag.
This is false. There are 9 black marbles.
There are 24 red marbles in the bag.
This is true.
Have a wonderful day! :D
Answer:
1,2,4,6,8
Step-by-step explanation:
plzZZZZZZzzzzzzzzzZZZZZzzzzzzzZZZzzzzzZZzzzzZZzzzzZzz help for my friend thank you
Answer:
Likely
Step-by-step explanation: Mathematically it is likely because there are 4 options certain is the thing that will defiantly happen so it would be 4/4. The impossible thing would be 1/4 this is because 1/4 is the smallest so it is obviously going to be impossible. Likely would be 3/4 and unlikely would clearly be 2/4
Answer:
it is likely
Step-by-step explanation:
it is not certant because it is not 4/4 but it is not impossible because its not 0/4 so the answer is likely 3/4
The profit y (in dollars) for a company for selling x games is represented by y=32x. Graph the equation. ANSWER BEFORE 11 FOr BOnUs PoINTS!!!
Answer:
I guess that we have the linear equation:
y = 32*x
Where y is the profit, and x is the number of games sold.
Then the first step may be doing a table.
Give x different values, then find the value of y.
if x = 0
y = 32*0 = 0
if x = 1, y = 32*1 = 32
if x = 2, y = 2*32 = 64
Then the points:
(0,0) (1,32) and (2, 64) belong to this line, now we need to conect them with a straigth line and its ready.
The graph will be:
Which could be the area of one lateral face of the triangular prism?
6.5 ft
6 ft
8 ft
2.5 ft
[Not drawn to scale]
7.5 ft2
15 ft?
20 ft
39 ft
Answer:
[tex](A)7.5 ft^2\\(C)20 ft^2[/tex]
Step-by-step explanation:
The diagram is attached below.
Area of the Rectangular Faces
[tex]8 X 6.5 =52$ ft^2\\8 X 2.5 =20$ ft^2\\8 X 6= 48$ ft^2[/tex]
Area of the Triangular face
[tex]=\dfrac12 X 2.5 X 6 =7.5$ ft^2[/tex]
Therefore, Options A and C could be the area of one lateral face of the triangular prism.
Answer:
C
Step-by-step explanation:
A sign company is creating a pennant in the shape of an equilateral triangle
The length of each side is 8 inches. What is the alttitude length so the
company will know what size box to ship the pennant in?
Hey there! :)
Answer:
4√3 in.
Step-by-step explanation:
Given:
-Equilateral triangle
-Side lengths of 8 in
Find the altitude using the Pythagorean Theorem (c² = a² + b²) where:
'a' is the shorter leg, or half of the base to find the altitude
'b' is the altitude
'c' is the Hypotenuse, or 8 in.
Therefore:
8² = 4² + b²
64 = 16 + b²
48 = b²
b = √48 or 4√3 in.
Therefore, the altitude of the triangle is 4√3 in.
FOR BRAINLIEST ANSWER HURRY HELP THANKS If (a,b) is a point in quadrant IV, what must be true about a? What must be true about b?
Answer:
Well if (a,b) is in Quadrant IV which is the last quadrant the a or x is a positive number and the b or y is a negative number.
Answer:
a should be a positive number
b should be a negative number
18. Which of the following equations is equivalent to 25x = 7?
A. x=
log2 (3)
+1+9= 3? Is
B.
log27
5
C.
X=
log, 2
5
log, 5
D. x=
2
Answer:
x = log (7)/ 2log 5
Step-by-step explanation:
25^ x = 7
Replace 25 with 5^2
5^ 2x = 7
Take log on each side
log (5 ^2x) = log ( 7)
We know that log a^ b = b log a
2x log 5 = log (7)
Divide each side by log 5
2x log 5/ log 5= log (7)/ log 5
2x = log (7)/ log 5
Divide each side by 2
x = log (7)/ 2log 5
Below are the jersey numbers of 11 players randomly selected from a football team. Find the range, variance, and standard deviation for the given sample data.
33 29 97 56 26 78 83 74 65 47 58
What do the results tell us?
A. Jersey numbers are nominal data that are just replacements for names, so the resulting statistics are meaningless.
B. Jersey numbers on a football team vary much more than expected.
C. The sample standard deviation is too large in comparison to the range.
D. Jersey numbers on a football team do not vary as much as expected.
Answer:
Option(A) is correct
Jersey numbers are nominal data that are just replacements for names, so the resulting statistics are meaningless.
Step-by-step explanation:
The given data set in the question are ;33, 29, 97, 56, 26, 78, 83, 74, 65, 47, 58
the range can be determined by finding the highest value and subtract it to the lowest value. In this case the values are:
Highest = 97
Lowest = 71
Range = highest value - Minimum value
Range = 97 - 26 = 71
[tex] Range= 71[/tex]
mean of the data is the summation of all the numbers in the data set divided by the number of given samples.
Mean = (33 + 29 + 97 + 56+ 26 + 78 + 83 74+ 65 + 47 + 58)/11
= 647/11
[tex]Mean value =58.7[/tex]
Now to find the variance of the data set by using below formular
σ²=[ (xᵢ -mean)²]/n-1
[(33-58.7)² +(29-58.7)²+( 97-58.7)²+( 56-58.7)²+( 26 -58.7)²+(78-58.7)²+( 83 -58.7)²+(74-58.7)²+( 65-58.7)²+( 47 -58.7)²+(58 -58.7)²]/10
[tex]Variance=546[/tex]
Now, we will calculate standard deviation by taking square root over variance
σ =√(variance)
σ =√(546)
[tex]Standard deviation= 23.4[/tex]
Hence, the range is 71 ,variance is 546 and standard deviation is 23.4 therefore,
Option A is the answer that is Jersey numbers are nominal data that are just replacements for names, so the resulting statistics are meaningless.
3
Easton mixed
kg of flour with
kg of sugar.
6
Determine a reasonable estimate for the amount of flour and sugar combined.
Choose 1 answer:
1
Less than
2
kg
B
More than
1
kg but less than 1 kg
2
More than 1 kg
Find the mean and standard deviation for each binomial random variable:
Answer: a) Mean = [tex]=37.80[/tex]
Standard deviation=[tex]=1.9442[/tex]
b) Mean = [tex]56.00[/tex]
Standard deviation=[tex]4.0988[/tex]
c) Mean = [tex]=24[/tex]
Standard deviation=[tex]2.4495[/tex]
Step-by-step explanation:
To compute Mean and standard deviation , we use following formula:
Mean = [tex]n\pi[/tex]
Standard deviation=[tex]\sqrt{n\pi(1-\pi)}[/tex]
a. [tex]n=42,\ \pi=0.90[/tex]
Mean = [tex]42\times0.90=37.80[/tex]
Standard deviation=[tex]\sqrt{42(0.90)(0.10)}=\sqrt{3.78}\approx1.9442[/tex]
b. [tex]n=80,\ \pi=0.70[/tex]
Mean = [tex]80\times0.70=56.00[/tex]
Standard deviation=[tex]\sqrt{80(0.70)(0.30)}=\sqrt{16.8}\approx4.0988[/tex]
c. [tex]n=32,\ \pi=0.75[/tex]
Mean = [tex]32\times0.75=24[/tex]
Standard deviation=[tex]\sqrt{32(0.75)(0.25)}=\sqrt{6}\approx2.4495[/tex]
(SAT Prep) Find the value of x.
Answer:
x = 65°
Step-by-step explanation:
Naming the sides of the parallelogram formed ABCD as shown in the attached image to this solution.
Angle A = 2x (vertically opposite angles are equal)
Angle A = Angle C (opposite angles of a parallelogram are equal)
Angle A = Angle C = 2x
(Angle C) + 50° = 180° (Sum of angles on a straight line is 180°)
2x + 50° = 180°
2x = 180° - 50° = 130°
x = (130°/2) = 65°
Hope this Helps!!!
Answer:
65 degrees
Step-by-step explanation:
How will the metric system be used in your furture career
Answer:
i feel as if in the United States, both the metric system and the English system of measurement are used, although the English system predominates. This discussion question has three parts:
Look around you to find something in the U.S. that is measured in metrics. Describe it to the class.
Give an example of how you think the metric system will be used in your future career.
Do you think the U.S. should switch to metric system exclusively? Why or why not?
This week we learned about the metric and U.S. customary measurement systems. Please upload and submit your responses to the following questions in at least 150 words:
In reflecting on both measurement systems, what did you find most important?
Explain how both measurement systems could relate to your life, community, or current/future career.
Expert Answer
Step-by-step explanation:
Suppose a city official conducts a hypothesis test to test the claim that the majority of voters oppose a proposed school tax. Assume that all of the conditions fro proceeding with a one-sample test on proportions have been met. The calculated test statistic is approximately 1.23 with an associated p-value of approximately 0.1093. Choose the conclusion that provides the best interpretation for the p-value at a significance level of alpha = 0.05.
A. If the null hypothesis is true, then the probability of getting a test statistic that is as or more extreme than the calculated test statistic of 1.23 is 0.1093. This result is surprising (or considered unusual) and could not easily happen by chance.
B. If the null hypothesis is true, then the probability of getting a test statistic that is as or more extreme than the calculated test statistic of 1.23 is 0.1093. This result is not surprising (or considered unusual) and could easily happen by chance
C. The p-value should be considered extreme: therefore, the hypothesis test proves that the null hypothesis is true
D. none of the above
Answer:
The correct option is (B).
Step-by-step explanation:
The p-value is well-defined as per the probability, [under the null-hypothesis (H₀)], of attaining a result equivalent to or more extreme than what was the truly observed value of the test statistic.
In this case, we need to test the claim that the majority of voters oppose a proposed school tax.
The hypothesis can be defined as follows:
H₀: The proportion of voters opposing a proposed school tax is not a majority, i.e. p ≤ 0.50.
Hₐ: The proportion of voters opposing a proposed school tax is a majority, i.e. p > 0.50.
It is provided that the test statistic value and p-value are:
z = 1.23
p-value = 0.1093
The probability, [under the null-hypothesis (H₀)], of attaining a result equivalent to or more extreme than what was the truly observed value of the test statistic is 0.1093.
The significance level of the test is:
α = 0.05
The p-value of the test is larger than the significance level of the test.
p-value = 0.1093 > α = 0.05
The null hypothesis will not be rejected.
Concluding that there is not enough evidence to support the claim.
Thus, the correct option is:
"If the null hypothesis is true, then the probability of getting a test statistic that is as or more extreme than the calculated test statistic of 1.23 is 0.1093. This result is not surprising (or considered unusual) and could easily happen by chance"
A line passes through the points ( – 4, – 2) and ( - 1, - 2). Determine the slope of the line.
Answer: -4/3
Step-by-step explanation:
Formula to find a slope of two given points is
y(sub2) - y(sub1) / x(sub2) - x(sub1)
Plug the values in to get the answer.
-2 - 2 / -1 - (-4)
-4/3
a truck and a car drive uniformly among the expressway from city a to city b. The truck leaves at 09:15 am and arrives at 1:15 pm. The car leaves at 10:00 am and arrives at 12:45 pm. At what times does the car overtake the truck? please help
Answer:
the car overtake the truck at time 11:40 am.
Step-by-step explanation:
We have both vehicules going at constant speed from city a to city b. The distance is unknown, but can be written as d.
We will express the time in hours (and decimals of hours).
The truck speed can be calculated estimating the time between arrival and start:
- The arrival time is 1.15 pm. This is t2=13.25.
- The starting time is 9:15 am. This is t1=9.25.
The truck took t2-t1=13.25-9.25=4 to go from city a to b.
The average speed is then:
[tex]v_t=\dfrac{\Delta x}{\Delta t}=\dfrac{d}{4}[/tex]
We can write the equation for the position x(t) for the truck as:
[tex]x(t)=x_0+v_t\cdot t=x_0+\dfrac{d}{4}t\\\\\\x(13.25)=x_0+\dfrac{d}{4}(13.25)=d\\\\x_0=d-3.3125d=-2.3125d\\\\\\x(t)=-2.3125d+0.25d\cdot t[/tex]
For the car we have:
- The arrival time is 12:45 am. This is t2=12.75.
- The starting time is 10 am. This is t1=10.
The car took t2-t1=12.75-10=2.75.
The average speed is then:
[tex]v_c=\dfrac{\Delta x}{\Delta t}=\dfrac{d}{2.75}[/tex]
We can write the equation for the position x(t) for the car as:
[tex]x(t)=x_0+v_c\cdot t=x_0+\dfrac{d}{2.75}t\\\\\\x(12.75)=x_0+\dfrac{d}{2.75}(12.75)=d\\\\x_0=d-4.6363d=-3.6363d\\\\\\x(t)=-3.6363d+0.3636d\cdot t[/tex]
The time at which the car overtake the car is the time when both vehicles have the same position:
[tex]x(t)/d=-2.3125+0.25\cdot t = -3.6363+0.3636\cdot t\\\\-2.3125+3.6363=(0.3636-0.25)t\\\\1.3238=0.1136t\\\\t=1.3238/0.1136\approx11.65[/tex]
The car overtakes the truck at t=11.65 hours or 11:39 am.
If the sample size is nequals9, what is the standard deviation of the population from which the sample was drawn?
Answer:
13.33
Step-by-step explanation:
As in the attached diagram, we can see that the points belong to [tex]\mu\pm \sigma[/tex] interval
Data provided in the question as per the details below:
[tex]\mu_{\bar x}[/tex] = 440
[tex]\mu_{\bar x} + \sigma_{\bar x}[/tex] = 480
So,
[tex]\sigma_{\bar x}[/tex] = 480 - 440
= 40
Now the standard deviation of the population is
[tex]V(\bar{x}) = \frac{\sigma}{\sqrt n} \\\\ = \frac{40}{\sqrt 9}[/tex]
= 13.33
Hence, the standard deviation of the population for which the sample is drawn is 13.33
At noon, ship A is 70 km west of ship B. Ship A is sailing south at 35 km/h and ship B is sailing north at 25 km/h. How fast is the distance between the ships changing at 4:00 PM
Answer:
57.6 km/h
Step-by-step explanation:
We are told that At noon, ship A is 70 km west of ship B.
Thus, coordinates of initial position of A and B is;
A(0,0) and B(70,0)
Now, we are told that Ship A is sailing south at 35 km/h and ship B is sailing north at 25 km/h. Thus, the final position of ship A and B after t hours are;
A(0,-35t) and B(70,25t)
Thus, distance between the two ships at time t hours is;
d(t) = √[(70 - 0)² + (25t - (-35t))²]
d(t) = √(4900 + 3600t²)
Now, to find how fast the distance between the ships changing, let's differentiate using the chain rule;
d'(t) = [1/(2√(4900 + 3600t²))] × 7200t
d'(t) = 3600t/√(4900 + 3600t²)
d'(t) = 3600t/10√(49 + 36t²)
d'(t) = 360t/√(49 + 36t²)
Now, at 4pm,it would have been 4 hours from noon. Thus, t = 4.
So;
d'(t) = (360×4)/√(49 + 36(4²))
d'(t) = 1440/√(49 + 576)
d'(t) = 1440/√625
d'(t) = 1440/25
d'(t) = 57.6 km/h
Suppose that MNO is isosceles with base NM. Suppose also that =m∠N+4x7° and =m∠M+2x29°. Find the degree measure of each angle in the triangle.
Answer:
m∠N = 51°
m∠M = 31°
m∠O = 98°
Step-by-step explanation:
It is given that ΔMNO is an isosceles triangle with base NM.
m∠N = (4x + 7)° and m∠M = (2x + 29)°
By the property of an isosceles triangle,
Two legs of an isosceles triangle are equal in measure.
ON ≅ OM
And angles opposite to these equal sides measure the same.
m∠N = m∠M
(4x + 7) = (2x + 29)
4x - 2x = 29 - 7
2x = 22
x = 11
m∠N = (4x + 7)° = 51°
m∠M = (2x + 9)° = 31°
m∠O = 180° - (m∠N + m∠M)
= 180° - (51° + 31°)
= 180° - 82°
= 98°
Hong buys a bag of 11 tangerines for $2.86.
Find the unit price in dollars per tangerine.
If necessary, round your answer to the nearest cent.
Answer:
$0.26
Step-by-step explanation:
To find the unit price, divide the cost by the amount you have.
$2.86/11 = $0.26
The unit price is $0.26.
A sample of 4 different calculators is randomly selected from a group containing 42 that are defective and 20 that have no defects. What is the probability that all four of the calculators selected are defective? No replacement. Round to four decimal places.
Answer:
0.2006
Step-by-step explanation:
The probability the first calculator is defective is 42/62.
The probability the second calculator is defective is 41/61.
The probability the third calculator is defective is 40/60.
The probability the fourth calculator is defective is 39/59.
The probability all four calculators are defective:
(42/62) (41/61) (40/60) (39/59) = 0.2006
Zen spent $255 on a bag and a belt. She wanted to buy another
similar bag with the remaining money but was short of $30. In the
end, she bought another similar belt and had $15 left in the end.
(a) How much more did the bag cost than the belt?
(b) How much did the belt cost?
Answer:
A)$ 45
B) $105
Step-by-step explanation:
Bag and a belt cost $255
Let bag = x
Let belt = y
X+y= 255 equation 1
Let total money be z first
Remaining money= z-255
X-30 = z-255
Y +15 = z-255
Equating the left side of the equation
X+30 = y+15
X-y= 45 equation 2
Solving simultaneously
X+y= 255
X-y= 45
2x = 300
X= 150
If x= 150
150-y= 45
150-45= y
105=y
Bag = $150
Belt = $105
Bag Is 150-105 more than the belt
150-105= $45
A bag contains six balls labeled 1 through 6. One ball will be randomly picked.
What is the probability of picking an odd number?
Write your answer as a fraction in simplest form.
S = sample space = set of all possible outcomes
S = set of whole numbers 1 through 6
S = {1,2,3,4,5,6}
E = event space = set of outcomes we want to happen
E = set of odd numbers between 1 through 6
E = {1,3,5}
We have 3 items in set E and 6 items in set S. So there are 3 ways to get what we want to happen out of 6 ways total. The probability is therefore 3/6 = 1/2
Answer: 1/2