A house is infested with mice and to combat this the householder acquired four cats cyd, Greg, Ken, and Rom, The householder observes that only half of the creatures caught are mice. A fifth are voles and the rest are birds. 20% of the catches are made by Cyd, 45% by Greg, 10% by Ken and 25% by rom. a) What is the probability of a randomly selected catch being a mouse caught by Cyd? b) Bird not caught by Cyd? c) Greg's catches are equally likely to be a mouse, a bird or a vole. What is the probability of a randomly selected d) The probability of a randomly selected catch being a mouse caught by Ken is 0.05 . What is the probablity that a catch being a mouse caught by Greg? e) Given that the probability of a randomly selected catch is a mouse caught by Rom is 0.2 verify that the catch made by Ken is a mouse? probability of a randomly selected catch being a mouse is 0.5 . f) What is the probability that a catch which is a mouse was made by Cyd?
Note that the probabilities are given below.
a) the probability of a randomly selected catch being a mouse caught by Cyd
p(Catching a mount) x p(Cyd made the catch)
= 0.5x .2
= 0.1
b) the probability of a bird not caught by Cyd is 0.5 x 0.8 = 0.4.
Thus
P(that a catch is a bird) x p(the Cyd didn't make the catch)
= 0.3 x 0.8
=0.24
c) The probability of a randomly selected catch being caught by Greg is 0.45
To calculate, we say
(0.5 x0.45) + (0.3 x 0.45) + (0.2 x .45)
= 0.45.
d)
P (mouse caught by Greg) = (0.45 x 0.5) / 1
= 0.225.
e) P(catch is a mouse caught by Ken and catch is a mouse)
= P(catch is a mouse | catch is made by Ken) x P(catch is made by Ken)
= 0.05 x 0.1
= 0.005
f)
P (catch made by Cyd | catch is a mouse)
= 0.1 x 0.2 / 0.5
= 0.04
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If x and y vary directly and y is 2 when x is 3, what is why when x is 2
Step-by-step explanation:
Direct variation means y = k x
when y = 2 x= 3
2 = k *3
2/3 = k
so the variation becomes y = 2/3 x
when x = 2
y = 2/3 (2)= 4/3
Let the vector v have an initial point at (1,−1) and a terminal point at (7,2) what is the direction angle?
The direction angle of the vector with initial point (1, -1) and terminal point (7, 2) is approximately 26.57 degrees, found by calculating the arctangent of the ratio of the y and x components of the vector.
The direction angle of the vector v is the angle it makes with the positive x-axis, measured counterclockwise.
To find this angle, we need to calculate the difference between the y-coordinates and x-coordinates of the terminal and initial points of the vector, respectively. Then, we can use the arctangent function to find the angle.
Let's first find the components of the vector v
v = <7 - 1, 2 - (-1)> = <6, 3>
Now, we can find the direction angle as follows
θ = arctan(3/6)
θ = 0.4636 radians (in decimal form)
To convert this to degrees, we can multiply by 180/π
θ ≈ 26.57°
Therefore, the direction angle of the vector v is approximately 26.57 degrees.
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Mr Greenwood paid $11 for 5 buns and 2 sausages last week. His wife bought 8 such buns and 4 such sausages for $19.60 this week.
(a)
How much was each bun?
(b) How much was each sausages?
Answer:
Step-by-step explanation:
mark me brainliest
10. Bond A is zero-coupon bond paying $100 one year from now. Bond B is a zero-coupon bond paying
$100 two years from now. Bond C is a 10% coupon bond that pays $10 one year from now and $10 plus the $100 principal two years from now. The yield to maturity on bond A is 10%, and the price of bond B is $84.18. Assuming annual
compounding, what is the yield to maturity on Bond B?
*Make sure to input all percentage answers as numeric values without symbols,
0.0600.
The yield to maturity on Bond B is 9%
How to calculate the yield to maturityWe know that Zero Coupon Bond Value= F/(1+r)^t
F= Face Value =100
r= Rate of interest
t= time to maturity =2Yrs
Price= F/(1+r)^t
84.18 = 100/(1+r)^t
(1+r)^t=100/84.18
(1+r)^2=1.18793
1+r=(1.18793)^(1/2)
r = 1.089922 - 1
r = 8.9922%
r = 9% (Approx)
In conclusion, the yield to maturity on Bond B is 9%
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A restaurant manager recorded the number of people in different age groups who attended their food festival. They created the following histogram:
Histogram with title Food Festival Participants, horizontal axis labeled Age Group (year) with bins 0 to 19, 20 to 39, 40 to 59, and 60 to 79, and vertical axis labeled Number of People with values from 0 to 60 at intervals of 10. The first bin goes to 20, the second goes to 40, the third goes to 60, and the last goes to 50.
What percentage of the participants are ages 40 to 59? Round to the nearest whole percent.
Work out and simplify where possible. A) 3/4 + 5/6. B) 4/7 - 1/3
Factor cards is a one - player game using numbered cards. To begin with, all cards are in a central pile with their numbers visible. At each turn , exactly one card is moved from the central pile to the score pile and one or more cards are moved from central pile to the discard pile according to these rules.
Rule 1: A card may be moved to the score pile only if the number on the card has at least one of its factors, other than itself, still on the central pile.
Rule 2: When a card is moved to the score pile, all the cards that have factors of its number and are still in the central pile are moved to the discard pile.
Play stops when no card in the control pile has a factor other than itself in the central pile. The players score is the sum of all numbers on the cards in the score pile at the end of play.
In the following questions, the game starts with 20 cards numbered 1 to 20 and are therefore called 20-games.
A) Show steps that will produce a score of more than 100 points in a 20- game
B) What is the maximum score for a 20- game. Explain why it is the maximum
C) Explain why every 20- game ends with 8 or fewer cards in the score pile .
The match terminates as soon as the central heap runs out of cards whose factor are not present elsewhere, resulting in a score of 92 - falling short from 100.
How to explain the informationIt should be noted that to acquire a higher point achievement, alternative approaches can be tested; however, reaching beyond the hundred mark is not guaranteed.
Conversely, with each 20-game, the final outcome should contain 8 or fewer pieces in the tally pile since there are strictly 17 cards eligible to be shifted into this collection. Subsequently, due to the 138 maximum points potential (stated in part B), and the entire set amounting for 210 points - the minimum count for items within the discard pool will be 3 (as calculated from 20 - 17).
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Given u = 4i - 7j and v = -6i + 9j, what is u • v?
-87
-82
26
39
Answer: A
Step-by-step explanation: -87
Give me the domain and range
Tell me if the graph is a function or not
The domain and range of the graph are domain = [-2, 5] and range is [-6, 2] and the graph is not a function
Calculating the domain and range of the graphFrom the question, we have the following parameters that can be used in our computation:
The graph
On the graph, we have the x values to be
x = -2 to 5
On the graph, we have the y values to be
y = -6 to 2
This means that domain = [-2, 5] and range is [-6, 2]
If the graph is a function or notThe graph is the graph of a circle
A circle does not represent a function
Hence, the graph is not a function
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10. Find the surface area of the
polyhedron that can be
assembled from this net. Show
your reasoning.
The surface area of the polyhedron is calculated be equal to 224 square inches.
How to evaluate for the area of the polyhedronThe polyhedron can be observed to have a large rectangle between two identical triangles by the sides
area of rectangle = length × width
The large rectangle have;
length = (12 + 10 + 10) in = 32 in
width = 4 in
area of large rectangle the = 32 in × 4 in = 128 in²
area of one identical triangles = 1/2 × 12 in × 8 in = 48 in²
area of 2 identical triangles = 2 × 48 in² = 96 in²
Surface area of the polyhedron = 128 in² + 96 in²
Surface area of the polyhedron = 224 in²
Therefore, the surface area of the polyhedron is calculated be equal to 224 square inches.
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Rebecca Kate Foster is starting a new job. She is 23 years old and graduated from college
with no student loan debt. This is her only job, and she makes a salary that allows her to
bring home $3,300 a month. She's not married and has no children or anyone else who
is supported by her income. Over the past year, she has given a total of $3,960 to charity.
Her address is 1234 Main St., New York, NY 12345, and her Social Security number is
123-45-6789.
Note that the above prompt requires you to under stand what a W-4 form is and how to complete one.
What is the process for comleting the W-4 form?Rbecca needs to s tart by entering your personal information in boxes 1-4, including your name, address, Social Security number, and filing status. In this case, Rebecca Kate Foster's information is:
Box 1: Rebecca Kate Foster
Box 2: 1234 Main St.
Box 3: New York, NY 12345
Box 4: 123-45-6789
Box 5: Single
In box 6, write "1" since Rebecca only has one job.
Rebecca can claim the standard deduction or itemize deductions in box 7. She may benefit from itemizing deductions because she has donated $3,960 to charity in the last year.
Rebecca can claim whatever excess tax withholding she wants each paycheck in box 8. She may not need to withhold any further taxes because she has no dependents and is not married. If she prefers, she can leave this section blank.
Rebecca can claim any extra withholding for the year in box 9. If she anticipates to owing taxes at the end of the year, she may want to withhold more from each paycheck to prevent a hefty tax payment later. If she anticipates a reimbursement, she should withhold less. She can use the IRS's withholding calculator to determine the right amount.
Finally, sign and date the form in box 5 before submitting it to your company.
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Full Question:
Although part of your question is missing, you might be referring to this full question:
DIRECTIONS Read the scenario below and fill out the W-4 form using the information provided. Then, read the W-2 form and answer the questions that follow. W-4 Form Rebecca Kate Foster is starting a new job. She is 23 years old and graduated from college with no student loan debt. This is her only job, and she makes a salary that allows her to bring home $3,300 a month. She’s not married and has no children or anyone else who is supported by her income. Over the past year, she has given a total of $3,960 to charity. Her address is 1234 Main St., New York, NY 12345, and her Social Security number is 123-45-6789.
A motorboat travels 234 miles in 6 hours going upstream. It travels 342 miles going downstream in the same amount of time. What is the rate of the boat in still water and what is the rate of the current
The boat is moving at 48 mph while the current is moving at 9 mph in still water.
To solve this problemLet's use the letters "B" for the boat's speed in still water and "C" for the current's speed.
The boat's effective speed upstream is B - C because it is moving against the current.
Since the boat is moving downstream against the tide, its effective speed is equal to B plus C.
Based on the supplied data, we can construct the following two equations:
234 = 6(B - C)
342 = 6(B + C)
Making these equations simpler:
39 = B - C
57 = B + C
Now that we have added the two equations, we may solve for B and C:
39 + 57 = 2B
96 = 2B
B = 48
Therefore, the boat's speed in calm water is 48 mph.
To find C, we can rewrite one of the initial equations with this value as a substitute:
39 = 48 - C C = 9
Thus, the current is moving at a 9 mph velocity.
Therefore, the boat is moving at 48 mph while the current is moving at 9 mph in still water.
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For the given rectangular equation give its equivalent polar equation
Answer:
The last option
[tex]r = \dfrac{14}{6\cos\theta - \sin\theta}[/tex]
Step-by-step explanation:
Given equation is 6x - y = 14
To convert an equation in rectangular(cartesian) form, f(x, y) to polar f(r, θ) we use the following information
x = rcosθ
y = rsinθ
Substituting for x and y in the original rectangular equation 6x - y = 14,
6(rcosθ) - rsinθ = 14
Factoring out r on the left side,
r(6cosθ - sinθ) = 14
which gives
[tex]r = \dfrac{14}{6\cos\theta - \sin\theta}[/tex]
That would be choice 4
When Emilia looked at her cell phone bill for the month, she saw that she had spent 1/12 of her minutes talking to her mother and 5/12 of her minutes talking to her best friend. What fraction of the minutes did Emilia spend talking to either her mom or her best friend?
Answer:
The answer to your problem is, She spend more talking to her friend then her mother
Step-by-step explanation:
The question asking:
What fraction of the minutes did Emilia spend talking to either her mom or her best friend?
So we can see that she talks to her friend instead of her mother shown;
[tex]\frac{1}{12} < \frac{5}{12}[/tex]
The total equals to [tex]\frac{6}{12} or\frac{1}{2}[/tex]
So, She spend more talking to her friend then her mother
Thus the answer to your problem is, She spend more talking to her friend then her mother
PLEASE HELP ASAP WILL GOVE BRAINLIEST NEED THIS AWNSERED IN 15 MINUTES
The segment lengths on the right triangle are given as follows:
JL = 13.[tex]KL = 13\sqrt{3}[/tex]What are the trigonometric ratios?The three trigonometric ratios are the sine, the cosine and the tangent, and they are defined as follows:
Sine of angle = length of opposite side to the angle divided by the length of the hypotenuse.Cosine of angle = length of adjacent side to the angle divided by the length of the hypotenuse.Tangent of angle = length of opposite side to the angle divided by the length of the adjacent side to the angle.The sum of the internal angle measures of a triangle is of 180º, hence the missing angle is given as follows:
m < L = 180 - (30 + 60)
m < L = 90º.
Hence the segment JL represents the hypotenuse of the figure.
JL is opposite to the angle K, hence it's length is obtained as follows:
sin(30º) = JL/26
1/2 = JL/26
2JL = 26
JL = 13.
Segment KL is adjacent to the angle of 30º, hence it's length is obtained as follows:
cos(30º) = KL/26
[tex]\frac{\sqrt{3}}{2} = \frac{KL}{26}[/tex]
[tex]2KL = 26\sqrt{3}[/tex]
[tex]KL = 13\sqrt{3}[/tex]
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(06.06 MC)
The table below shows the amount of money, in cents, Celine had in her savings account after different
number of years:
Years 251463
Money in
36 112 12 85 150 60
cents
Approximately, what will be the amount of money, in cents, that Celine will save in 12 years?
250
300
400
200
Approximately, the amount of money, in cents, that Celine will save in 12 years is: B. 300
How to determine the equation of line of best fit?In this scenario, the years would be plotted on the x-axis (x-coordinate) of the scatter plot while the money (in cents) would be plotted on the y-axis (y-coordinate) of the scatter plot through the use of Microsoft Excel.
On the Microsoft Excel worksheet, you should right click on any data point on the scatter plot, select format trend line, and then tick the box to display an equation for the line of best fit (trend line) on the scatter plot.
From the scatter plot (see attachment) which models the relationship between the years and the money (in cents), an equation for the line of best fit is given by
y = 26.9x - 18.5
when x = 12, the amount of money, in cents, that Celine will save in 12 years is given by;
y = 26.9(12) - 18.5
y ≈ 300 cents.
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gingerbread house is shaped like the image below. How many square centimeters of frosting will take to cover the outside?
(NEED HELP!!!)
There are 32 cm² of frosting will take to cover the outside.
Given that;
Base of house = 2 cm
And, Height of house = 3 cm
Since, The shape of house is like a prism.
We know that;
Area of Prism is,
SA = 2B + ph,
where B, stands for the area of the base, p represents the perimeter of the base, and h stands for the height of the prism.
Hence, We get;
SA = 2 × (2 × 2) + 2 (2 + 2) × 3
SA = 8 + 24
SA = 32 cm²
Hence, There are 32 cm² of frosting will take to cover the outside.
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3. Olivia is constructing a monument to honor the heroes in her community. It will be in
the shape of a regular pentagonal prism and stand 10 feet tall. She will need 5,119.5
cubic feet of concrete to fill the prism. Olivia will run lights across the top of the
monument from the center to the midpoint of one side.
17.25 ft
SCRATCHPAD
10 ft
The height will be 61.8 ft
How to solve for the heightFind the volume of prism
Volume = Base Area × Height
since height = 10 feet
5,119.5 ft³ / 10 ft
= 511.95 ft²
formula for the area of a regular polygon is:
Area = (Perimeter × Apothem) / 2
ide length of the pentagon as 's' and the apothem as 'a'
511.95 ft² = (5s × a) / 2
angle at the center of the pentagon is 360° / 5 = 72°
72 / 2 = 36 degrees
tan(36°) = (s/2) / 17.25
solve for the value of s
s = 2 × 17.25 × tan(36°)
= 12.36 ft
5 s =
5 x 12.36 ft
= 61.8 ft
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Consider the sequence 4,323,313,3
The explicit rule for the sequence 4, 3 2/3, 3 1/3, 3.... is f(n) = 4 - 1/3(n - 1)
Finding the explicit rule for the sequenceFrom the question, we have the following parameters that can be used in our computation:
4, 3 2/3, 3 1/3, 3....
In the above sequence, we can see that 1/2 is subtracted from the previous term to get the new term
Take for instance
2nd = 4 - 1/3 = 3 2/3
3rd = 3 2/3 - 1/3 = 3 1/3
4th = 3 1/3 - 1/3 = 3
And so on
This means that
First term, a = 4Common difference, d = -1/3So, the explicit rule is
f(n) = a + (n - 1)d
This gives
f(n) = 4 - 1/3(n - 1)
Hence, the explicit formula is f(n) = 4 - 1/3(n - 1)
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Complete question
Consider the sequence 4,3 2/3,3 1/3, 3....
What is the explicit rule for this sequence
The coordinate of the points below represents the vertices of a rectangle what is the perimeter in units of the rectangles WXYZ
The perimeter of the rectangle is P = 18 units
Given data ,
Let the rectangle be represented as ΔWXYZ
Now , the coordinates of the triangle are
W ( 3 , 3 ) , X ( 8 , 3 ) , Y ( 8 , 7 ) and Z ( 3 , 7 )
The perimeter of the rectangle = 2 ( length + width )
The width of the rectangle W = ( 7 - 3 ) = 4 units
The length of the rectangle L = ( ( 8 - 3 ) = 5 units
So , P = 2 ( 4 + 5 )
P = 2 x 9
P = 18 units
Hence , the perimeter is 18 units
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Is it 65 and 5 bag variability????
The estimate of the population mean is 80 and the variability in the distribution is 120
The estimate of the population meanHere, we have
The dot plots
From the dot plots, we can see that the data are normally distributed
This means that the mean, the median and the mode are equal
From the distribution of the random variable, we have the following readings
mean = 80Hence, the estimate of the population mean is 80
The variability in the distributionHere, we use the range
So, we have
Variability = Highest - Least
This gives
Variability = 140 - 20
Variability = 120
So, the variability in the distribution is 120
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I can prove that 2=1, where is the error?
X = 1
X+X = 1+X
2x = 1+X
2x = X+1
2X-2 = X+1-2
2x-2 = X-1
2 (x-1)/(x-1) = X-1/X-1
2 times 1 = 1 1-1 / 1-1
2 = 1
I subtracted -2
because thats the # I chose to subtract with.
Answer:The algebraic steps you have taken are incorrect, leading to an invalid conclusion. Let's go through each step and see where the mistake is made:
X = 1 (given)
X+X = 1+X (adding X to both sides)
2X = 1+X (combining like terms)
2X = X+1 (rearranging terms)
2X-2 = X+1-2 (subtracting 2 from both sides)
2X-2 = X-1 (simplifying)
2(x-1)/(x-1) = (x-1)/(x-1) (dividing both sides by x-1, note that x cannot be 1 as it would result in division by 0)
2 = 1 (canceling out the (x-1)/(x-1) on both sides)
The error lies in dividing both sides by (x-1) in step 7. Although (x-1) appears on both sides of the equation, it is not equal to zero as x cannot be 1 due to division by zero. Dividing by (x-1) effectively cancels it out, leading to the incorrect result of 2=1.
Step-by-step explanation:
(Please help in image)
Answer:
[tex] {x}^{2} + 11x + 18 = [/tex]
[tex](x + 2)(x + 9)[/tex]
The two numbers are 2 and 9.
2 + 9 = 11, and 2 × 9 = 18.
What happens to a consistent slope when the y value starts to decrease and the x value remains the same over time?
A. Y decreases and X decreases
B. Y decreases and X increases
C. Y increases and X increases
D. Y increases and X decreases
The correct answer is option B:
⇒ Y decreases and X increases.
Given that;
the y value starts to decrease and the x value remains the same over time.
Now, We know that;
the slope remains constant, but the y value decreases as you move along the slope in the negative y direction, while the x value increases.
Hence,
If the y value starts to decrease while the x value remains the same over time on a consistent slope,
Thus, The correct answer is option B:
⇒ Y decreases and X increases.
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find the inverse of the function f(x)=-1/25x^2, x<0
The function is :
[tex]f(x) =\frac{-1}{25x^{2} },x < 0[/tex] the inverse function is:
Inverse function: [tex]f^-^x(x)=-\frac{\sqrt{\frac{-1}{x} } }{5}[/tex]
Domain: (-[tex]\infty[/tex],9]
Range: [tex](-\infty,0][/tex]
What is an inverse function ?If the inverse function of f is the function g, then x = f(x) gives x = g(y). We just need to reverse the function.
An inverse function or an anti function is defined as a function, which can reverse into another function. In simple words, if any function “f” takes x to y then, the inverse of “f” will take y to x. If the function is denoted by ‘f’ or ‘F’, then the inverse function is denoted by f-1 or F-1. One should not confuse (-1) with exponent or reciprocal here.
If f and g are inverse functions, then f(x) = y if and only if g(y) = x
The function is :
[tex]f(x) =\frac{-1}{25x^{2} },x < 0[/tex]
We have to find the inverse of the function.
The inverse, interchange the variables solve for y,
Now,
[tex]f(x) =\frac{-1}{25x^{2} },x < 0[/tex]
[tex]f^-^x(x)=\frac{\sqrt{\frac{-1}{x} } }{5}[/tex]
So, [tex]f^-^x(x)=-\frac{\sqrt{\frac{-1}{x} } }{5}[/tex]
Hence,
Inverse function: [tex]f^-^x(x)=-\frac{\sqrt{\frac{-1}{x} } }{5}[/tex]
Domain: (-[tex]\infty[/tex],9]
Range: [tex](-\infty,0][/tex]
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The insurance premium of a new bus is GH¢93.30 plus 15% of the insured value. What is the insurance premium of a bus whose insured value is GH¢250.00?
The requried insurance premium of a bus whose insured value is GH¢250.00 is GH¢130.80.
The insurance premium of a bus is GH¢93.30 plus 15% of the insured value.
Let's first calculate 15% of¢250.00:
15% of GH¢250.00 = 0.15 x 250.00 = GH¢37.50
Now, we can add this amount to the base premium of GH¢93.30 to find the total insurance premium for the bus:
GH¢93.30 + GH¢37.50 = GH¢130.80
Therefore, the insurance premium of a bus whose insured value is GH¢250.00 is GH¢130.80.
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Find the equation of the circle if (-3,-7) is a point on the circle and the midpoint of the circle's diameter is (2,5).
A. (x - 2)2 + (y - 5)2 = 169
B. (x - 2)2 + (y - 5)2 = 25
C. (x + 3)2 + (y + 7)2 = 169
D. (x + 3)2 + (y + 7)2 = 25
(x+3)²+(y+7)²=169 is the equation of the circle if (-3,-7) is a point on the circle and the midpoint of the circle's diameter is (2,5).
The equation of the circle if (-3,-7) is a point on the circle and the midpoint of the circle's diameter is (2,5).
The radius of the circle is 13
The equation of circle in standard form is (x-h)²+(y-k)²=r²
(h, k) is centre of circle
(-3, -7) is centre
(x+3)²+(y+7)²=13²
(x+3)²+(y+7)²=169
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A marketing research company desires to know the mean consumption of milk per week among people over age 30 . They believe that the milk consumption has a mean of 3.5 liters, and want to construct a 85% confidence interval with a maximum error of 0.07 liters. Assuming a standard deviation of 1.4 liters, what is the minimum number of people over age 30 they must include in their sample? Round your answer up to the next integer.
The minimum number of people over age 30 they must include in their sample is: 829 people
How to calculate the standard error?The formula for calculating the standard error is:
SE = μ ± Z(σ/√N)
Where:
σ = the standard deviation,
N = the sample size,
Z = the Z value for the percent confidence level desired.
We must find the Z value, at the 85% confidence level from a Cumulative Standardized Normal table for the 99% confidence level. This gives us the value of Z = 1.44
σ = 1.4 liters
N = 0.07
Thus:
0.07 = 1.44(1.4/√N)
0.07/1.44 = 1.4/√N
1.4/√N = 0.04861
√N = 1.4/0.04861
N = (1.4/0.04861)²
N = 829 people
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What has no solutions in common with 6x+2y=12
Answer:
-6x - 2y = 12
Step-by-step explanation: