Using the Poisson distribution, it is found that the probabilities are:
a) 0.149
b) 0.6993
c) 0.5503
We are given only the mean, hence, the Poisson distribution is used.
In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by:
[tex]P(X = x) = \frac{e^{-\mu}\mu^{x}}{(x)!}[/tex]
The parameters are:
x is the number of successes e = 2.71828 is the Euler number [tex]\mu[/tex] is the mean in the given interval.The mean is of 7 births per minute, hence [tex]\mu = 7[/tex].
Item a:
The probability is P(X = 6), hence:
[tex]P(X = x) = \frac{e^{-\mu}\mu^{x}}{(x)!}[/tex]
[tex]P(X = 6) = \frac{e^{-7}(7)^{6}}{(6)!} = 0.149[/tex]
Item b:
This probability is:
[tex]P(X \geq 6) = 1 - P(X < 6)[/tex]
In which:
[tex]P(X < 6) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5)[/tex]
Following the logic used in item a to find each probability, we have that [tex]P(X < 6) = 0.3007[/tex], hence:
[tex]P(X \geq 6) = 1 - P(X < 6) = 1 - 0.3007 = 0.6993[/tex]
Item c:
This probability is:
[tex]P(X > 6) = 1 - P(X \leq 6)[/tex]
[tex]P(X \leq 6) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) + P(X = 6)[/tex]
We have that [tex]P(X \leq 6) = 0.4497[/tex], hence:
[tex]P(X > 6) = 1 - P(X \leq 6) = 1 - 0.4497 = 0.5503[/tex]
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1. Andrea’s car has broken down for the third time this month, and she has decided to buy a different car. Her dream car, a 2016 Chevrolet Camaro, costs $38,000. She has a $4,000 down payment saved, and the bank is offering 3.00% APR on 60 month loans for new cars.
a. How much will Andrea need to borrow to buy the Camaro?
b. What would Andrea need to type in Excel to figure her monthly payment, and what will her monthly payment be?
c. What will the total of all of Andrea’s payments be over the lifetime of the car loan?
d. How much will Andrea pay in interest over the lifetime of the car loan?
A) Andrea will need to borrow $34,000 to buy the Camaro
B) Andrea will need to type =(34000x1.03 ^ 5) / 60 in Excel to figure her monthly payment, which will be $656,92.
C) The total of all of Andrea’s payments be over the lifetime of the car loan will be $39.415,31
D) Andrea will pay $5415.31 in interest over the lifetime of the car loan
Since Andrea's car has broken down for the third time this month, and she has decided to buy a different car, and her dream car, a 2016 Chevrolet Camaro, costs $ 38,000, and she has a $ 4,000 down payment saved, and the bank is offering 3.00% APR on 60 month loans for new cars, to determine A) how much will Andrea need to borrow to buy the Camaro; B) what would Andrea need to type in Excel to figure her monthly payment from her, and what will her her monthly payment be from her; C) what will the total of all of Andrea’s payments be over the lifetime of the car loan; and D) how much will Andrea pay in interest over the lifetime of the car loan, the following calculations must be performed:
A) 38000 - 4000 = X 34000 = X
B) = (34000x1.03 ^ 5) / 6039.415,31 / 60656,92C) 34000 x 1.03^5 = X34000 x 1.1592 = X39.415,31 = XD) (34000 x 1.03^5) - 34000 = X(34000 x 1.1592) - 34000 = X39415.31 - 34000 = X5415.31 = X
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Suppose that the universal set U is the set of all even integers from 1 to 16 inclusively and A={2,4,8,16}. Find Ac by using a Venn diagram.
Answer:
Correct answer is {6,10,12,14}
Step-by-step explanation:
Maria wrote her 606 word
essay in 20 1/5 minutes. At
what rate is she typing?
Answer:
29.5
Step-by-step explanation:
Multiply 606 and 20.5 and get 29.5.
Juan wants to buy a video game for $63. He saves $12 every Friday. Part A. Create an equation to represent Juan's total savings, y, in dollars, after x Fridays. y
Answer:
Answer in explanation.
Step-by-step explanation:
An equation to represent Juan's total savings y, in dollars, after x Fridays will be;
⇒ y = 12x
What is an expression?
Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
Juan wants to buy a video game for $63.
And, He saves $12 every Friday.
Now,
Let total dollars after x Friday = y
And, He saves $12 every Friday.
So, We can formulate;
⇒ Total money (y) = 12x
⇒ y = 12x
Thus, An equation to represent Juan's total savings y, in dollars, after x Fridays will be;
⇒ y = 12x
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12.) Samuel is 30.75 inches tall. His younger brother, Spencer, is 6 inches shorter. How tall is Spencer?
Answer: Spencer is 24.75 inches tall
Step-by-step explanation: Just subtract 6 from 30.75 to find the answer
Answer:
The percentage increase in Spencer's height is 125%
Step-by-step explanation:
Solution:
Initial height of spencer = 28 inches
Increased height of spencer = 5 feet 3 inches
= 5 feet + 3 inches
(5 feet = 5 ×12=60 inches)
= 60 + 3
In which quadrant does the angle t lie if tan(t)>0 and cos(t)<0?
A) II
B) IV
C) Cannot be determined
D) III
E) I
Quadrant is a quarter of a coordinate plane
The location of angle t is in quadrant 3
The trigonometry equations are given as:
tan(t)>0 and cos(t)<0
The cosine of an angle is negative in the following quadrants
Quadrant 2Quadrant 3The cosine of an angle is positive in the following quadrants
Quadrant 3The intersection of the above points is quadrant 3
This means that the angle is in quadrant 3
Hence, the true option is (D) III
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Please help! Cant figure this one out!
Answer:
20.5
Step-by-step explanation:
Given that shapes are similar:
45 = 2x + 4 subtract 4 from both sides
41 = 2x divide both sides by 2
20.5 = x
please help me calculation completing square?
x²+2x-24=0?
Answer:
x = 4, -6
Step-by-step explanation:
x = 4, -6
Find an expression that gives you a quotient
of 16
Answer: Does 32/2 work it equals 16
Step-by-step explanation:
The number expression would be 32/2 which gives 16 after applying the arithmetic operation.
What is an arithmetic operation?It is defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has a basic four operators that is +, -, ×, and ÷.
It is given that:
The quotient is 16
Let us assume 32 and 2 are the numbers that can be use in the number expression
The number expression is:
= 32/2
= 16
Thus, the number expression would be 32/2 which gives 16 after applying the arithmetic operation.
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Im so confused- please help
Step-by-step explanation:
a/q
x + x - 3 + 2x - 9 = 36
4x - 12 = 36
4x = 36 + 12 = 48
x = 48/4 = 12
x = 12
so,
x = 12
x - 3 = 12 - 3 = 9
2x - 9 = 2(12) - 9 = 15
we know,
area = 1/2 × base × height
so,
→ 1/2 × 12 × 9
→ 1 × 6 × 9
→ 54 inches.
HOPE THIS ANSWER HELPS YOU DEAR! TAKE CARE
Given the following exponential function, identify whether the change represents growth or decay, and determine the percentage rate of increase or decrease.
y=21(0.97)^x
what is the % increase
Answer:
Step-by-step explanation:
As the number under the exponent is less than 1, this is a decay function.
y decreases by (1 - 0.97)100 = 3% for each unit increase in x
so the increase would be -3%
Calculate the volume of the pyramid. Round your answer to the nearest hundredth 10in 7in
Answer:
Place the numbers in their places. b=base h=height.
Step-by-step explanation:
What is the 5th row of Pascal's triangle?
Answer:
Row 5 115 161051
Step-by-step explanation:
A radioactive substance decays exponentially. A scientist begins with 150 milligrams of a radioactive substance. After 20 hours, 75 mg of the substance remains. How many milligrams will remain after 27 hours?
Answer:
Step-by-step explanation:
Identify the initial amount a and the rate of growth r (as a percent) of the exponential function f(t) = 1500(1.074)t. Evaluate the
function when t=5. Round your answer to the nearest tenth.
A=
R=%
When t=5, f(5)=
The initial amount is the first number = 1500
Rate of growth is inside the parentheses and is added to 1, the rate of growth is 7.4%
Replace t with 5 and solve
1500(1.074) ^5 = $2143.45
Answer:
The growth rate is 7.4% and the initial amount is 1500. The answer when t=5 is 2143.45.
Step-by-step explanation:
Assuming this is actually supposed to be written as 1500*(1.074)^t, then this equation follows the standard growth form y = A(1+r)^t where A represents the initial amount, r represents the rate as a decimal, and t represents time. This means that 1500 (A) would be the initial amount, and if you subtract 1 from what's inside the paratheses, you will get the r rate as a decimal. To get this as a percent, simply multiply it by 100, so you will get 7.4% as your growth rate.
To find what the answer would be when t = 5, just plug in 5 for the value of t in the equation.
f(5) = 1500*(1.074^5)
f(5) = 1500*(1.42896)
f(5) = 2143.45
Một người tiêu dùng có thu nhập I = 1.200 đ dùng để mua hai sản phẩm X và Y với giá tương ứng là PX = 100đ/sp và PY = 300đ/sp. Mức thoả mãn được thể hiện qua hàm số:
TUX = -1/3X2 + 10X
TUY = -1/2Y2 + 20Y
a. Hãy xác định phương án tiêu dùng tối ưu của người này?
b. Tính tổng hữu dụng tương ứng đạt được?
gak bisa bahasa inggris.
Step-by-step explanation:
maap.
Find the values of p and q so that (-2,5) is the midpoint of the segments joining points (p,p+q) and (p+4, 3q+6)
Answer:
Step-by-step explanation:
( [tex]x_{1}[/tex] , [tex]y_{1}[/tex] ) and ( [tex]x_{2}[/tex] , [tex]y_{2}[/tex] )
midpoint is ( [tex]\frac{x_{1} +x_{2} }{2}[/tex] , [tex]\frac{y_{1} +y_{2} }{2}[/tex] )
~~~~~~~~~~~~~
( p , p + q )
( p + 4 , 3q + 6 )
( p + p + 4 ) ÷ 2 = - 2
p = - 4
( - 4 + q + 3q + 6 ) ÷ 2 = 5
2q = 4
q = 2
What is the probability of rolling a number greater than 7 on a 6-sided die rolled
15. A farmer records the number of eggs that chickens on the farm produce each week. The table
shows the results.
143
160
117
137
152
108
128
If during the next week, the chickens on the farm produce 60 eggs, which statement is true?
A The value 60 is an outlier that will skew the data to the left.
B The value 60 is an outlier that will skew the data to the right.
С The value 60 is not an outlier, and it will not skew the data in either direction.
D
The value 60 is not an outlier, and the effect on the data is unknown.
(a) Write an equation of the line that passes through the point and is parallel to the given line.
(b) Write an equation of the line that passes through the point and is perpendicular to the given line.
9514 1404 393
Answer:
parallel: y = x -1perpendicular: y = -x -3Step-by-step explanation:
The given line has a rise of 1 for each run of 1, so a slope of 1. If you draw a line with a slope of 1 through the given point, you can see that it intersects the y-axis at y = -1. Then the slope-intercept equation is ...
y = x -1 . . . . . equation of parallel line
__
The perpendicular line will have a slope that is the opposite reciprocal of the slope of the given line: m = -1/1 = -1
A point that is 1 unit right and 1 unit down from the given point is -3 on the y-axis. This is the y-intercept of the perpendicular line. The equation is ...
y = -x -3 . . . . . equation of perpendicular line
9514 1404 393
Answer:
parallel: y = x -1
perpendicular: y = -x -3
Step-by-step explanation:
The given line has a rise of 1 for each run of 1, so a slope of 1. If you draw a line with a slope of 1 through the given point, you can see that it intersects the y-axis at y = -1. Then the slope-intercept equation is ...
y = x -1 . . . . . equation of parallel line
__
The perpendicular line will have a slope that is the opposite reciprocal of the slope of the given line: m = -1/1 = -1
A point that is 1 unit right and 1 unit down from the given point is -3 on the y-axis. This is the y-intercept of the perpendicular line. The equation is ...
y = -x -3 . . . . . equation of perpendicular line
PLEASE HELPPP!! I need help with both questions
9514 1404 393
Answer:
borrow: $21,056.60interest: $1,983.40Step-by-step explanation:
The relation between the monthly payment (A) and the principal borrowed (P) is ...
A = P(r/12)/(1 -(1 +r/12)^-n)
where the annual interest rate is r and n is the number of monthly payments.
Then the principal P can be found as ...
P = $384(12/0.036)(1 -(1 +0.036/12)^-60) ≈ $21,056.60 . . . loan amount
The sum of payments is ...
$384 × 60 = $23,040.
The difference between the payments made and the loan principal amount is the interest paid:
$23,040.00 -21,056.60 = $1,983.40 . . . total interest
Suppose that you take 1000 simple random samples from a population and that, for each sample, you obtain a 95% confidence interval for an unknown parameter. Approximately how many of those confidence intervals will contain the value of the unknown parameter?
Using the interpretation of a confidence interval, it is found that approximately 950 of those confidence intervals will contain the value of the unknown parameter.
A x% confidence interval means that we are x% confident that the population mean is in the interval.
Out of a large number of intervals, approximately x% will contain the value of the unknown parameter.In this problem:
95% confidence interval.1000 samples.0.95 x 1000 = 950
Hence, approximately 950 of those confidence intervals will contain the value of the unknown parameter.
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Can someone please help me with #14 and #15?
14.Given y=2(x - 10)+3, write an equation in point slope and slope intercept form that is:
a) Parallel and goes through (-4,1).
b) Perpendicular and goes through (-4,1).
15.Given 5x+2y=7
a.Find an equation parallel to the equation and through (0,10).
b.Find an equation perpendicular to the equation and through (0,10).
This picture is an example of what the answers should look like.
Problem 14, Part (a)
The given equation y = 2(x-10)+3 has a slope of m = 2. Anything parallel to this will also have the same slope, but a different y intercept.
Let's find the point slope form of the parallel line through (-4,1)
[tex]y-y_1 = m(x - x_1)\\\\y-1 = 2(x - (-4))\\\\y-1 = 2(x + 4)\\\\[/tex]
The point slope form is: y-1 = 2(x+4)Now solve for y to get the slope intercept form.
[tex]y-1 = 2(x + 4)\\\\y = 2(x + 4)+1\\\\y = 2x + 8+1\\\\y = 2x + 9\\\\[/tex]
The slope intercept form is: y = 2x+9============================================================
Problem 14, Part (b)
The original slope is m = 2. Apply the negative reciprocal to go from 2/1 to -1/2. The perpendicular slope is -1/2.
Using the same point (-4,1), we find that the point slope form is...
[tex]y-y_1 = m(x - x_1)\\\\y-1 = -\frac{1}{2}(x - (-4))\\\\y-1 = -\frac{1}{2}(x+4)\\\\[/tex]
The point slope form is: y-1 = (-1/2)*(x+4)Now solve for y
[tex]y-1 = -\frac{1}{2}(x+4)\\\\y = -\frac{1}{2}(x+4)+1\\\\y = -\frac{1}{2}x-2+1\\\\y = -\frac{1}{2}x-1\\\\[/tex]
The slope intercept form is: y = (-1/2)x - 1============================================================
Problem 15, Part (a)
Anything parallel to Ax+By = C will be in the form Ax+By = D. The only thing changes is the C becomes D, where [tex]C \ne D[/tex]. If C = D, then we'd be talking about the exact same line rather than two parallel lines.
We're given 5x+2y = 7. The answer is in the form 5x+2y = D. Plug in (x,y) = (0,10) to find the value of D
5x+2y = D
D = 5x+2y
D = 5(0)+2(10)
D = 20
The equation 5x+2y = D updates to 5x+2y = 20
Answer: 5x+2y = 20============================================================
Problem 15, Part (b)
If you are given Ax+By = C, then anything perpendicular to this is Bx-Ay = D. Here it's possible that C = D; however, it's likely that they'll be different.
The given equation 5x+2y = 7 is perpendicular to anything of the form 2x-5y = D. We'll plug in the given point to find D.
2x-5y = D
D = 2x-5y
D = 2(0)-5(10)
D = -50
Answer: 2x-5y = -50Please verify how [tex]\frac{1-cos(x)}{sin(x)} =\frac{sin(x)}{1+cos(x)}[/tex]
Answer/Step-by-step explanation:
[tex]\frac{1-\cos \left(x\right)}{\sin \left(x\right)}=\frac{\sin \left(x\right)}{1+\cos \left(x\right)}[/tex]
When you have an equation like this, you can start from either side. So, let us start from the left side.
[tex]\underline{\mathrm{Left\:side:}} \quad\frac{1-\cos \left(x\right)}{\sin \left(x\right)}[/tex]
[tex]\sf{Rewrite\: using \:Trig \:identities=\frac{\sin \left(x\right)}{1+\cos \left(x\right)}}\\\\\mathrm{Therefore,\: it \:is \:true}[/tex]
I need help with the question
Answer:
[tex]A = 25\pi[/tex] or 25 × 3.14 = 78.5m
Step-by-step explanation:
The radius is half of the diameter. So the radius = 5m (10/2)
[tex]A = \pi r^{2}[/tex]
[tex]A = \pi (5^{2} )[/tex]
[tex]A = 25\pi[/tex]
solve pls brainliest
Answer:
1. -64
2.-27
Step-by-step explanation:
Hopes this helps
:)
Which equation models this situation?
The sum of 23 and a number is 39.
O A. 23 + x = 39
B. 23 - x = 39
C. 39 + x = 23
O D. 23+ 39 = x
8
There are 5 times as many pens in box A as in box B.
Teddy moves 82 pens
from box A to box B.
Both boxes now have the same number of
pens.
How many pens are in box A now?
Answer:
123 pens in Box A
Step-by-step explanation:
To solve this we will rewrite the word problem as an equation...
5x (A)
x (B)
When Teddy moves 82 pens from A to B, he is subtracting 82 pens from Box A and adding 82 pens to Box B...
5x - 82 (Change in Box A - subtraction)
x + 82 (Change in Box B - addition)
The problem now states that Box A and Box B are equal...
5x - 82 = x + 82
--- subtract x from both sides ---
4x - 82 = 82
--- add 82 to both sides ---
4x = 164
--- divide both sides by 4 ---
x = 41 pens
Now, we replace the x in the expression "5x - 82" with 41...
5(41) - 82 = 205 - 82
205 - 82 = 123
123 pens in Box A
Hope this Helps!
Anna ate 1/5 of her candy bar. What decimal represents the amount she ate?
Answer:
.25
Step-by-step explanation:
okay this is what i need help with its kinda easy
Answer:
B is the answer .......+4+$#88#!$
