Answer:
D. x=y+2z
Step-by-step explanation:
if you expand out the first equation (x) you will get: a^2+b^2+c^2+2ab+2bc+2ac
then looking at all of the choices, it can be seen that the third equation (z) needs to be multiplied by to get 2ab+2bc+2ac and then added to the second equation (y) which would result in D being the correct answer.
D. x=y+2z
The Denver Post reported that, on average, a large shopping center had an incident of shoplifting caught by security 1.4 times every eight hours. The shopping center is open from 10 A.M. to 9 P.M. (11 hours). Let r be the number of shoplifting incidents caught by security in an 11-hour period during which the center is open.
(a) Explain why the Poisson probability distribution would be a good choice for the random variable r.
Frequency of shoplifting is a common occurrence. It is reasonable to assume the events are dependent.
Frequency of shoplifting is a rare occurrence. It is reasonable to assume the events are independent.
Frequency of shoplifting is a rare occurrence. It is reasonable to assume the events are dependent.
Frequency of shoplifting is a common occurrence. It is reasonable to assume the events are independent.
What is ? (Round your answer to three decimal places.)
(b) What is the probability that from 10 A.M. to 9 P.M. there will be at least one shoplifting incident caught by security? (Round your answer to four decimal places.)
(c) What is the probability that from 10 A.M. to 9 P.M. there will be at least three shoplifting incidents caught by security? (Round your answer to four decimal places.)
(d) What is the probability that from 10 A.M. to 9 P.M. there will be no shoplifting incidents caught by security? (Round your answer to four decimal places.)
Using the Poisson distribution, it is found that:
a) Frequency of shoplifting is a common occurrence. It is reasonable to assume the events are independent.b) 0.8541 = 85.41% probability that from 10 A.M. to 9 P.M. there will be at least one shoplifting incident caught by security.c) 0.303 = 30.3% probability that from 10 A.M. to 9 P.M. there will be at least three shoplifting incidents caught by security.d) 0.1459 = 14.59% probability that from 10 A.M. to 9 P.M. there will be no shoplifting incidents caught by security.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.Item a:
In this problem, we are given the mean during an interval, which is a common event(1.4 every 8 hours), and intervals can be assumed to be independent, hence, the correct option is:
Frequency of shoplifting is a common occurrence. It is reasonable to assume the events are independent.Item b:
Mean of 1.4 every 8 hours, hence, every 11 hours, the mean is:
[tex]\mu = 11 \times \frac{1.4}{8} = 1.925[/tex]
The probability is:
[tex]P(X \geq 1) = 1 - P(X = 0)[/tex]
In which:
[tex]P(X = x) = \frac{e^{-\mu}\mu^{x}}{(x)!}[/tex]
[tex]P(X = 0) = \frac{e^{-1.925}(1.925)^{0}}{(0)!} = 0.1459[/tex]
Then
[tex]P(X \geq 1) = 1 - P(X = 0) = 1 - 0.1459 = 0.8541[/tex]
0.8541 = 85.41% probability that from 10 A.M. to 9 P.M. there will be at least one shoplifting incident caught by security.
Item c:
The probability is:
[tex]P(X \geq 3) = 1 - P(X < 3)[/tex]
In which:
[tex]P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2)[/tex]
Then:
[tex]P(X = x) = \frac{e^{-\mu}\mu^{x}}{(x)!}[/tex]
[tex]P(X = 0) = \frac{e^{-1.925}(1.925)^{0}}{(0)!} = 0.1459[/tex]
[tex]P(X = 1) = \frac{e^{-1.925}(1.925)^{1}}{(1)!} = 0.2808[/tex]
[tex]P(X = 2) = \frac{e^{-1.925}(1.925)^{2}}{(2)!} = 0.2703[/tex]
[tex]P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2) = 0.1459 + 0.2808 + 0.2703 = 0.697[/tex]
[tex]P(X \geq 3) = 1 - P(X < 3) = 1 - 0.697 = 0.303[/tex]
0.303 = 30.3% probability that from 10 A.M. to 9 P.M. there will be at least three shoplifting incidents caught by security.
Item d:
[tex]P(X = x) = \frac{e^{-\mu}\mu^{x}}{(x)!}[/tex]
[tex]P(X = 0) = \frac{e^{-1.925}(1.925)^{0}}{(0)!} = 0.1459[/tex]
0.1459 = 14.59% probability that from 10 A.M. to 9 P.M. there will be no shoplifting incidents caught by security.
To learn more about the Poisson distribution, you can take a look at https://brainly.com/question/13971530
help me plsssssssssssssssssssssssssss
Answer:
This answer would be c
Step-by-step explanation:
y-5=2(x-3) slope intercept.
Answer:
y=2x-1
Step-by-step explanation:
Because this equation is in point-slope form and we need it in slope-intercept form, all we need to do is simplify y-5=2(x-3).
y-5=2x-6 Distribute.
+5 +5 Add 5 to both sides of the equation.
y=2x-1
Hope this helped! Have a great day ♥
the points (0, p) and (1, 4) lie on a line with a slope of 3. what is the value of p?
Answer:
p=1
Step-by-step explanation:
[tex]\frac{4-p}{1-0}[/tex]=3
4-p=3
p=1
It cost Joseph $21.90 to send 146 text messages. How many text messages did he send if he spent $6.45?
Answer:
43 messages
Step-by-step explanation:
Given:
146 messages = $21.90
x messages = $6.45
Finding x by cross-multiplication:
x = 146*6.45/21.90 = 43
Hope this helps! :)
Fill in the missing numbers below.
5 feet + 12 inches = blank
yard(s)
Blank inches = 1 foot + 1 yard
Blank feet = 3 feet + 24 inches
Answer:
5 feet + 12 inches = 2 yards
48 inches = 1 foot + 1 yard
5 feet = 3 feet + 24 inches
Step-by-step explanation:
To help solve these equations, you must know how to convert feet to inches, inches to yards, etc. Use the information below:
1 feet = 12 inches
3 feet = 1 yard
To solve 5 feet + 12 inches = blank yard(s), convert 5 feet & 12 inches to yards. Since 5 feet would be complicated to convert, let's convert 12 inches to feet first.
12 inches = 1 feet
Instead of 12 inches, we can substitute it as 5 feet + 1 feet = blank yard(s). That would be 6 feet = ? yards. 3 feet = 1 yard, which tells us we must divide both sides by 3. Thus, 5 feet + 12 inches = 2 yards.
Blank inches = 1 foot + 1 yard
To find the # of inches in a yard, you must first know that 3 feet = 1 yard. If there are 12 inches in a foot, we must multiply 3 by 12, getting us 36. You add 12 inches (1 foot), getting us 48 inches in total. Thus 48 inches = 1 foot + 1 yard.
Blank feet = 3 feet + 24 inches
Since 3 feet is already feet, we do not need to convert it. If 12 inches is 1 foot, we must divide 24 inches by 12. So, there is 2 feet in 24 inches. 2 + 3 is 5. Thus, 5 feet = 3 feet +24 inches.
Choose yes or no to tell whether each expression is equivalent to -4/3p-2/5
A. -2/5-4/3p
B.2/5-4/3p
C.-2/5-4/3p
D.-4/3p+(-2/5)
The cylindrical container shown below can be completely filled with 24 litres of water. The base area of the container is 600 cm2. What is the height of the container? PLEASE FAST!!
Answer:
40cm
Step-by-step explanation:
volume of a cylinder= πr²h
V=24litres, Area=πr²=600cm², height=?
converting litres to cm³
1litre=1000cm³
24litres= 24×1000
=24000cm³
24000=600× h
h= 24000/600
= 40cm
Solve the following formula for x y = 7 m x − 8 b
Answer: It depends on which variable you're solving for.
Step-by-step explanation:
Solving for b: b=7/8mx + -1/8xy
Solving for m: m=xy+8b
______
7x
Solving for x: x=-8b
___
-7m+y
Solving for y: y=7mx-8b
______
x
Please help!! Best answer gets brainliest<3
There are 4 circles and 16 squares. What is the simplest ratio of circles to the total of shapes
Answer:
Not including circles in total shapes: 1 circle to every 4 squares or 1:4
Including circles in total shapes: 1 circle to every 5 shapes or 1:5
Step-by-step explanation:
16 ÷ 4 = 4
20 ÷ 4 = 5
Answer: 1:5
Step-by-step explanation:
Write g(x)=40x+4x2 in vertex form
3. Find the total tax using the expanded expression. Did you get the same answer as
you did by evaluating the original expression? (3 points)
Answer:
To evaluate an algebraic expression means to find the value of the expression when the variable is replaced by a given number. To evaluate an expression, we substitute the given number for the variable in the expression and then simplify the expression using the order of operations
Answer:
To evaluate an algebraic expression means to find the value of the expression when the variable is replaced by a given number. To evaluate an expression, we substitute the given number for the variable in the expression and then simplify the expression using the order of operations
Step-by-step explanation: Hope it Helpss :D
A circle with radius of 9 cm sits inside iſ circle with radius of 11 cm.
What is the area of the shaded region?
Round your final answer to the nearest hundredth
Answer:
Step-by-step explanation:
it is two left night
11. The profit Samantha's company makes is
given by the expression 0.1(1000 + 300m)
where m is the total number of sales.
Rewrite the expression using the distributive
property. What is the profit if her company
sells 50 pieces of merchandise?
Answer: 0.1(1000 + 300m)
Use the distributive property: a x (b + c) = a x b + a x c
0.1 x 1000 + 0.1 x 300m
Evaluate both products: 100 + 30m (1)
Note: Multiplying a number by 0.1 is the same as dividing the number by 10.
We need to determine the profit when 50 pieces are sold.
Substitute m with 50 in equation (1).
100+30(50)
Evaluate product: 100 + 1500
Evaluate sum" 1600
Thus the profit is $1600.
Step-by-step explanation: I hope this helps you on any other problem! :)
Good Luck!
−10sin(x)=−4csc(x)+3
-10 sin(x) = -4 csc(x) + 3
Recall that csc(x) = 1/sin(x) :
-10 sin(x) = -4/sin(x) + 3
Multiply both sides by sin(x) :
-10 sin²(x) = -4 + 3 sin(x)
Move everything to one side:
10 sin²(x) + 3 sin(x) - 4 = 0
Factorize the left side:
(2 sin(x) - 1) (5 sin(x) + 4) = 0
Then we have two cases,
2 sin(x) - 1 = 0 or 5 sin(x) + 4 = 0
Solve for sin(x) :
sin(x) = 1/2 or sin(x) = -4/5
Solve for x :
• if sin(x) = 1/2, then
x = arcsin(1/2) + 2nπ or x = π - arcsin(1/2) + 2nπ
x = π/6 + 2nπ or x = 5π/6 + 2nπ
• if sin(x) = -4/5, then
x = arcsin(-4/5) + 2nπ or x = π - arcsin(-4/5) + 2nπ
x = -arcsin(4/5) + 2nπ or x = π + arcsin(4/5) + 2nπ
(where n is any integer)
In November 2017, the monthly profit of a company was £9,197
In December, Christmas increased sales and the profit has doubled.
What was the company's profit in December 2017?
Answer:
18394
Step-by-step explanation:
9197 × 2 = 18394 You double 91972
to work out the profit in December
the graph shows data relating sodium per serving and price per serving of different brands of peanut butter, Using this model, predict the amount of sodium in Peanut Butter that costs $.35 per serving.
A linear model that best fits the overall pattern of points is given by the
regression line of the data.
a. Please find attached the graph showing the linear model of the scatter plot created with MS Excel.b. The slope of the line is -6.2173.c. The relationship is as the price per Serving increases by 1 cent, the sodium per Serving decreases by -6.2173 mg.Reasons:
a. Points on the graph are;
(6, 218),
The slope, b, regression line equation is given by the following formula;
[tex]b = \mathbf{\dfrac{\sum \left(x_i - \overline x\right) \times \left(y_i - \overline y\right) }{\sum \left(x_i - \overline x\right )^2 }}[/tex]
The regression line equation is; [tex]\overline y = b \cdot \overline x + a[/tex]
Where;
[tex]\overline x[/tex] = 18.732
[tex]\overline y[/tex] = 187.24
[tex]\sum \left(x_i - \overline x\right) \times \left(y_i - \overline y\right)[/tex] = -4926.59
[tex]\sum \left(x_i - \overline x\right )^2[/tex] = 792.3944
Therefore;
[tex]b = \dfrac{-4926.59}{792.3944 } \approx -6.2173[/tex]
[tex]a = \overline y - b \cdot \overline x[/tex]
Which gives;
a = 187.24 - (-6.2173) × 18.732 ≈ 303.70
The equation of the line is therefore; [tex]\overline y = \mathbf{-6.2173 \cdot \overline x + 303.70}[/tex]
Using the above regression line equation, the linear model of the scatter
plot can be drawn as presented in the graph created with MS Excel.
b. The slope of the line is b = -6.2173
c. The relationship between price per serving and sodium per serving is
as follows;
When the price per serving increases by 1 cent, the sodium per serving
decreases by 6.2173 mg.
Learn more about the regression line formula here:
https://brainly.com/question/14747095
Select the two pairs of figures that are similar
Find the equation ( in slope - intercept form ) of the line with the given slope that passes through the point with the given coordinates . slope : 4/3 ordered pair : (1, 4)
help pls!
Answer:
y = 4/3x +8/3
Step-by-step explanation:
The point-slope form is ...
y -k = m(x -h) . . . . . . . line with slope m through point (h, k)
For the given point and slope, this is ...
y -4 = 4/3(x -1)
Adding 4 and eliminating parentheses, you have ...
y = 4/3x -4/3 +4
y = 4/3x +8/3
Which type of correlation does this scatterplot show?
Answer:
i think the answer to this question is positive correlation
Step-by-step explanation:
this image below may help u
Can someone help me find w and X for my parallelogram ?? Will mark brainiest :)
Answer:
5x+3x=8x, 6w+2w=8w is the answer
What's does A equal?
Answer:
x = 65
Step-by-step explanation:
2x + 2(2x-15) = 360
2x + 4x - 30 = 360
6x = 390
x = 65
evaluate 3c + 6y for c=5 and y=6
Answer:
51
Step-by-step explanation:
because 3(5)+6(6)
Answer:
51
Step-by-step explanation:
3c+6y
3(5)+6(6)
15+36
51
please help!!! i dont understand
Answer:
C(t)=0.10t + 25
Step-by-step explanation:
gradient = change in y/ change in x = 5/50 = 0.10
the y intercept is 25
so the equation is y = 0.1t + 25
I’m unsure why I keep getting this wrong
Answer:
the answer is 5
HEY!!^^
have a good day!!^^
thank me later
carryonlearing
Answer:
26/25x^2+25x or x=0,x=-1
Step-by-step explanation:
i need help plz
thanks
A car is driving at 100kilometers per hour. How far, in meters, does it travel in 2 seconds? Give answer to
nearest meter.
Answer:
72
Step-by-step explanation:
brainlest pls
What percent of 38 is 12
Answer:
31%
Step-by-step explanation:
hope this helps
PLEASE HELP -7y + 11 = 75 + y
Answer:
y = -8
Step-by-step explanation:
-7y + 11 = 75 + y
Bring the "y" variable on one side, and rest on the other.
Rearranging, we get,
-7y - y = 75 - 11
-8y = 64
-y = 8
y = -8
Hope it helps :)