Answer:
a) 0.0879 = 8.79% probability that among the next 5 theft cases reported in this district, exactly 2 resulted from the need for money to buy drugs.
b) 0.3672 = 36.72% probability that among the next 5 theft cases reported in this district, at most 3 resulted from the need for money to buy drugs.
Step-by-step explanation:
For each theft, there are only two possible outcomes. Either it was motivated by a need to buy drugs, or it wasnt. Thefts are independent, which means that we use the binomial probability distribution to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
In a certain city district, the need for money to buy drugs is stated as the reason for 75% of all thefts.
This means that [tex]p = 0.75[/tex]
Next 5 theft cases
This means that [tex]n = 5[/tex]
(a) exactly 2 resulted from the need for money to buy drugs;
This is P(X = 2).
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 2) = C_{5,2}.(0.75)^{2}.(0.25)^{3} = 0.0879[/tex]
0.0879 = 8.79% probability that among the next 5 theft cases reported in this district, exactly 2 resulted from the need for money to buy drugs.
(b) at most 3 resulted from the need for money to buy drugs.
This is
[tex]P(X \leq 3) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)[/tex]
In which
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{5,0}.(0.75)^{0}.(0.25)^{5} = 0.0010[/tex]
[tex]P(X = 1) = C_{5,1}.(0.75)^{1}.(0.25)^{4} = 0.0146[/tex]
[tex]P(X = 2) = C_{5,2}.(0.75)^{2}.(0.25)^{3} = 0.0879[/tex]
[tex]P(X = 3) = C_{5,3}.(0.75)^{3}.(0.25)^{2} = 0.2637[/tex]
[tex]P(X \leq 3) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) = 0.0010 + 0.0146 + 0.0879 + 0.2637 = 0.3672[/tex]
0.3672 = 36.72% probability that among the next 5 theft cases reported in this district, at most 3 resulted from the need for money to buy drugs.
Write 247 000 in standard form.
Can u help
Answer:
2.47 x 10 to the power of 4 (2.47x10^4)
247,000
two hundred, forty, seven, thousand,
200,000+40,000+7,000=247,000
5 11/12 + 3 9/12? Step by step
Answer:
Simplified: 9 2/3
Step-by-step explanation:
Convert the mixed numbers into improper fractions
To do this, multiply the denominator by the whole number and add the numerator: (denominator × whole number + numerator)/denoninator
First fraction:
5 11/12
(12 × 5 + 11)/12
(60 + 11)/12
71/12
Next fraction:
3 9/12
(12 × 3 + 9)/12
(36 + 9)/12
45/12
Substitute these fractions in the original problem now:
71/12 + 45/12
Add the numerators only. The denominators stay the same.
(71 + 45)/12
116/12
Now that the calculations are done, convert this back into a whole number
How many times does 12 fit into 116 equally? If you answered 9 times, then you are correct. This 9 will sit as the whole number in the fraction
12 × 9 = 108
This doesn't equal 116 perfectly so we must find the left over
116 - 108 = 8 left over (which is used as the numerator)
9 8/12
If your class or problem asks that you simplify your answer, then look at both the numerator and denominator to determine any common factors within them
8 and 12 both have common factors of 2 and 4
Since 4 is the bigger number, divide both 8 and 12 by 4 to simplify your answer
9 2/3
Solve for c.
a(c- b) =d
Answer:
c=[tex]\frac{d}{a}[/tex]+b
Step-by-step explanation:
a(c-b)=d
c-b=[tex]\frac{d}{a}[/tex]
c=[tex]\frac{d}{a}[/tex]+b
Hope this helps! :)
6 am
10 cm
Find the lateral surface area of the cylinder Round your answer to the nearest hundredth.
A)
354.18 cm?
B)
362.16 cm
C)
367.59 cm
D)
376,99 cm
Answer:
[tex]A=376.99\ cm^2[/tex]
Step-by-step explanation:
We need to find the lateral surface area of the cylinder of radius 6 cm and height of 10 cm.
We need to find the lateral surface area of the cylinder. The formula for the lateral surface area of a cylinder is given by :
[tex]A=2\pi rh\\\\A=2\pi \times 6\times 10\\A=376.99\ cm^2[/tex]
So, the lateral surface area of the cylinder is [tex]376.99\ cm^2[/tex].
Can someone please Solve x^2+2x -3 =x^2
The answer i worked out is x=3/2
Which of the following statements is TRUE about the relationship between the numerical values?
A. The opposite of 15 is equal to 15 greater than zero.
b. 15 greater than zero is less than the opposite of 15.
c. 15 greater than zero is farther from 0 on a number line than the opposite of 15.
D. The opposite of 15 is the same distance from zero on a number line as 15 greater than zero
Answer:
D is the answer
Step-by-step explanation:
-15 Is the same as 15 its just negative but they have the same distance.
What are the solutions to the quadric equation x^2-16=0
Answer:
x=4, x=-4
Step-by-step explanation:
x^2-16=0
Add 16 to both sides;
x^2-16+16=0+16
Simplify;
x^2=16
x=[tex]\sqrt{16}[/tex], x[tex]-\sqrt{16}[/tex]
[tex]\sqrt{16}[/tex]
=4
factor the number;16
[tex]\sqrt{4^2}[/tex]
=[tex]\sqrt{4}[/tex]
-[tex]\sqrt{16}[/tex]
Factor the number 16;
[tex]\sqrt{4^2}[/tex]
=-4
find the area of the kite please. image included!!!
A researcher wants to see if a kelp extract helps prevent frost damage on tomato plants. One hundred tomato plants in individual containers are randomly assigned to two different groups. Plants in both groups are treated identically, except that the plants in group 1 are sprayed weekly with a kelp extract, while the plants in group 2 are not. After the first frost, 12 of the 50 plants in group 1 exhibited damage and 18 of the 50 plants in group 2 showed damage. Let p1 be the actual proportion of all tomato plants of this variety that would experience damage under the kelp treatment, and let p2 be the actual proportion of all tomato plants of this variety that would experience damage under the no-kelp treatment.
Required:
Construct and interpret a 95% confidence interval for the true difference in the proportion of tomato plants like these that would experience damage after receiving the kelp treatment and no-kelp treatment.
Answer:
The 95% confidence interval for the true difference in the proportion of tomato plants like these that would experience damage after receiving the kelp treatment and no kelp treatment is -0.2690 < [tex]\hat{p}_1-\hat{p}_2[/tex] < 0.02901
Step-by-step explanation:
The given data are;
The number of the group 1 plants that exhibited damage = 12
The number of plants in group 1, n₁ = 50
The number of the group 2 plants that exhibited damage = 18
The number of plants in group 2, n₂ = 50
The proportion of group 1 plants that exhibited damage, [tex]\hat p_1[/tex] = 12/50 = 0.24
The proportion of group 2 plants that exhibited damage, [tex]\hat p_2[/tex] = 18/50 = 0.36
The z-value at 95% = 1.64
The confidence interval is given by the following formula;
[tex]C.I. = \hat{p}_1-\hat{p}_2\pm z^{*}\sqrt{\dfrac{\hat{p}_1\left (1-\hat{p}_1 \right )}{n_{1}}+\dfrac{\hat{p}_2\left (1-\hat{p}_2 \right )}{n_{2}}}[/tex]
Plugging in the values, we get;
[tex]C.I. = 0.24-0.36\pm 1.64 \times \sqrt{\dfrac{0.24\left (1-0.24 \right )}{50}+\dfrac{0.36\left (1-0.36 \right )}{50}}[/tex]
Therefore, C.I. = -0.2690 < [tex]\hat{p}_1-\hat{p}_2[/tex] < 0.02901
x/64 = 2 im being timed
Answer:
128
Step-by-step explanation:
x/64=2
x=64*2
x=128
Answer:
=128
Step-by-step explanation:
64=2
64⋅64=64⋅2
64⋅64=64⋅2
=64⋅2
=64⋅2
=128
hope it helps <3
Find the area of the polygon
Answer:
14 square units
A rectangular box is to have a square base and a volume of 40 ft3. If the material for the base costs $0.34 per square foot, the material for the sides costs $0.05 per square foot, and the material for the top costs $0.16 per square foot, determine the dimensions of the box that can be constructed at minimum cost.
Answer:
The dimensions of the box so that total costs are minimum are a side length of 2 feet and a height of 5 feet.
Step-by-step explanation:
Geometrically speaking, the volume of the rectangular box ([tex]V[/tex]), in cubic feet, is represented by this formula:
[tex]V = l^{2}\cdot h[/tex] (1)
Where:
[tex]l[/tex] - Side length of the box, in feet.
[tex]h[/tex] - Height of the box, in feet.
In addition, the total cost of the box ([tex]C[/tex]), in monetary units, is defined by this formula:
[tex]C = (c_{b}+c_{t})\cdot l^{2} + 4\cdot c_{s}\cdot l\cdot h[/tex] (2)
Where:
[tex]c_{b}[/tex] - Unit cost of the base of the box, in monetary units per square foot.
[tex]c_{t}[/tex] - Unit cost of the top of the box, in monetary units per square foot.
[tex]c_{s}[/tex] - Unit cost of the side of the box, in monetary units per square foot.
By (1), we clear [tex]h[/tex] into the expression:
[tex]h = \frac{V}{l^{2}}[/tex]
And we expand (2) and simplify the resulting expression:
[tex]C = (c_{b}+c_{t})\cdot l^{2}+4\cdot c_{s}\cdot \left(\frac{V}{l} \right)[/tex] (3)
If we know that [tex]c_{b} = 0.34\,\frac{m.u.}{ft^{2}}[/tex], [tex]c_{s} = 0.05\,\frac{m.u.}{ft^{2}}[/tex], [tex]c_{t} = 0.16\,\frac{m.u.}{ft^{2}}[/tex] and [tex]V = 40\,ft^{3}[/tex], then we have the resulting expression and find the critical values associated with the side length of the base:
[tex]C = 0.5\cdot l^{2} + \frac{8}{l}[/tex]
The first and second derivatives of this expression are, respectively:
[tex]C' = l -\frac{8}{l^{2}}[/tex] (4)
[tex]C'' = 1 + \frac{16}{l^{3}}[/tex] (5)
After equalizing (4) to zero, we solve for [tex]l[/tex]: (First Derivative Test)
[tex]l-\frac{8}{l^{2}} = 0[/tex]
[tex]l^{3}-8 = 0[/tex]
[tex]l = 2\,ft[/tex]
Then, we evaluate (5) at the value calculated above: (Second Derivative Test)
[tex]C'' = 3[/tex]
Which means that critical value is associated with minimum possible total costs. By (1) we have the height of the box:
[tex]h = 5\,ft[/tex]
The dimensions of the box so that total costs are minimum are a side length of 2 feet and a height of 5 feet.
A quadrilateral has angles that measure 60 , 115, and 80°. What is the measure of the missing angle?
Answer:
105
Step-by-step explanation:
The sum of a quadrilateral's angles is always equal to 360
360 - 60 - 115 - 80 = 105
Hope this helps :)
Plz help ASAP 20 points 10. What is the equation of a circle with radius, r = 4, and the center at (0,0)?
A.X² + y² = 4
B.22 + y2 = 16
C.2 - 4)+ (y – 4) = 4
B.(.2 - 4)? + (y – 4)2 = 16
Answer:
a
Step-by-step explanation:
the equation for a circle centered at orgin is x^2+y^2=r where r is the radius. multiplying, adding, or subtracting any numbers to the x and y components such as the other choices here causes the circle to be translated about the graph.
Nancy bought 2 packs of basketball cards for 3.78 each and 4 decks of basketballs cards for 7.38 each with 2 20 bills. How much change did Nancy get?
Answer:
3.78*2=7.56
7.38*4=29.52
29.52+7.56=37.08
220-37.08=182.92
PLEASE HELP ME!!!!!!!!!!!!!!!!!!!!!
Nancy has a lot of things in her locker. There are 14 items in her locker, including 6 pencils. What is the probability that a randomly selected item from Nancy's locker will be a pencil?
A. 8/14
B 7/14
C 3/7
Answer: B 7/14
Step-by-step explanation:
D
E
с
Look at ABC. Points D, E, and F are the midpoints of their respective sides. Point G is the point of
concurrency for AD BE. and CF.
Which statement about point G is NOT true?
Answer:
D. Point G is the center of a circle that can be inscribe in ΔABC
Step-by-step explanation:
To inscribe implies constructing a required shape or figure within a given shape, thus touching the boundaries or sides of the given shape internally.
In the given figure if point G is used as the center of a circle, it would not form an inscribed circle in the given triangle. So that the appropriate answer is Point G is the center of a circle that can be inscribe in ΔABC. Thus, option D is not true.
Answer:
this was correct
Step-by-step explanation:
thank u
Slope= -1/2 Line passes through the point (9,8). Write equation with point slope form
Find the least common denominator. Then express each fraction using the least common denominator. 1/9 and 2/15
Answer:
10/90,12/90
Step-by-step explanation:
least common denominator is 90
Traffic on Rosedale Road in Princeton, NJ, follows a Poisson process with rate6cars per minute. Adeer runs out of the woods and tries to cross the road. It takes the deer a random time (independentof everything else), uniformly distributed between2and5seconds, to cross the road. If there is acar passing while the deer is on the road, it will hit the deer with portability2/3(independent ofeverything else). Find the probability of a collision.
Answer:
Step-by-step explanation:
From the given information:
6 cars pass on the road per minute. This implies that per minute, we will have:
6/60 passes = 0.1 car passing the road per second
Thus, for 5 sec; we have:
5 × 0.1 = 0.5
Let assume X signifies to be a random variable which denote the no of cars in the next 5 minutes and which follows a Poisson distribution.
i.e.
[tex]X \sim Poisson (0.5)[/tex]
[tex]\text{P(collision occurs) = 1 - P(no car coming in the following 5 seconds)} \\ \\ =1 - P(X=0)[/tex]
[tex]= 1- \dfrac{[e^{-0.5\times 0.5^0}]}{0!}[/tex]
[tex]= 1 - e^{-0.5}[/tex]
[tex]= 1 - 0.6065[/tex]
[tex]= 0.3935[/tex]
However, the possibility of collision supposes the deer requires 2 seconds to cross the road can be computed as follows:
Suppose Y denote the arbitrary variable that addresses the no. of cars passing the road in 2 secs, then;
[tex]Y \sim Poisson (0.2)[/tex]
[tex]\text{P(collision occurs) = 1 - P(no car coming in the following 2 seconds)} \\ \\ =1 - P(Y=0)[/tex]
[tex]= 1- \dfrac{[e^{-0.2\times 0.2^0}]}{0!}[/tex]
[tex]= 1 - e^{-0.2}[/tex]
[tex]= 1 - 0.8187[/tex]
[tex]= 0.1813[/tex]
Find the Borda score for the Mustangs in a competition between Mustangs, Avengers, Falcons and Ravens. The voting results by preference are shown:
MAFR: 3
AMFR: 6
FAMR: 1
RAFM: 4
Answer:MAFR: 3
Step-by-step explanation:
Eric has 4 lb of blueberries to make into pie. How many pies can Eric make if each pie needs the given amount of blueberries.
Answer:
2 pies because you need 2 lb for each pie
Step-by-step explanation:
The area of the Pacific Ocean is more than 60 million square miles.
What is that in scientific notation?
0 6 x 107
0 6x 107
60 x 10-6
60 106
The scientific notation for this is :-6x10⁷
Given the side lengths, determine whether the triangle is acute, right, obtuse, or not a triangle.
15, 16, 21
A Not a Triangle
B Acute
Obtuse
D Right
9514 1404 393
Answer:
B acute
Step-by-step explanation:
We can define a "form factor" for a triangle as ...
f = a² +b² -c²
where c is the longest side length. It will be interpreted as follows:
negative -- obtuse trianglezero -- right trianglepositive -- acute triangleFor this triangle, our "form factor" is ...
f = 15² +16² -21² = 225 +256 -441 = 40 . . . . a positive number
The triangle is Acute.
Translate this sentence into an inequality:
Five subtracted from c is less than −17
Answer:
-17 < c < 5
Step-by-step explanation:
I think that's the answer
I can't confirm anything
What is the value of 6(2b-4) when b=5?
Replace b with 5:
6(2(5)-4)
Simplify:
6(10-4)
Subtract:
6(6)
Multiply to get the answer: 36
The answer is 36
Hey there!
6(2b - 4)
= 6(2(5) - 4)
= 6(10) - 4)
= 6(10) + 6(4)
= 60 - 24
= 36
Therefore, your answer should be: 36
Good luck on your assignment and enjoy your day!
~Amphitrite1040:)
The growing interest in and use of the Internet have forced many companies into considering ways to sell their products on the Web. Therefore, it is of interest to these companies to determine who is using the Web. A statistics practitioner undertook a study to determine how education and Internet use are connected. She took a random sample of 15 adults (20 years of age and older) and asked each to report the years of education they had completed and the number of hours of Internet use in the previous week. These data follow.
Education 11 11 8 13 17 11 11 11
Internet use 10 5 0 14 24 0 15 12
Education 19 13 15 9 15 15 11
Internet use 20 10 5 8 12 15 0
a. Employ a suitable graph to depict the data.
b. Does it appear that there is a linear relationship between the two variables? If so, describe it.
Answer:
Kindly check explanation
Step-by-step explanation:
Given the data:
Education : 11 11 8 13 17 11 11 11 19 13 15 9 15 15 11
Internet use 10 5 0 14 24 0 15 12 20 10 5 8 12 15 0
Labeled scatter plot of Education and Internet Use is attached in the picture below.
Yes there appears to be a linear relationship between the two variables (Education and Internet Use) as the data points appears to have an upward trend depicted by the linear trend line in the graph.
The correlation Coefficient value which is measures the degree of linear relationship between education and internet use is 0.7048
Which expression is equivalent to −3 2/3
Answer:
The answer is -3 - 2/3
Step-by-step explanation:
Just subtract
Click or tap the location where the first dot should be
placed.
CI
Answer:
C.I
Step-by-step explanation:
Answer:
two on the top
one to the left
two to the right
two on the bottom
Step-by-step explanation:
Find the area of the circle.
Answer:
uhhh i got 113.09, so im assuming its 113.04
This is strange there's some sort of mistake with I-ready
Step-by-step explanation: