The probability that between 35 and 37 of the murders, inclusive, were cleared is 0.12.
(a) The probability that exactly 40 of the murders were cleared can be found using the binomial probability formula.
In this case, n = 50, k = 40, and p = 0.65. Thus, the probability that exactly 40 of the 50 murders were cleared is P(40 successes) = (50C40)(0.65)⁴⁰(0.35)¹⁰ = 0.064.
(b) The probability that between 35 and 37 of the murders, inclusive, were cleared can be found by adding the probabilities of each individual outcome.
For example, the probability of exactly 35 successes is (50C35)(0.65)³⁵(0.35)¹⁵ = 0.069.
Similarly, the probability of exactly 36 successes is (50C36)(0.65)³⁶(0.35)¹⁴ = 0.051.
Adding these two probabilities together gives the probability of between 35 and 37 successes, inclusive, as 0.069 + 0.051 = 0.120.
(c) It would not be unusual if fewer than 20 of the murders were cleared. This is because the probability of this outcome can be calculated using the same formula as before. In this case, if k = 19, then P(19 successes) = (50C19)(0.65)¹⁹(0.35)³¹ = 0.057, which is a relatively high probability.
Therefore, the probability that between 35 and 37 of the murders, inclusive, were cleared is 0.12.
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I need help finding this answer please.
Angles in a Triangle
Answer:
No
Step-by-step explanation:
The angles of a triangle must add up to 180. 140+15+15 = 140 +30 = 170. This is not 170, so no. Hope this helps!
Answer:
It is not possible to draw a triangle with these angles because 140 + 15 + 15 = 170, triangle angles must add up to 180 and 180=170 is a false statement.
Step-by-step explanation:
4
Please help
Question in image
The value of x is given as follows:
B. 6.
How to obtain the value of x?The value of x is obtained applying the two secant segment theorem, which means that the following equation will hold true:
4(x + 4) = 5(5 + 3)
(we add the two parts), with the outer part being the multipler.
Expanding the operations, the value of x is obtained as follows:
4x + 16 = 40
4x = 24
x = 6.
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sin2x=
please help!!
Answer:
A
Step-by-step explanation:
It is a double angle identity.
sin2x = 2sinxcosx
Answer: 2sinxcosx
Step-by-step explanation:
A trucker had a load of grain containing 2 tons. She unloaded 1 ton and 500 pounds at the warehouse. How much grain does she still have left on the truck?
Answer:
1500 pounds Or 0.75 tons
Step-by-step explanation:
To solve this problem, we need to convert all units to the same unit, either tons or pounds. Let's convert 1 ton and 500 pounds to pounds:
1 ton = 2000 pounds
1 ton and 500 pounds = 2000 + 500 = 2500 pounds
Now we can subtract the amount of grain that was unloaded from the total amount:
2 tons = 2 * 2000 = 4000 pounds
4000 pounds - 2500 pounds = 1500 pounds
Therefore, the trucker still has 1 ton and 500 pounds, or 1500 pounds, of grain left on the truck.
To convert 1500 pounds to tons, we can use the conversion factor:
1 ton = 2000 pounds
Dividing both sides by 2000, we get:
1 pound = 1/2000 tons
Multiplying both sides by 1500, we get:
1500 pounds = 1500/2000 tons
Simplifying the fraction, we get:
1500 pounds = 0.75 tons
Therefore, 1500 pounds is equivalent to 0.75 tons.
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Q5. If you heat a 0.45 kg sample of an unknown substance to a temperature of 80 °C then quickly transfer it into a beaker that contains 0.70 kg of water at 15 °C (the specific heat capacity of the water is 4200 J/kg: C), the highest temperature that the sample and water will attain is 21 °C. What is the heat capacity of the sample? [4 marks]
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The probability solutions are given as follows;
- P(CS Major and Not Hired) = 43.6% (Marginal)
- P(Other Major) = 31.5% (Marginal)
- P (Hired + CS Major) = 36.3% (Conditional)
- P (Not Hired + Other Major) = 48.5% (Conditional)
How did we arrive at this conclusion?First we need to clarify the meaning of Joint, Marginal, and conditional probability.
Joint probabilities are statistical measures defining how likely two or more distinct occurrences are to happen at once; whereas marginal probabilities represent individual probabilities by isolating each characteristic being measured separate from others around them. Conversely, conditional probabilities measure statistical chances for events conditioned on previously known outcomes.Note that the table of values are attached.
So, the calculation is shows as follows:
P(CS Major and Not Hired) = 102/234 = 43.6% (Marginal)
- P(Other Major) = 74/234 = 31.5% (Marginal)
- P (Hired + CS Major) = 58/160 = 36.3% (Conditional)
- P (Not Hired + Other Major) = 36/74 48.5% (Conditional)
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School pictures come in 8 in. by 10 in., 5 in. by 7 in., and wallet size 2¼ in. by 3¼ in. Are the pictures similar to each other? Why?
The three sizes of school pictures may feature the same subject, but they are not similar to each other in terms of size and aspect ratio.
The 8 in. by 10 in. size has an aspect ratio of 5:4, which is wider than the 5 in. by 7 in. size that has an aspect ratio of 7:5. The wallet size 2¼ in. by 3¼ in. has an aspect ratio of 9:13, making it even more elongated. This means that the relative proportions of the images are different.
Furthermore, the larger sizes such as 8 in. by 10 in. and 5 in. by 7 in. provide a lot more detail than the wallet size, which is smaller and often used as a miniature version of the larger sizes. The larger sizes also have a higher resolution, making them more suitable for framing and displaying.
Therefore, while the school pictures may depict the same subject, they are not similar in size, aspect ratio, and level of detail.
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Caris has a carton of 12 eggs, two of which have brown shells while the rest have white shells. Caris randomly chooses a brown egg from the carton.
Answer:
The probability of choosing a brown egg from the carton is 2/12 or 1/6. This is because there are two brown eggs in the carton and a total of twelve eggs, so the probability of choosing a brown egg is 2/12 or 1/6.
Scores on the GRE (graduate record examination) are normally distributed with a mean of 553 and a standard deviation of 112. Use the 68-95-99.7 rule to find
the percentage of people taking the test who score between 421 and 645
The percentages of people taking the test who scores between 421 and 645 is__%
The percentages of people taking the test who scores between 421 and 645 is: 68 %
How to use the empirical rule of statistics?The empirical rule, also referred to as the three-sigma rule or the 68-95-99.7 rule, is defined as a statistical rule which states that almost all observed data for a normal distribution will fall within three standard deviations (denoted by σ) of the mean or average (denoted by µ).
We are given:
Sample mean: x' = 553
standard deviation; s = 112
Thus:
x' - ns = 421
x' + ns = 645
Where n is the number of standard deviations from the mean. Thus:
553 - 112s = 421
112s = 553 - 421
112s = 132
s = 132/112
s ≈ 1
So 1 standard deviation from the means indicates a percentage of 68%
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what is the break even points in coming year?
2
At the end of a baseball game, the players were given the choice of having a bottle of
water or a box of juice. Of all of the players, 12 chose a bottle of water, which was
of the total number of players. Write and solve an equation to determine p.
3
4
the total number of players at the baseball game.
Show your work.
An equation to determine p is 12 = 3p/4.
The total number of players at the baseball game is 16 players.
How to write an equation to model this situation?In order to write a linear equation to describe this situation, we would a assign variable to the total number of players at the baseball game, and then translate the word problem into a linear equation as follows:
Let the variable p represent the the total number of players at the baseball game.
Since the players had the choice of having a bottle of water or a box of juice., and of all of the players, only 12 chose a bottle of water, which was of the total number of players, a linear equation that can be used to model this situation is given by;
12 = 3/4 × p
48 = 3p
p = 48/3
p = 16 players.
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Jordan, Jessica, Eloise, and James travel to Europe. They see many famous places.
\
The friends hiked on a trail in the Austrian Alps. They hiked 1.08 kilometers on Monday and 0.94 kilometer on Tuesday.
How many kilometers did they hike in all? Describe how to use the grids to solve the problem. Then use the grids to find the solution.
The total number of kilometers that the friends hiked in all would be 2. 02 km.
How to solve for the total distance ?The total distance that Jordan, Jessica, Eloise, and James hiked in the Austrian Alps, can be found to be :
= Distance on Monday + Distance on Tuesday
= 1. 08 + 0. 94
= 2. 02 km
Using grids, you can represent a single box as 0. 1 km so that for 1. 08 km you will have a grid of 108 cubes. Do the same for Tuesday to get 94 cubes.
Add them up and you will get 202 cubes which would be 2.02 km.
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f(x)=x^2. What is g(x)?
Answer:
A. g(x) = -x^2 - 2
Step-by-step explanation:
Okay so it has the same slope as f(x) which means it's x^2, however, it's negative and going the other way so it's -x^2
Since the y-intercept is -2,
g(x) = -x^2 - 2
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5. Jack sold the laptop that he ka vong for his business, He purchased It in 2012 for 64,000. The current book value ing of the laptop IS 18,000 Jack Gold it for 28,000- Compte Gain in sale of the laptop. 48 000
The gain on sale of the laptop which Jack purchased in 2012 for $64,000 with a current book value of $18,000 but sold for $28,000 is $10,000.
What is the book value of an asset?The book value of an asset is the difference between the original value or purchase cost and the accumulated depreciation.
Accumulated depreciation represents the depreciation from the purchase date to the current period. It can be determined as the difference between the purchase price and the current value.
The purchase price of the laptop in 2012 = $64,000
Current book value = $18,000
Accumulated depreciation = $46,000 ($64,000 - $18,000)
Sales price = $28,000
Gain on sale = $10,000 ($28,000 - $18,000)
Thus, when the laptop is sold by Jack, he realized a gain of $10,000 because the sales price exceeded the current book value.
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You deposited $5,000 in your account earning 2.5 simple interest how long would it take for the balance of the account to earn $1,500 in interest?
To solve this problem, we can use the formula for simple interest:
I = P * r * t
where I is the interest earned, P is the principal amount (the initial deposit), r is the interest rate as a decimal, and t is the time in years.
We want to find how long it will take for the account balance to earn $1,500 in interest, so we can set up the equation:
$1,500 = $5,000 * 0.025 * t
where t is the time in years.
Simplifying this equation, we get:
t = $1,500 / ($5,000 * 0.025)
t = 12 years
Therefore, it will take 12 years for the balance of the account to earn $1,500 in interest
x²+x-72=0 rewrite the equation by completing the square
The solution of the equation written by completing square is (x + 1/2)² = 289/4.
What is completing square?In algebra, the process of "completing the square" is used to transform a quadratic expression into a perfect square trinomial. Using this method, a constant term is either added or subtracted from the quadratic expression to produce a perfect square trinomial that may be factored as the square of a binomial. Solving quadratic equations, locating the vertex of a parabola, and simplifying formulas with square roots all involve the completion of the square.
The value of the equation x² + x = 72 can be written as a completer square by taking half of the coefficient of the x-term.
(1/2)² = 1/4
Add this to both sides of the equation:
x² + x + 1/4 = 72 + 1/4
Now, the LHS is:
(x + 1/2)² = 289/4
x = -1/2 ± (17/2)
Hence, the solution of the equation written by completing square is (x + 1/2)² = 289/4.
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What formula could you use to help find the area of the given triangle?
Angle Addition Postulate
Pythagorean Theorem
Midpoint Formula
The formula that will be useful in finding the area of the triangle is: Pythagoras theorem
How to find the area of a triangle?The formula to find the area of the triangle is expressed by the formula:
A = ¹/₂bh
Where:
b is base
h is height
Now, we have the base but we don't have the height.
Pythagoras Theorem is defined as the way in which we find the missing length of a right angled triangle.
The triangle has three sides, namely the hypotenuse (which is always the longest), Opposite (which doesn't touch the hypotenuse) and the adjacent (which is between the opposite and the hypotenuse).
Pythagoras is in the form of;
a² + b² = c²
where c is the hypotenuse
Thus, to find the height of the triangle, we will use Pythagoras theorem to get:
h = √(6² - 4²)
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A student claims that all squares are congruent to each other. is this true or false?
Answer: False.
Step-by-step explanation:
Squares have to have the same shape and size to be congruent. Therefore, not all squares are congruent, since not all of them are the same size. ... This means that they have the same shape, although not necessarily the same size.
Can someone please help me
The height of point A is 0 feet. However, this is not the actual height of point A, as it is at the highest point on the Ferris Wheel, which is 185 feet as calculated previously.
How to solveThe height of point A on the Ferris Wheel can be calculated using the sine function, as it is the vertical component of the point's position. The center of the Ferris Wheel is 100 feet off the ground, and its radius is 85 feet.
Let's denote the height of point A as h_A, which is the vertical distance from the center of the Ferris Wheel to point A.
Since point A is at the 0 radian position, it is at the highest point on the Ferris Wheel. At this point, the height of point A is equal to the sum of the radius and the center's height:
h_A = radius + center's height
h_A = 85 + 100
h_A = 185 feet
So, the height of point A off the ground is 185 feet.
To estimate the value of h_A using the sine function, we can use the fact that at any given angle θ on the unit circle, the height of the point on the circle is given by the sine of that angle multiplied by the radius. In this case, since point A is at the highest point on the Ferris Wheel, we can use the sine of 0 radians (which is 0) to estimate the height of point A:
h_A = radius * sin(0)
h_A = 85 * 0
h_A = 0
So, using the sine function, we estimate that the height of point A is 0 feet. However, this is not the actual height of point A, as it is at the highest point on the Ferris Wheel, which is 185 feet as calculated previously.
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2 quantities, a and b, have a proportional relationship, where a is -3 and b is -4. Create an equation to represent this relationship
The equation to represent the relationship is a = [tex]\frac{3}{4}[/tex] b.
What is proportion?
A percentage is created when two ratios are equal to one another. We write proportions to construct equivalent ratios and to resolve unclear values. a comparison of two integers and their proportions. According to the law of proportion, two sets of given numbers are said to be directly proportional to one another if they grow or shrink in the same ratio.
Here the given two quantities in proportional relationship . Then,
=> a∝ b
=> a=kb
Where k is constant. Then, put a=-3 and b=-4 rhen,
=> -3=-4k
=> k = 3/4
Then the equation is ,
=> a = [tex]\frac{3}{4}[/tex] b.
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The graph shows the square root parent function.
-5
5
5
Which statement best describes the function?
OA. The function is negative when x > 0.
OB. The function is negative when x<0 and also when x > 0.
OC. The function is negative when x < 0.
D. The function is never negative.
The function is never negative.
option D is the correct answer.
What is a negative function?A negative function is a function in which the resulting y value is negative.
Also, a negative function is a function that has y values that are less than zero for any x values. In other words, a negative function has a negative sign in front of its output.
From the given graph, the x and y values started from 0 and increases into the positive direction, so we can conclude that the function can never be negative.
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P = $5000
r = 6.25%
Compounded daily for 5 years
Answer:
Account balance = $6,834.01
Interest accrued = $1,834.01
Step-by-step explanation:
To find the account balance of an initial investment of $5,000 at 6.25% compounded daily for 5 years, use the Compound Interest Formula.
Compound Interest Formula[tex]\large \text{$ \sf A=P\left(1+\frac{r}{n}\right)^{nt} $}[/tex]
where:
A = Final amount.P = Principal amount.r = Interest rate (in decimal form).n = Number of times interest is applied per year.t = Time (in years).As the interest is compounded daily, n = 365.
Therefore, the values to substitute into the formula are:
P = $5,000r = 6.25% = 0.0625n = 365t = 5Substitute the values into the formula and solve for A:
[tex]\implies A=5000\left(1+\dfrac{0.0625}{365}\right)^{365 \cdot 5}[/tex]
[tex]\implies A=5000\left(1.000171232...\right)^{1825}[/tex]
[tex]\implies A=5000\left(1.3668013759...\right)[/tex]
[tex]\implies A=6834.0068795...[/tex]
[tex]\implies A=6834.01\; \sf (2\;d.p.)[/tex]
Therefore, the account balance after 5 years is $6,834.01, and the total amount of interest earned is $1,834.01.
ACCOUNTING
Differential Analysis for a Lease-or-sell Decision
Stowe Construction Company is considering selling excess machinery with a book value of $280,200 (original cost of $399,900 less accumulated depreciation of $119,700) for $277,800, less a 5% brokerage commission. Alternatively, the machinery can be leased for a total of $286,800 for 5 years, after which it is expected to have no residual value. During the period of the lease, Stowe Construction Company's costs of repairs, insurance, and property tax expenses are expected to be $24,900.
On the basis of the data presented, it would be advisable to sell the machinery based on the differential analysis.
For selling the machinery,
Revenues = $277,800
Costs = 277,800 × 5% = $13,890
Profit = Revenues - Cost = $277,800 - $13,890 = $263,910
For leasing the machinery,
Revenues = $286,800
Costs = $24,900
Profit = Revenues - Cost = $286,800 - $24,900 = $261,900
Here the profit generated by selling the machinery is greater, which is the better option.
Hence selling the machinery is the better option.
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On the basis of the data presented, it would be advisable to sell the machinery based on the differential analysis.
For selling the machinery,
Revenues = $277,800
Costs = 277,800 × 5% = $13,890
Profit = Revenues - Cost = $277,800 - $13,890 = $263,910
For leasing the machinery,
Revenues = $286,800
Costs = $24,900
Profit = Revenues - Cost = $286,800 - $24,900 = $261,900
Here the profit generated by selling the machinery is greater, which is the better option.
Hence selling the machinery is the better option.
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In the conversion of fractions to decimals, the fraction should be thought of as (n) ___ problem
In the conversion of fractions to decimals, the fraction should be thought of as a division problem.
A fraction represents the division of the numerator (n) by the denominator (d). So, when you have a fraction like n/d, you can convert it to a decimal by dividing n by d.
Karla drove her vehicle 12,000 miles last year. How many gallons of gasoline would she have saved last year had she driven a fuel-efficient hybrid car averaging 48 miles per gallon rather than an SVU averaging 15 miles per gallon?
Step-by-step explanation:
so, she drove the 12,000 miles with an SUV that gave her 15 miles per gallon.
that means she used
12000 / 15 = 800 gallons of gasoline.
if she would have used a car that gave her 48 miles per gallon, she wound have needed
12000 / 48 = 250 gallons of gasoline.
so, she would have saved
800 - 250 = 550 gallons of gasoline.
6th grade math whats the surface area
Answer:
416
Step-by-step explanation:
The front and back are triangles
a = 1/2 bh
a = 1/2(12)(8)
a = 48
We times this by 2 to find the front and the back.
96
Bottom
a = lw
a = 10 x 12
a = 12
120
Right and left sides
a = lw
a = 10 x10 = 100
Multiply this by 2 to find the right and the left sides.
200
Add the numbers together:
96 + 120 + 200 = 416
Helping in the name of Jesus.
To find the surface area of a three-dimensional object, you need to add up the area of all its faces.
This can be done using formulas specific to the shape of the object. For example, the surface area of a rectangular prism (a box) can be found using the formula SA = 2lw + 2lh + 2wh, where l, w, and h represent the length, width, and height of the box, respectively. Other common three-dimensional shapes include spheres, cones, and cylinders, each with their own unique formulas for finding surface area. So, to answer your question, I would need to know what specific object you are referring to in order to provide an accurate answer about its surface area.
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There are 19 Keurig pods in the green basket next to the Keurig machine. Maddy, Charlie, and Ben each want coffee. There are five Donut Shop, six Swiss Miss hot chocolate, and 7 Breakfast Blend flavors. Maddy and Charlie each grabbed one Donut Shop pod and two Swiss Miss pods. What is the probability that Ben will get the Donut Shop pod after Maddy or Charlie’s selection?
The probability that Ben will get the Donut Shop pod after Maddy or Charlie's selection is 3/17.
We know that, probability of an event = Number of favorable outcomes/Total number of outcomes
There are 5 Donut Shop pods and Maddy and Charlie each took 2, leaving 3 Donut Shop pods in the green basket.
There are 17 pods left in the basket after Maddy and Charlie's selection (5 Donut Shop, 6 Swiss Miss, and 6 Breakfast Blend), so the probability that Ben will get the Donut Shop pod is 3/17.
Therefore, the probability that Ben will get the Donut Shop pod after Maddy or Charlie's selection is 3/17.
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Mr. Pearson drives a bus for the city of Greenwood. Last month, he kept track of the number of bus riders each day. 50 60 Bus riders 70 What was the least number of bus riders? 80 90 100
In a case wherebyMr. Pearson drives a bus for the city of Greenwood and Last month, he kept track of the number of bus riders each day the least number of bus riders is 50.
How can the least number be known?The least number can be described as the number that serves as the smallest among the given number.
Based on the record that was kept, t can be deduced that the highestnumber is 100 whereby the least of the number is 50 which implies that option A is correct because it is considered to be smallest number hence te least number.
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compete question;
Mr. Pearson drives a bus for the city of Greenwood. Last month, he kept track of the number of bus riders each day.
Bus riders
50
60
70
80
90
100
What was the least number of bus riders?
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The probabilities for this problem are given as follows:
Purchase price less than $20,000, repair cost less than $10,000: 45.74% -> about 46%.Repair costs less than $10,000, purchase cost more than $40,000: 20.3 -> about 20%.How to calculate a probability?A probability is calculated as the division of the desired number of outcomes by the total number of outcomes in the context of a problem/experiment.
The number of cars with purchase prices less than $20,000 is given as follows:
86 + 67 + 35 = 188.
Of those 188 cars, 86 had repair costs less than $10,000, hence the probability is given as follows:
p = 86/188
p = 0.4574.
The number of cars with repair costs less than $10,000 is given as follows:
86 + 71 + 40 = 197.
Of those, 40 had a purchase price of more than $40,000, hence the probability is given as follows:
p = 40/197
p = 0.203.
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