A lock has a disk with 36 numbers written around its edge. The combination to the lock is made up of three numbers. What is the probability of correctly guess the combination?
The probability of correctly guessing the combination will be 1/7140.
What are permutation and combination?A permutation is an act of arranging items or elements in the correct order. Combinations are a way of selecting items or pieces from a group of objects or sets when the order of the components is immaterial.
A lock has a disk with 36 numbers written around its edge. The combination of the lock is made up of three numbers.
The total number of the events will be
Total event = ³⁶C₃
Total event = 36! / [(36 - 3)! x 3!]
Total event = 7140
The favorable number of the event will be one.
Then the probability of correctly guessing the combination will be
P = 1 / 7140
The probability of correctly guessing the combination will be 1/7140.
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A restaurant offers two different kinds of soup and three different kinds of salad.
(a) If you are having either soup or salad, how many choices do you have?
(b) If you are having both soup and salad, how many choices do you have?
a. There could be 5 different choices and b. There could be 6 different choices.
What is the fundamental principle of multiplication?Multiplication is the mathematical operation that is used to determine the product of two or more numbers. If an event can occur in m different ways and if following it, a second event can occur in n different ways, then the two events in succession can occur in m × n different ways.
Given tha the number of different kinds of soups = 2
The number of different kinds of salad = 3
(a) If you are having either soup or salad, then the total number of choices you have;
2 + 3 = 5
Hence, the total number of choices you have 5.
(b) If you are having both soup and salad, then the number of choices you have;
2 x 3 = 6
Hence, the total number of choices you have 6.
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Find the exact solution using common logarithms 2^5x+3= 3^2x+1
fibd the length of the strapping needed to secure the pipe in the corner of the room as shown. the distance from a to b is 5.657 feet.
Find the value of I given that p=300,r=0.14,andt=2
Write the given expression in terms of x and y only.
sin(sin−1(x) + cos−1(y))
your classmate says he can write the equation of a quadratic function that passes through the points (3,4), (5,-2),and (3,0). Explain his error.
The classmate's claim is incorrect, as a parabola cannot pass through two points with the same x-coordinate but different y-values, making it impossible for a single quadratic function to pass through points (3,4), (5,-2), and (3,0).
The error in your classmate's assertion that he can write the equation of a quadratic function that passes through the points (3,4), (5,-2), and (3,0) lies in the fact that a quadratic function is a parabola, and no parabola can pass through two points that have the same x-coordinate but different y-values. In other words, any vertical line (like x=3) can intersect a parabola at most once because a quadratic function has only one y value for each x value. Since (3,4) and (3,0) both have the x-coordinate of 3 but different y-coordinates, they cannot both lie on the same parabola. The equation of a quadratic function is typically written as [tex]y = ax^2 + bx + c[/tex], where a, b, and c are constants. To pass through specific points, these constants must be determined such that the function satisfies the coordinates of the points. However, due to the reason explained, no set of constants will satisfy the condition for the mentioned points.
whats between 0 and [tex] \pi /2[/tex]
For what amount Chris can be paid in one of two ways. Plan A is a salary of$430Per month, plus a commission of8%of sales. Plan B is a salary of$607permonth, plus a commission of5%of sales. For what amount of sales is Chris better off selecting plan A?
a bag contains five batteries, all the same size and equally likely to be selected. Each battery is a different brand. If you select three batteries at random, use the counting principle to determine how many points will be in the sample space if the batteries are selected with replacement and without replacement?
When selecting three batteries at random with replacement, there are 125 points in the sample space. When selecting three batteries at random without replacement, there are 60 points in the sample space.
Explanation:To determine the number of points in the sample space when selecting three batteries at random with replacement, we use the counting principle. Since there are 5 batteries, each with an equal likelihood of being selected, and we are selecting three batteries, we can calculate the number of points in the sample space as follows:
Number of points = Number of possible outcomes for the first battery * Number of possible outcomes for the second battery * Number of possible outcomes for the third battery
Since there are 5 batteries, the number of possible outcomes for each battery is 5. Therefore,
Number of points = 5 * 5 * 5 = 125
So, there are 125 points in the sample space when selecting three batteries at random with replacement.
When selecting three batteries at random without replacement, the number of points in the sample space will be different. We can calculate it using a similar approach, but taking into account that once a battery is selected, it is removed from the bag and cannot be selected again. Therefore, for the first battery, there are 5 possible outcomes. For the second battery, there will be 4 possible outcomes since one battery has already been selected. For the third battery, there will be 3 possible outcomes. Therefore,
Number of points = 5 * 4 * 3 = 60
So, there are 60 points in the sample space when selecting three batteries at random without replacement.
The number of possible outcomes for selecting three batteries with replacement is 125. For selecting three batteries without replacement, the total is 60. The counting principle multiplies the number of options for each choice to calculate the sample space.
Explanation:When selecting three batteries from a bag containing five different brands at random, the number of points in the sample space can be determined using the counting principle. The sample space represents all possible outcomes of an experiment.
a. Sampling with replacement
When batteries are selected with replacement, after each selection, the chosen battery is put back into the bag, making it available for the next selection. Thus, for each pick of the three batteries, there are five choices. The total number of points in the sample space for selecting three batteries with replacement is therefore 5 × 5 × 5 = 125.
b. Sampling without replacement
When batteries are selected without replacement, the chosen battery is not put back in the bag, which means the options decrease with each selection. The first pick has five choices, the second pick will have four (since one battery is already picked), and the third pick will have three. The total number of points in the sample space for selecting three batteries without replacement is therefore 5 × 4 × 3 = 60.
A marketing firm randomly sends a mass promotional mailing to 21 %of the households in a new market area. From experience the firm knows that the probability of response to a mailing is 0.14 Number .What is the probability that a household receives the mailing and responds?
A brace for a shelf has the shape of a right triangle. Its hypotenuse is 10 inches long and the two legs are equal in length. How long are the legs of the triangle?
A building in a city has a rectangular base. The length of the base measures 70ft less than twice the width. The perimeter of the base is 910 ft. What are the dimensions of the base?
you have to answer 3 essay questions for an exam. there are 6 essays to check choose from. how many different groups of 3 essays could you possibly choose?
Find the amount of tax rate. Round to the nearest hundredth of a percent Cost of item $102 selling price 113.08
From a marginal analysis perspective, what is the inventory carry cost for Andrews if the company carries one additional unit of Able in inventory at the end? Select: 1Save Answer $9.98 $1.20 $1.92 $3.85
Make a down payment of $1500 and finance the rest of $20000 at 1.9% interest rate, making equal monthly payments for 5 years.
Calculate the total interest you will pay over the term of the loan. Show the computations that lead to your answer.
A department store holds a year-end clearance sale that includes a 14.5% discount on cosmetics. Find the sales price of the bottle of perfume if it's original price was 56.69
56.69 - 0.145(56.69)
= 56.69 - 8.22
= 48.47
How to calculate discount and sale price?Find the original price (for example $90 )Get the discount percentage (for example 20% )Calculate the savings: 20% of $90 = $18.Subtract the savings from the original price to get the sale price: $90 - $18 = $72.the formula for discount price
Subtract the final price from the original price. Divide this number by the original price. Finally, multiply the result by 100. You've obtained a discount in percentages.
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At noon, ship A is 170 km west of ship B. Ship A is sailing east at 30 km/h and ship B is sailing north at 25 km/h. How fast is the distance between the ships changing at 4:00 PM?
Final answer:
To find how fast the distance between two ships is changing, we calculate the distance they have covered, form a right triangle, and use the Pythagorean theorem and related rates to find that the distance is changing at approximately 8.94 km/h at 4:00 PM.
Explanation:
To determine how quickly the distance between ship A and ship B is changing, we can use the concept of related rates from calculus. At noon, the ships are 170 km apart. Ship A travels east (towards ship B) at 30 km/h, and ship B travels north at 25 km/h. By 4:00 PM, four hours have passed.
First, let's calculate the distance each ship has traveled after 4 hours. Ship A would have covered 30 km/h * 4h = 120 km eastward. Ship B would have traveled 25 km/h * 4h = 100 km northward.
Next, we need to calculate the distance between the two ships at 4:00 PM. Since ship A is moving east and ship B is moving north, they are traveling at right angles to each other. The distance between the two ships forms the hypotenuse of a right triangle, with the sides being the distances traveled by each ship. Using the Pythagorean theorem, the distance between the two ships at 4:00 PM (D) is:
² = (170 km - 120 km)² + (100 km)²
² = (50 km)² + (100 km)²
² = 2500 km² + 10000 km²
= √12500 km²
= 111.80 km (approx)
Finally, we have to find the rate at which this distance is changing. Let x be the east-west distance from ship B to ship A, and y be the northward distance ship B has covered. Taking the derivative of the Pythagorean relation we have, x² + y² = ², with respect to time (t) gives us:
2x(/) + 2y(/) = 2(/)
Given that dx/dt = -30 km/h (since it's decreasing as ship A sails east) and dy/dt = 25 km/h, we can solve for d/dt:
2*50*(-30) + 2*100*(25) = 2*111.80*(d/dt)
-3000 + 5000 = 223.60*(d/dt)
2000 = 223.60*(d/dt)
d/dt = 2000 / 223.60
d/dt = 8.94 km/h (approx)
Therefore, the distance between the ships is changing at approximately 8.94 km/h at 4:00 PM.
a printer charges a fixed setup cost plus $0.40 for every 40 copies. if 320 copies cost $43.20 how much will it cost to print 1200 copies
The cost to print 1200 copies is $52.00.
The given data tells us that 320 copies cost $43.20. Each set of 40 copies costs $0.40, so 320 copies are 8 sets (320/40). The variable cost for 320 copies is 8 × $0.40 = $3.20.
We can then determine the fixed setup cost by subtracting the variable cost from the total cost for 320 copies: $43.20 - $3.20 = $40.00.
The total cost C for printing x copies can be expressed as:
C = fixed setup cost + variable cost per set × (x/40)
So the total cost for 1200 copies is:
C = $40.00 + $0.40 × (1200/40)
Calculating this, we get:
C = $40.00 + $0.40 × 30 = $40.00 + $12.00 = $52.00
Therefore, the cost to print 1200 copies is $52.00.
Wesly is 5 feet 3 inches tall. If one inch equals 2.54 centimeters, what is wesly's height in centimeters
Answer:
152.4 cm
Step-by-step explanation:
Wesly is 5 feet and 3 inches tall. Since there are 12 inches in one foot, 5 feet has 60 inches. This means Wesly is 63 inches tall. If one inch is 2.54 cm then 60(2.54) is Wesly's height in centimeters. 60(2.54) = 152.4
Crafty grandma Edith set her family down during Thanksgiving and told them they couldn't have any pet can pass until they worked out this puzzle are six-year-old granddaughter was the first to solve it can you work out what 9183 equals
8809=6 3590=2
7111=0 6855=3
9881=5 1012=1
6660=4 5731=0
5531=0 9191=2
2516=1 9193=?
how many different ways can you make 82 cents using current u.s. currency
Dawn took two pies to a school bake. She cut Pie A into 8 slices and Pie B into 6 slices. She sold two slices of Pie A and three slices in Pie B, how much total Pie Dawn has remaining?
Dawn has 6 slices of Pie A and 3 slices of Pie B remaining.
Explanation:Dawn brought two pies to a bake sale. Pie A was cut into 8 slices and Pie B was cut into 6 slices. She sold 2 slices of Pie A and 3 slices of Pie B. To calculate how much pie Dawn has remaining, we need to subtract the slices sold from the total slices in each pie. So, for Pie A, we have 8 slices - 2 slices = 6 slices remaining. And for Pie B, we have 6 slices - 3 slices = 3 slices remaining. Therefore, Dawn has a total of 6 slices of Pie A and 3 slices of Pie B remaining.
Final answer:
Dawn originally had two pies, with Pie A cut into 8 slices and Pie B cut into 6 slices. She sold two slices from Pie A and three from Pie B, leaving her with a total of 9 slices remaining from both pies.
Explanation:
To determine how much total Pie Dawn has remaining after selling some slices, we can use simple subtraction.
Dawn originally had two pies:
Pie A was cut into 8 slices, and she sold 2 slices.
Pie B was cut into 6 slices, and she sold 3 slices.
To find out how much of each Pie is left, we subtract the number of slices sold from the total number of slices:
Pie A remaining: 8 - 2 = 6 slices
Pie B remaining: 6 - 3 = 3 slices
To find the total amount of Pie remaining, we add the slices remaining from Pie A and Pie B:
Total Pie remaining: 6 (from Pie A) + 3 (from Pie B) = 9 slices
Dawn is left with 9 slices of Pie in total after the sales.
An insurance office has 65 employees. If 39 of the employees have cellular phones, what portion of the employees do not have cellular phones?
In a poll of travelers, 85% said that traveling by air makes them nervous, and 450 travelers said that it does not make them nervous. How many travelers were polled?
alana bought 6 books each book costs 13$ and each bookmark cost 2$ how much did she spend on books
In our solar system, 666 of the 888 planets have moons. What percentage of the planets have moons?
Answer:
75% of the planets have moons
Step-by-step explanation:
In order to calculate this you just have to do a simple rule of three, in which you will use 888 as the 100 percent and you want to discover what percentage of that does 666 represents:
[tex]\frac{888}{100} \frac{666}{x} \\x=\frac{666*100}{888}\\ x=75\\[/tex]
So you have that 666 is the 75% of 888, that means that 75% of the planets have moons.
two angles are supplementary. their difference is 22°. find the angles
Write a number from 20 to 50 that has both tens and ones
Answer:
45
Step-by-step explanation:
We know that,
If we have the numbers of the form xyz.
This gives that, x is placed at the hundredth place, y is placed at the tens place and z is located at ones place.
Since, we need a number between 20 and 50 having both tens and ones place.
We can take any number from 20 to 50.
For e.g. Let us take 45.
In 45, 4 is placed at the tens place and 5 is placed at the ones place.
Hence, 45 is the number between 20 to 50 having both tens and ones place.