The probabilities of randomly entering each room in the maze shown at right are:
P(A) = 5/18
P(B) = 1
What is the probability?The probabilities can be determined from the formulas below:
P(A) = 1/3 * 1/2 * 1 + 1/3 * 1/3
P(B) = 1/3 * 1 + 1/3 * 1 + 1/3 *1
To calculate the probabilities, we need to simplify the expressions and do the arithmetic.
Using the formulas you provided:
P(A) = (1/3 * 1/2 * 1) + (1/3 * 1/3) = 1/6 + 1/9 = 5/18
P(B) = (1/3 * 1) + (1/3 * 1) + (1/3 * 1) = 1
Therefore, the probabilities, evaluated to their simplest form, are:
P(A) = 5/18
P(B) = 1
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PLEASE HURRY DUE TODAY WILL MARK BRAINLESTIS RIGHT
what is √29 Place a dot on the number line at the BEST approximation
Answer:
5.4
Step-by-step explanation:
square of 29 = 5.385164807
5.385164807 estimated is 5.4
using truth table show that (p^q) =~pv~q please help meeee
The truth table for the given expression can be given using p= T q = T, p^q = T, ~p = F, ~q = F, ~q v ~p = T, and (p ^ q) =~p v ~q = T, thus proving the required.
What is propositional logic?The field of symbolic logic known as propositional logic, also referred to as sentential logic or statement logic, is concerned with propositions or statements, which are declarative phrases that can be true or untrue. To represent propositions and their relationships, propositional logic employs symbols and operators.
Many disciplines, including mathematics, computer science, philosophy, and others, employ propositional logic as a tool for debating the truth or falsity of propositions and analysing arguments.
The truth table for the given expression can be given as:
p | q | p ^ q | ~p | ~q | ~q v ~p | (p ^ q) =~p v ~q
-------------------------------------------------------------
T | T | T | F | F | T | T
T | F | F | F | T | T | T
F | T | F | T | F | T | T
F | F | F | T | T | T | T
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) Rewrite as an exponential equation.
log8 1/64 =2
(b) Rewrite as a logarithmic equation.
3 0=1
a) the exponential equation equivalent to log8 1/64 = 2 is 1/64 = [tex]8^{(-2)}[/tex]
b) the logarithmic equation equivalent to 3^0 = 1 is log3 1 = 0.
What is exponential equation?
An exponential equation is one in which the exponent contains a variable.
(a) We can rewrite the logarithmic equation as an exponential equation by using the definition of logarithms. The logarithmic equation
log8 1/64 = 2
means that 8 raised to the power of 2 is equal to 1/64:
[tex]8^2 = 1/64[/tex]
Thus, we can write the exponential equation as:
[tex]1/64 = 8^{(-2)}[/tex]
Therefore, the exponential equation equivalent to log8 1/64 = 2 is 1/64 = [tex]8^{(-2)}.[/tex]
(b) We can rewrite the exponential equation as a logarithmic equation by using the definition of logarithms. The exponential equation
[tex]3^0 = 1[/tex]
means that the logarithm of 1 to the base 3 is equal to 0:
log3 1 = 0
Therefore, the logarithmic equation equivalent to 3^0 = 1 is log3 1 = 0.
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The Greenfield Community Picnic is today. The organizers are making 2 pulled-pork sandwiches for every 5 barbeque chicken sandwiches.
Answer: What is the ratio of pulled-pork sandwiches to barbeque chicken sandwiches at the Greenfield Community Picnic?
Let's call the number of pulled-pork sandwiches "P" and the number of barbeque chicken sandwiches "C". According to the problem, the organizers are making 2 pulled-pork sandwiches for every 5 barbeque chicken sandwiches. This means that:
P/C = 2/5
To simplify this ratio, we can multiply both sides by a common factor that will make the denominators the same. In this case, the smallest common multiple of 2 and 5 is 10, so we can multiply both sides by 10:
10(P/C) = 10(2/5)
Simplifying this expression, we get:
2P = 4C
Dividing both sides by 2, we get:
P/C = 2/4
Simplifying this fraction, we get:
P/C = 1/2
Therefore, the ratio of pulled-pork sandwiches to barbeque chicken sandwiches at the Greenfield Community Picnic is 1:2.
Step-by-step explanation:
Chloe claims that Point A=−6 and Point B=1 . Which of the following statements provide support for Chloe's claim? Select ALL that apply. A A<0 because A is to the left of zero B A>0 because A is to the left of zero C A 0 because B is to the left of zero F B>0 because B is to the right of zero
The statements that provide support for Chloe's claim are A<0 because A is to the left of zero, B>0 because B is to the right of zero. So correct option is A and F.
Describe Comparison Algebra?Comparison algebra is a branch of algebra that deals with inequalities and comparisons between different quantities or expressions. In comparison algebra, the goal is to determine the relationships between different expressions or quantities, such as whether one expression is greater than, less than, or equal to another expression.
Comparison algebra involves the use of comparison symbols, such as "<" (less than), ">" (greater than), and "=" (equal to), to express these relationships. For example, if we have two expressions, A and B, we can use the "<" symbol to express the relationship that A is less than B, as in A < B.
In comparison algebra, we can also manipulate inequalities and equations in similar ways as we do with regular algebraic expressions. For instance, we can add, subtract, multiply, or divide both sides of an inequality or equation by the same number or expression, while maintaining the inequality's direction.
The statements that provide support for Chloe's claim are:
A. A<0 because A is to the left of zero.
F. B>0 because B is to the right of zero.
Statement A supports Chloe's claim because Point A is to the left of zero on the number line, which means its value is negative. Statement F also supports Chloe's claim because Point B is to the right of zero on the number line, which means its value is positive.
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50pts!!!!
Many investors use interest-only loans to buy shares or property. For such loans the principal stays constant and only the interest is paid back each month.
She buys an investment property for $300 000 and borrows the full amount at 7% p.a. simple interest. She rents out the property at $1500 per month and pays $3000 per year in rates and other costs to keep the property.
Find the amount of interest she needs to pay back every month.
Find her yearly income from rent.
By considering the other costs in keeping the property, calculate her overall loss in a year.
she hopes that the property’s value will increase enough to cover any loss she is making. By what percentage of the original price will the property need to increase in value per year?
Step-by-step explanation:
to find the interest she needs to pay back every month, we need to use this formula:
I = PRT/12
in this case the principle is $300,000, the rate is 7% p.a. and the amount of time is 1 year, if we substitute in our values we:
I = (300,000)(7)(1)/12 = $17,500 in interest every month
to find her yearly income from rent, we have to multiply the monthly rent by 12
1500 × 12 = $18,000
to calculate her loss percentage in a year, we have to subtract 18,000 from 3000 which is 15,000
she said that she hopes the property's value will increase to cover the loss she made.
to cover the loss of $15000 per year, the property needs to increase in value by at least $15000. the percentage increases value can be written as
Percentage increase = (difference in increase/Original price) × 100
so
percentage increase = (15000/300000) × 100 = 5%
so the property needs to increase in value by at least 5% per year to cover the loss.
The woman needs to pay $1750 monthly as interest. Her yearly income from the rent is $18,000. After considering all other costs, she is at a loss of $6000 per year, so the property needs to increase in value by 2% per year to cover this loss.
Explanation:First, let's calculate the monthly interest she needs to pay. 7% of $300,000 is $21,000 for a year. To find the monthly interest, we divide this by 12, resulting in $1750.Her yearly income from rent is $1500 multiplied by 12, giving us $18,000.To calculate her overall loss, we add the yearly interest and the costs to keep the property, then subtract the yearly rent income. So, $21,000 + $3000 - $18,000 = $6000 loss per year.Lastly, to find out by what percentage the property value needs to increase, we divide the loss by the original price and multiply by 100, giving us 2% increase per year.Learn more about Interest and Profit Calculation here:https://brainly.com/question/32651816
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Solve for x.
A. 7
B. 4
C. 3
D. 5
The correct option -D. 5; Thus, the value of x for the given external secant segment and the tangent on the circle is found as:x = 5.
Explain about the secant of circle:A line that precisely intersects a circle at two points is said to be a secant.
The size of the angle created when two tangents, two secants, or two tangents cross outside of a circle is equal to one-half a positive difference between the sizes of the intercepted arcs.
Using the Theorem:
The square of a length of tangent is equal the the product of such external secant segment and the overall length of the secant if one secant and one tangent both drawn to a circle from a single exterior point:
4(4 + x) = 6²
16 + 4x = 36
4x = 36 - 16
4x = 20
x = 20/4
x = 5
Thus, the value of x for the given external secant segment and the tangent on the circle is found as:x = 5.
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ii) The door is 0.9 m wide and 2.1 m high. Each of the four windows is 1.5 m wide and 1.2 m high work out the toral area of the door and the four windows
Answer: The area of the door can be calculated as:
Area of door = width x height
= 0.9 m x 2.1 m
= 1.89 square meters
The area of one window can be calculated as:
Area of window = width x height
= 1.5 m x 1.2 m
= 1.8 square meters
Since there are four windows, the total area of the four windows is:
Total area of four windows = 4 x Area of window
= 4 x 1.8 square meters
= 7.2 square meters
Therefore, the total area of the door and the four windows is:
Total area = Area of door + Total area of four windows
= 1.89 square meters + 7.2 square meters
= 9.09 square meters
Hence, the total area of the door and the four windows is 9.09 square meters.
Step-by-step explanation:
An ice cream stand uses the expression 1 + 0.75x to determine the cost (in dollars) of an ice cream cone that has x scoops of ice cream. How much does an ice cream cone with 3 scoops cost?
Answer:
$3.25
Step-by-step explanation:
An ice cream cone that has x scoops of ice cream costs 1 + 0.75x.
So an ice cream cone that has 3 scoops of ice cream costs
1 + 0.75×3 = 3.25 (dollars)
Rewrite 6x2 + 2xy + 9x + 3y in factored form. (2x + 3)(3x + y) (2x + y)(3x + 3) (3x + 2)(3x + y) (3x + y)(2x + 1)
Answer:
(3x + y)(2x + 3)
Step-by-step explanation:
Factorizing the expression:6x² = 2 * 3 * x * x
2xy = 2*x * y
Common factor = 2x.
9x = 3 * 3 * x
3y = 3 * y
Common factor = 3
Take out the common factor 2x from the first and second term & take out the common factor 3 from third and fourth term.
6x² + 2xy + 9x + 3y = 2x(3x + y) + 3(3x + y)
= (3x + y)(2x + 3)
The owner of a stereo store wants to advertise that she has many different sound systems in stock. The store carries 5 different CD players, 8 different receivers, and 10 different speakers. A sound system consists of one of each item. How many different sound systems can the store owner advertise?
The owner can advertise 400 different sound systems. The solution has been obtained by using the arithmetic operations.
What are arithmetic operations?
All real numbers can be explained using the four fundamental operations, generally known as "arithmetic operations." In mathematics, operations like quotient, product, sum, and difference occur after operations like division, multiplication, addition, and subtraction.
We are given that the owner of a stereo store carries 5 different CD players, 8 different receivers, and 10 different speakers and each sound system consists of one of each item.
So, the different sound systems that the owner can advertise is obtained by using the multiplication operation, which gives:
⇒ Different sound systems = 5 * 8 * 10
⇒ Different sound systems = 400
Hence, the owner can advertise 400 different sound systems.
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Find the compound interest on Rs. 3,500 for 2 years at the rate of 8% per annum.
Answer: The formula for compound interest is:
A = P(1 + R/100)^t
where A is the amount after t years, P is the principal amount, R is the rate of interest per annum, and t is the time period in years.
Here, P = Rs. 3,500, R = 8%, and t = 2 years.
So, the amount after 2 years will be:
A = 3,500(1 + 8/100)^2
= 3,500(1.08)^2
= 3,892.32
Therefore, the compound interest for 2 years will be:
CI = A - P
= 3,892.32 - 3,500
= 392.32
Hence, the compound interest on Rs. 3,500 for 2 years at the rate of 8% per annum is Rs. 392.32.
Step-by-step explanation:
Help please i dont know
The histogram should be modified as follows:
The bin from 6 to 15 should be increased by 2.The bin from 16 to 25 should be increased by one.The bin from 26 to 35 should be increased by one.The bin from 46 to 55 should be increased by one.What is shown by an histogram?A histogram is a type of graphical representation that displays the distribution of a dataset. It is a bar graph-like chart where the data is divided into intervals, called "bins", which are represented by adjacent rectangular bars of varying heights.
Then the height of the histogram gives the number of observations into each data interval.
Hence the histogram should be modified as follows:
The bin from 6 to 15 should be increased by 2. -> two measures of 12.The bin from 16 to 25 should be increased by one. -> measure of 16.The bin from 26 to 35 should be increased by one. -> measure of 26.The bin from 46 to 55 should be increased by one. -> measure of 48.More can be learned about histograms at https://brainly.com/question/25983327
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A bag contains 2 gold marbles, 10 silver marbles, and 29 black marbles. The rules of the game are as follows: You randomly select one marble from the bag. If it is gold, you win $6, if it is silver, you win $4. If it costs $1 to play, what is your expected profit or loss if you play this game?
Answer:
33 thats with the 1 dollar subtracted for the entry fee
Step-by-step explanation:
first you add all the number of marbles you have then you get 41 then divide it by 12 because you have 2 gold and 10 silver and you get 3.4 and multiply that by 10 because its 6 and 4 and you get 34 subtract the entry fee
28) The number of hours per week that high school students spend on computers is normally distributed, with a mean
of 5 hours and a standard deviation of 2 hours. 70 students are chosen at random. Let y represent the mean number
of hours spent on the computer for this group. Find the probability that y is between 5.1 and 5.7.
The probability that y is between 5.1 and 5.7 is approximately 0.4292.
What is probability?Probability is a way to gauge how likely or unlikely something is to happen. It is a number between 0 and 1, where 0 denotes an improbable event and 1 denotes an inevitable one.
According to question:Since the sample size is large (n = 70), we can use the Central Limit Theorem to approximate the sampling distribution of the sample mean as normal with mean μ = 5 and standard deviation σ/sqrt(n) = 2/sqrt(70) ≈ 0.24.
Now we want to find the probability that y, the sample mean, is between 5.1 and 5.7. We can use the standard normal distribution to do this by standardizing y:
z = (y - μ) / (σ / sqrt(n)) = (y - 5) / 0.24
The probability that y is between 5.1 and 5.7 is equivalent to the probability that z is between:
z1 = (5.1 - 5) / 0.24 ≈ 0.42
and
z2 = (5.7 - 5) / 0.24 ≈ 2.92
Using a standard normal distribution table or calculator, we can find that the probability of z being between z1 and z2 is approximately 0.4292.
Therefore, the probability that y is between 5.1 and 5.7 is approximately 0.4292.
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carpet is sold in square yards how much carpet would a person need to buy for a rectangle that has dimensions of 10 yards by 18 feet
A person would need to buy 60 square yards of carpet for a rectangular room with dimensions of 10 yards by 18 feet.
How to determine the amount of carpet needed for a rectangular room?
To determine the amount of carpet needed for a rectangular room, you need to convert the measurements to the same unit of measurement. Since the carpet is sold in square yards, we need to convert the dimensions of the room to yards.
The length of the room is given in yards, so we don't need to make any conversions for that dimension. However, the width of the room is given in feet, so we need to convert it to yards by dividing by 3 (since there are 3 feet in a yard),
18 feet ÷ 3 feet/yard = 6 yards
So the dimensions of the room in yards are 10 yards by 6 yards.
To find the total area of the room, we need to multiply the length and width,
10 yards × 6 yards = 60 square yards
Therefore, a person would need to buy 60 square yards of carpet for a rectangular room with dimensions of 10 yards by 18 feet.
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Help corrections due in 3 hours! giving 25 points and brainlist
The value of GH in the right angle triangle, given FH and Angle FHG is 22.46 inches.
How to find the value of GH ?Since we have the adjacent side (FH) and want to find the hypotenuse (GH), we can use the cosine function.
cos(35°) = adjacent side (FH) / hypotenuse (GH)
We know that FH = 18.4 in. So, we can write the equation as:
cos(35°) = 18.4 / GH
GH = 18.4 / cos(35°)
GH = 18.4 / 0.81915
= 22.46 inches
So, the length of GH, the hypotenuse, is approximately 22.46 inches.
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Please help me please tysm and have a great day :)
Answer:
mean: 20mins
Step-by-step explanation:
add them all together to get 240
then divide by how many there are
240÷12=20
so the mean is 20mins
find the factors to this polynomials i need help SHOW YOUR WORK.
Answer:
hope this will help you...
As seen in the diagram below, Austin is building a walkway with a width of x feet to go around a swimming pool that measures 8 feet by 10 feet. If the total area of the pool and the walkway will be 360 square feet, how wide should the walkway be?
Using the total area of the rectangular pool we know that the required width of the pathway is 3.6 ft respectively.
What is a rectangle?In the Euclidean plane, a rectangle is a quadrilateral with four right angles.
A parallelogram with a right angle or an equiangular quadrilateral, where equiangular means that all of its angles are equal, are other ways to define it.
A rectangle with four equal-length sides is a square.
Squares are not always rectangles, but rectangles are always squares.
So, the pool and walkway together have a 360 square foot total space.
Assume that the walkway is w feet in width.
Since the pool has an additional w feet of width on both sides, the total area's measurements can be expressed as (8 + 2w) by (10 + 2w).
Thus, we can construct the following equation:
(8 + 2w) x (10 + 2w) = 360
By enlarging and condensing the left side, we obtain:
4w² + 36w - 80 = 0
Using the quadratic formula, we can find w:
w = (-b ± √(b² - 4ac)) / 2a
Here, an equals 4, b equals 36, and c equals -80. When these values are added to the formula, we obtain:
w = (-36 ± √(36² - 4(4)(-80))) / 8
w = (-36 ± √(1872)) / 8
w ≈ -5.6 or w ≈ 3.6
We can ignore the first option because the width cannot be negative. Consequently, the pathway should be around 3.6 feet wide.
Therefore, using the total area of the rectangular pool we know that the required width of the pathway is 3.6 ft respectively.
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A factory that has 6 X 10³ workers makes 2.4 X 105 products each day.
What is the average amount of
products made per worker?
In a a case whereby factory that has 6 X 10³ workers makes 2.4 X 105 products each day, the average amount of products made per worker is 4 *10^1 products per worker
How can the average amount of products made per worker can be calculated?The term "average" in mathematics typically refers to a measure of central tendency, which is a way to describe the typical or common value in a set of numbers. There are several types of averages.
We can calculate the required value as
( 2.4 X 10^5 )/ (6 X 10³)
=4 *10^1 products per worker
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Equipment accusers on January 8 at cost of $212,000 has an estimated useful life of 15 years, has an estimated residual value of $14,000, and is depreciated by the straight line method
Answer: To calculate the annual depreciation expense of the equipment using the straight-line method, we need to first determine the depreciable cost of the asset, which is the cost of the asset minus its estimated residual value.
Depreciable Cost = Cost of asset - Estimated Residual Value
Depreciable Cost = $212,000 - $14,000
Depreciable Cost = $198,000
Next, we can use the following formula to calculate the annual depreciation expense:
Annual Depreciation Expense = Depreciable Cost / Useful Life
Annual Depreciation Expense = $198,000 / 15 years
Annual Depreciation Expense = $13,200 per year
Therefore, the annual depreciation expense of the equipment using the straight-line method is $13,200 per year.
Step-by-step explanation:
Divide and give your answer as a decimal. Round your answer to the nearest thousandth (3 digits behind the decimal).
2/9
Answer:
0.222
Step-by-step explanation:
2 divided by 9 is:
0.222 (rounded to the nearest thousandth)
Nick's new home had a purchase price of $145,500. He got a 30-year fixed mortgage for 75% of the purchase price. The interest rate on the loan is 3.15%. What is his monthly payment?
Nick's monthly mortgage payment is $482.16.
What is statistics?
Statistics is a branch of mathematics that deals with the collection, analysis, interpretation, presentation, and organization of numerical data.
To calculate Nick's monthly mortgage payment, we first need to find out the amount he borrowed from the bank, which is 75% of the purchase price:
$145,500 x 0.75 = $109,125
Next, we need to calculate the monthly interest rate. We can do this by dividing the annual interest rate (3.15%) by 12:
3.15% / 12 = 0.002625
Now we can use the following formula to calculate Nick's monthly payment:
M = P [ [tex]i(1 + i)^{n}[/tex] ] / [ [tex](1 + i)^{n}[/tex] – 1]
Where:
M = Monthly payment
P = Loan amount (principal)
i = Monthly interest rate
n = Number of payments (in months)
Plugging in the values we have:
M = $109,125 [ 0.002625 [tex](1 + 0.002625)^{360}[/tex] ] / [ [tex](1 + 0.002625)^{360}[/tex] – 1]
M = $482.16
Therefore, Nick's monthly mortgage payment is $482.16.
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Mohal plans to repaint some classroom bookcases. He has 1 1 /8 gallons of paint. All of the bookcases are the same size and each requires 1/8gallon of paint. How many bookcases will he be able to paint?
Mohal will be able to paint 9 bookcases for the amount of paint.
What is fraction?An expression for a portion of a whole is a fraction. It is represented by the numerator above the denominator, with a horizontal line separating the two numbers. In mathematics, fractions are used to represent fractions of a whole or values that are not whole numbers. Like whole numbers, they can be multiplied, split, added, and subtracted. Ratios and proportions, which are crucial ideas in many branches of mathematics and science, are also represented by fractions.
Given that, he has 1 1 /8 gallons of paint.
Thus, number of bookcases are:
1 1/8 ÷ 1/8 = (9/8) ÷ (1/8) = 9
Hence, Mohal will be able to paint 9 bookcases for the amount of paint.
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A patient takes 110 mg of a drug at the same time every day: Just before each tablet is taken, 5% of the drug present in th
preceeding time step remains in the body. What quantity of the drug remains in the body in the long run?
Hint: First find the quantity of drug present in the body after the second tablet, third tablet, etc to generalize the sequenc
formula for the nth tablet. Then use that sequence to predict the drug remains in the long run.
The requried quantity of drug that remains in the body, in the long run, is 220 mg.
Let's denote the amount of drug in the body just before taking the nth tablet by [tex]D_n[/tex]. We know that [tex]D_0 = 0[/tex](since the patient hasn't taken any tablets yet) and that 5% of the drug is present in the body just before taking a tablet remains in the body. Therefore, we can write:
[tex]D_1 = 110\\D_2 = 0.95 * D_1 + 110 = 203.5\\D_3 = 0.95 * D_2 + 110 = 292.225\\D_4 = 0.95 * D_3 + 110 = 376.81375[/tex]
We can see that the formula for [tex]D_n[/tex] is:
[tex]D_n = 110 * (1 - 0.05)^n + 110 * (1 - (1 - 0.05)^n) / 0.05[/tex]
Simplifying this formula, we get:
[tex]D_n = 220 * (1 - 0.95^n)[/tex]
Now, we want to find the amount of drug that remains in the body in the long run. This means we want to find the limit of [tex]D_n[/tex] as n goes to infinity. Using the formula above, we can see that:
[tex]lim_ {n- > oo} D_n = lim_ {n- > oo} 220 * (1 - 0.95^n) = 220[/tex]
Therefore, the quantity of drug that remains in the body, in the long run, is 220 mg.
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In order to develop a more appealing cheeseburger, a franchise uses taste tests with 11 5 different buns, 3 different cheeses, 4 types of lettuce, and types of tomatoes. If the taste tests were done at one restaurant by one tester who takes 10 minutes to eat each cheeseburger, approximately how long would it take the tester to eat all possible cheeseburgers?
It would take approximately 1,980 minutes (33 hours) for the tester to eat all possible cheeseburgers.
complete the equatiotin 3 over 4 x 6 =
PLEASE HELP
Answer:
1/8
Step-by-step explanation:
If "over" refers to (4 * 6) as a whole,
[tex]\frac{3}{4*6}\\\\=\frac{3}{24}\\\\=\frac{1}{8}[/tex]
If "over" refers to division,
[tex]3 \div 4 \times 6\\= 0.75 \times 6\\= 4.5[/tex]
I would suppose it's the first one, so, ignore the second one if you haven't learnt BODMAS yet.
Hope this helps and be sure to mark this as brainliest! :)
Help me on my math question pls!
Answer:
D
Step-by-step explanation:
A rotation and translation preserves the length measures of the sides, so FD is equal to 7 inches
Answer: D
Step-by-step explanation:
A hamster running in a wheel of radius 10 cm spins the wheel one revolution in 5 seconds.
a) What is the angular velocity of the wheel?
b) At what linear velocity is the hamster running?
just need the answer
a) The angular velocity = 0.4π rad/s b) The linear velocity of the hamster = 4π cm/s.
What is linear velocity?Linear velocity is the rate of change of an object's position with respect to time. It measures how fast an object is moving in a straight line, and is often expressed in units of distance per time, such as meters per second or kilometers per hour.
According to given information:a) The angular velocity of the wheel can be calculated as follows:
Angular velocity = (2π * number of revolutions) / time
Here, the wheel completes one revolution in 5 seconds, so the number of revolutions is 1 and the time is 5 seconds. Therefore,
Angular velocity = (2π * 1) / 5
Angular velocity = 0.4π rad/s (or approximately 1.26 rad/s)
b) The linear velocity of the hamster can be calculated as follows:
Linear velocity = radius * angular velocity
Here, the radius of the wheel is 10 cm, and the angular velocity we found in part (a) is 0.4π rad/s. Therefore,
Linear velocity = 10 cm * 0.4π rad/s
Linear velocity = 4π cm/s (or approximately 12.57 cm/s)
So the hamster is running at a linear velocity of approximately 12.57 cm/s.
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