Answer:
Step-by-step explanation:
c
8. (6 pts) At a local garden shop, the price of plants includes sales tax. The cost of 4 large plants and 8
medium plants is $40. The cost of 5 large plants and 2 medium plants is $28.
b) Could the cost of one large plant be $5.50 and the cost of one medium plant be $2.25? Justify your
answer.
c)
Determine algebraically both the cost of a large plant and the cost of a medium plant
By solving a system of equations we will see that a large plant costs $4.50 and a medium one $2.75
How to find the costs of the plants?Let's define the variables:
x = cost of a large plant.
y = cost of a medium plant.
We know that " The cost of 4 large plants and 8 medium plants is $40"
4*x + 8*y = 40
And "The cost of 5 large plants and 2 medium plants is $28."
5*x + 2*y = 28
So we have a system of equations:
4*x + 8*y = 40
5*x + 2*y = 28
We can isolate x on the first equation to get:
4x + 8y = 40
4x = 40 - 8y
x = (40 - 8y)/4
x = 10 - 2y
Replacing that in the other equation we will get:
5*(10 - 2y) + 2*y = 28
50 - 10y + 2y = 28
50 - 28 = 8y
22 = 8y
22/8 = y
2.75 = y
And the value of x is:
x = 10 - 2*2.75 = 4.5
Then the cost of a lare plant is $4.5 and the cost of a medium plant is $2.75.
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6.4 divided by 49.92
Answer:
12.82
Step-by-step explanation:
6.4/49.92
multiply both the numerator and denominator with 100 since the denominator is to hundredth place
6.4×100/49.92×100
640/49.92=
compute in the calculator to get answer as;
12.82
Answer:
This is an approximate answer so I not sure if it is accurate.
0.1282051282
Hoped it helped and was the right answer
You design a tree house using a coordinate plane in which the coordinates are measured in meters (m ).
The vertices of the rectangular floor are (0, 5), (4, 3), (4,13), and (8, 11).
Part A: What is the perimeter of the tree house floor?
__ m
Part B: What is the area of the tree house floor?
__ m²
Part A: The perimeter of the tree house floor is 32 m.
Part B: The area of the tree house floor is 40 m².
Tree House Area and PerimeterPart A: The perimeter of the rectangular floor can be found by adding up the lengths of all four sides.
The first side has a length of 4 m and extends along the x-axis from (0, 5) to (4, 5).The second side has a length of 10 m and extends along the y-axis from (4, 5) to (4, 15).The third side has a length of 8 m and extends along the x-axis from (4, 15) to (0, 13).The fourth side has a length of 10 m and extends along the y-axis from (0, 13) to (0, 5).So the perimeter is 4 + 10 + 8 + 10 = 32 m.Part B: The area of the rectangular floor can be found by multiplying the length by the width.
The length is 4 m and the width is 10 m, so the area is 4 * 10 = 40 m².This is about a tree house design using a coordinate plane in which the coordinates are measured in meters (m). The task is to calculate the perimeter and the area of the rectangular floor of the tree house, given the vertices of the floor. The perimeter is found by adding up the lengths of all four sides of the rectangular floor, and the area is found by multiplying the length by the width.
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Find the radius of convergence, R, of the series. [infinity] n = 1 n 7n (x + 5)n R = Find the interval, I, of convergence of the series. (Enter your answer using interval notation.) I =
The convergence interval, I, is the set of all x values for which the series converges. Because the series converges for all |x + 5| > 1, the convergence interval is I = (-∞, -6) ∪ (-4, ∞).
What is function?A function is an equation with just one solution for y for every x. A function produces exactly one output for each input of a certain type. Instead of y, it is usual to call a function f(x) or g(x). f(2) indicates that we should discover our function's value when x equals 2. Example. A function is an equation that depicts the connection between an input x and an output y, with precisely one output for each input. Another name for input is domain, while another one for output is range.
Here,
The radius of convergence, R, of a power series is the maximum value of x for which the series converges for all values of x within that range.
To find the radius of convergence for the given series, we can use the ratio test:
[infinity] n = 1 n 7n (x + 5)n
lim |(a_{n+1})/(a_n)| = lim |(7(n+1) (x + 5)^(n+1)) / (n 7n (x + 5)^n)|
= lim |(7(x + 5)) / n|
The series converges when the limit is less than 1 and diverges when the limit is greater than 1. If the limit is equal to 1, the test is inconclusive.
For |x + 5| < 1, the limit is equal to |7 * (x + 5)|, which is greater than 1, so the series diverges in this region.
For |x + 5| > 1, the limit is equal to |7| / n, which goes to zero as n approaches infinity, so the series converges in this region.
So, the radius of convergence, R, is R = 1.
The interval of convergence, I, is the set of all values of x for which the series converges. Since the series converges for all |x + 5| > 1, the interval of convergence is I = (-∞, -6) ∪ (-4, ∞).
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The base of the parallelogram-like figure is half the circumference of the circle, or b= 1/2 (2pir)= pir. Therefore, the area of the figure will be A=
The formula for the area of the parallelogram-like figure is A = πr
What is parallelogram?parallelogram can be defined as a simple quadrilateral with two pairs of parallel sides. The opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure.
bh, where h is the height of the parallelogram-like figure.
Therefore, The formula for the area of the parallelogram-like figure is A = πr.
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A company model it net income, in thouand of dollar, with the function f(x) = 9x2 – 54x – 144, where x i the number of unit of it product old. How many unit of it product doe the company need to ell in order for the net income to equal $0?
The company needs to produce 8 units in order for the net income to equal $0
What is factoring?Is a technique that consist of decomposition of a factor into a product of another factor, which when multiplied together give the original number.
the equation given can be simplified as:
f(x) = 9x² - 54x - 144.
f(x) = 9(x² - 6x - 16)
Then factoring we have:
f(x) = 9[(x + 2)(x - 8)]
It has a net income equals to 0 when:
f(x) = 0, so the variables are:
x + 2 = 0 -> x = -2
x - 8 = 0 -> x = 8
As the amount of products sold have to be positive the amount of product is 8
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Colin the Conservationist has been investigating the IUCN Red Data list of species.
Between 66 and 67 thousand species have been assessed and placed on the list.
Your task is to work out the number of species in each of 7 categories.
There are 78 species which are "extinct in the wild".
11 times that many have gone "extinct" since 1500AD.
Respectively 6 and 9 times as many species as have gone
"extinct" are on the "critically endangered" and "endangered" lists.
24,570 species are listed as threatened, which means they are
"vulnerable", "endangered" or "critically endangered".
The number of "near threatened"
species is 468 more than a third of
the number which are "vulnerable".
The good news is that there are
7,098 more species on the "least
concern" list than in all the other
categories combined
Based on the IUCN Red Data list of species, by solving the data we get the number of species in each category as
Extinct in the Wild = 78 Extinct = 858Critically Endangered = 5,148Endangered = 7,722Threatened = 24,570Vulnerable = 12,700Near Threatened = 4,838Least Concern = 7,098Total = 67,000
The answer which has been provided above gives the number of species that are present in each of the 7 categories of the IUCN Red Data List.
The IUCN Red Data List is a list of species that are globally threatened.
The categories that are present in the IUCN Red Data List are
Extinct in the Wild, Extinct, Critically Endangered, Endangered, Threatened, Vulnerable, Near Threatened, and Least Concern.
The number of species in each category is calculated based on the given information:
There are 78 species that are extinct in the wild.
Hence,
Extinct in the Wild: 7811 times that many have gone extinct since 1500 AD.
Hence,
Extinct: 78 × 11 = 858 species.6 and 9 times as many species have gone extinct are on the critically endangered and endangered lists respectively.
Hence,
Critically Endangered: 858 × 6 = 5,148 species.Endangered: 858 × 9 = 7,722 species.24,570 species are listed as threatened In the IUCN Red Data list.
Hence,
Threatened: 24,570.According to the list, the number of near-threatened species is 468 more than a third of the number which is vulnerable.
Hence,
Vulnerable = 12,700 Near Threatened: (12,700 ÷ 3) + 468 = 4,838 species.According to the data, there are 7,098 more species on the least
Least Concern = 7,098The total number of species on the IUCN Red Data List is calculated by adding up the number of species in each category:
Total: 78 + 858 + 5,148 + 7,722 + 24,570 + 4,838 + 7,098 = 67,000 species.Learn more about IUCN:
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A pair of gloves are on sale for 20% off
the original price of $4.99. About how
much will a person save buying the
gloves on sale?
Answer: 3.99
Step-by-step explanation:
Two athletes practice for a marathon by running back and forth on an 11-mile course. They start running simultaneously, one at a speed 2 mph faster than the other's speed. How fast does each run if they meet 1 hour 6 minutes after starting? (The faster runner is already returning at this point. ) How far from the starting point do the runners meet? The speed of the faster runner is mph. The speed of the slower runner is mph. The distance from the starting point is miles
The speed distance of the faster runner is 8 mph, and the speed of the slower runner is (8 - 2) = 6 mph.
The speed of the faster runner is 8 mph.
The speed of the slower runner is 6 mph.
The distance from the starting point is 5.5 miles.We can use the formula d = rt, where d is the total distance, r is the rate (speed) and t is the time taken to cover the distance.
Let us assume that the speed of the faster runner is x mph. Then, the speed of the slower runner is (x-2) mph.
Since the two runners meet 1 hour 6 minutes after starting, the total time taken is 1 hour 6 minutes = 66 minutes.
Thus, the total distance covered = (x * 66) + (x - 2) * 66 = 132x - 132
But, the total distance covered is 11 miles, so
132x - 132 = 11
Solving for x, we get
x = 8 mph
Therefore, the speed of the faster runner is 8 mph, and the speed of the slower runner is (8 - 2) = 6 mph.
Since they meet 1 hour 6 minutes after starting, they have travelled a total distance of (8 * 66) + (6 * 66) = 5.5 miles. Therefore, the distance from the starting point at which they meet is 5.5 miles.
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a box of 12 donuts will be distributed to 12 kids. each kid will get exactly one donut. there are 4 chocolate donuts, 4 jelly donuts, and 4 glazed donuts. how many ways are there to distribute the donuts? it matters which kid gets which flavor of donut.
The No Of ways are there to distribute the donuts = 34650
What is Probability?
Probability is an area of mathematics that deals with numerical descriptions of how probable an event is to occur or how likely a statement is to be true. The probability of an event is a number between 0 and 1, where 0 denotes the event's impossibility and 1 represents certainty.
Number of ways to distribute 12 donuts in 12 kids so that each kid got one donut = 12!
Though, there are 4 chocolate, 4 jelly and 4 glazed donuts.
Hence,
Total number of ways to distribution the donuts
= 12/4*4*4
= 34650
Total number of ways = 34650
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The No Of ways there to distribute the donuts = 34650
What is Probability?
Probability is an area of mathematics that deals with numerical descriptions of how probable an event is to occur or how likely a statement is to be true. The probability of an event is a number between 0 and 1, where 0 denotes the event's impossibility and 1 represents certainty.
Number of ways to distribute 12 donuts in 12 kids so that each kid got one donut = 12!
Though, there are 4 chocolate, 4 jelly and 4 glazed donuts.
Hence,
Total number of ways to distribute the donuts
= 12/4*4*4
= 34650
Total number of ways = 34650
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A random sample of 9th-grade students was asked if they prefer taking notes on a computer or using a pencil. Of the 180 students who were surveyed, 75 said they preferred using the computer. The resulting 99% confidence interval of the proportion of students who prefer taking notes on the computer was (0. 322, 0. 511). The school newspaper ran a story saying that less than half of the body prefers taking notes on a computer. Based on the interval, is the newspaper justified in this statement?
The newspaper's assertion is unjustified. It can be shown that the interval does not contain 0.5 based on the 99% confidence interval of (0.322, 0.511). (which is half).
This indicates that the population parameter (mean, percentage, and standard deviation) is between a and b with x% confidence.
This indicates that at least half of students prefer using a computer to take their notes. Since the interval's lower limit (0.322) is higher than 0.5, there is a 99% likelihood that the actual percentage of students who prefer taking notes on computers is higher than 0.5.
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how many 2-letter code words can be formed from the first 3 letters of the alphabet if no letter can be used more than once?
The number of 2 letter codes that can be formed is 6 with no letter repeated using Permutation.
What is Permutation and Combination ?A permutation of a set is, broadly speaking, a rearranging of its elements if the set is already sorted, or arranging its members into a sequence or linear order. The act or procedure of altering the linear order of an ordered set is referred to as a "permutation."
A permutation is a combination and an ordered arrangement of possible outcomes. For instance, there are 5 chairs, and 3 people should occupy them. There are five different methods to seat the first person, four ways to sit the person after them, and three ways to seat the third. As a result, we multiply the alternatives at our disposal to get the total number of configurations for seating 3 people in 5 seats. 5 4 3 are the methods we carry it out. It can be done in 60 different ways. You may write 5 4 3 as (5!) / (2!) (or) (5!) / (5 - 3), as you can see. .
Combinations are mathematical operations that count the number of potential configurations for a set of elements when the order of the selection is irrelevant. You can choose the components of combos in any order.
The first 3 letters of alphabet are a, b and c
The number of 2 letter codes that can be formed is 3*2 = 6 with no letter repeated.
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The first five terms of a pattern are given below.
37, 42, 47, 52, 57
Which expression can be used to determine the nth term of the pattern?
The expression aₙ = 37 + (n - 1)5 can be used to determine the nth term of the arithmetic sequence pattern?
What is an Arithmetic sequenceAn arithmetic sequence is a sequence of numbers such that the difference between the consecutive terms is constant.
The nth term of an arithmetic sequence is derived using; aₙ = a + (n - 1)d where a is the first term and d the common difference
Given the first term as 37, we have that;
a₁ = a + (1 - 1) d = 37
a₁ = a = 37
for the second term 42, substituting 37 for a;
a₂ = 37 +(2 - 1)d = 42
37 + d = 42
d = 42 - 37 {subtract 37 from both sides}
d = 5
Therefore, the arithmetic sequence increase by a common difference 5 and the expression aₙ = 37 + (n - 1)5 can be used to determine the nth term of the arithmetic sequence pattern?
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-5x+15
5x-25
4a+13
5x-25
The value of the equations if they are zero each are: 3, 5, -13/4 and 5
What is an equation?By definition, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =
The given equations are
-5x+15=0
-5x = -15
Making x the subject of the relation we have
x=3
2) 5x-25 = 0
Collecting like terms
5x=25
Making x the subject
x=5
3) 4a+13=0
4a = -13
Making a the subject of the relation
a=-13/4
4) 5x-25=0
Collecting like terms
5x=25
Making x the subject of the relation
x=5
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The middle school band is going to take a field trip either to a water park or to an amusement park. The band director surveyed all of the middle school band members to determine the preferred field trip. The results are displayed in the table below.
Field Trip Survey
Students Amusement Park Water Park Total
Seventh-Grade 14 26 40
Eighth-Grade 16 64 80
Total 30 90 120
Which statement is true about the results of the survey?
Responses
A 33% of the students prefer the amusement park.33% of the students prefer the amusement park.
B 25% of the eighth-grade students prefer the amusement park.25% of the eighth-grade students prefer the amusement park.
C 67% of the students prefer the water park.67% of the students prefer the water park.
D 65% of the seventh-grade students prefer the water park.
The statement which is true is D. 65% of the seventh-grade students prefer the water park.
What is Percentage?Percentage is defined as the parts of a number per fraction of 100. We have to divide a number with it's whole and then multiply with 100 to calculate the percentage of any number.
A : Total number of students = 120
Number of students who prefer amusement park = 14 + 16 = 30
Percentage of students who prefer amusement park = 30 / 120 = 0.25 = 25%
B : Total number of eighth grade students = 80
Number of eighth grade students who prefer amusement park = 16
Percentage = 16 / 80 = 0.2 = 20%
C : Total number of students = 120
Number of students who prefer water park = 26 + 64 = 90
Percentage = 90 / 120 = 0.75 = 75%
D : Total number of seventh grade students = 40
Number of seventh grade students who prefer water park = 26
Percentage = 26 / 40 = 0.65 = 65%
Hence the option D is the correct percentage.
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A____ is an algebraic expression that contains a variable to the power of one. _____ is an example. A _____ is a rational number that is multiplied by a variable. A _______ is a number that can be written as the ratio, or fraction, of two integers. ______ in the expression _____ is an example of a coefficient. ______ are terms whose variables and their exponents are the same. One example is _____ and -7y.
• 2y
• 6x + 5
• Like - terms
• linear expression
• rationan numbers
• 4z
• 4
• rational coefficient
A linear expression is an algebraic expression that contains a variable to the power of one. 2y is an example. A coefficient is a rational number that is multiplied by a variable. A rational number is a number that can be written as the ratio, or fraction, of two integers. 4 in the expression 4z is an example of a coefficient. Like terms are terms whose variables and their exponents are the same. One example is 4z and -7z.
In the linear expression 2y, the coefficient is the numerical factor 2. The coefficient is the rational number that is multiplied by the variable, which in this expression is y.
The coefficient of a linear expression is usually the first factor, and it is used to determine the rate of change for a variable.
For example, if the coefficient of 2y is 2, then for every increase in y by one, the result of the linear expression will increase by 2.
The coefficient of a linear expression is the numerical (or rational) factor that is multiplied by the variable. In the linear expression 2y, the coefficient is 2, since the expression is equivalent to 2*y. The coefficient is usually the first factor in a linear expression, followed by the variable and, if present, its exponent.
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8-2. Skills Practice. Multiplying a Polynomial by a Monomial.
To multiply a polynomial by a monomial, you must first identify the terms in the polynomial, as well as the factors in the monomial. Once you have identified the components, use the distributive property to multiply each term of the polynomial by the monomial. Then, combine like terms and simplify the resulting polynomial.
For example:
To multiply 3x2 + 2x - 5 by 2x, you would use the distributive property to multiply each term of the polynomial by the monomial: 3x2 * 2x = 6x3, 2x * 2x = 4x2, and -5 * 2x = -10x. The resulting polynomial is 6x3 + 4x2 - 10x.Learn more about Polynomial: https://brainly.com/question/24662212
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Write 5.2288888… repeating as a fraction
Answer: 529/8
Step-by-step explanation:
72+10t = 34+14t what is the anser
Answer:
9.5
Step-by-step explanation:
72 + 10t = 34 + 14t
72 - 34 = 14t - 10t
38/4 = 4t/4
9.5 = t
Mai played 10 basketball games. She recorded the number of points she scored and made a dot plot. Mai said that she scored between 8 and 14 points in most of the 10 games, but one game was exceptional. During that game she scored more than double her typical score of 9 points. Use the number line to make a dot plot that fits the description Mai gave. A blank dot plot for "points" with the numbers 8 through 22, in increments of 2, indicated
{9, 10, 11, 12, 14} U {x | x > 18} represents the values of x in Mai's dot plot.
Let's say x represents Mai's score in each basketball game. Based on Mai's description, the following can be inferred about the values of x:
8<=x<=14 for most of the 10 games.
x > 18 for one game
(because it was more than double Mai's typical score of 9 points).
Here is a representation of the dot plot
8___9___10___11___12___
14___16___18___20___22
The dots placed at 9, 10, 11, 12, and 14 represent the values of x where Mai scored between 8 and 14 points in most of the 10 games. The dot placed at a value greater than 18 represents the exceptional game where Mai scored more than double her typical score of 9 points.
Therefore, the set of values for x can be represented as:
{9, 10, 11, 12, 14} U {x | x > 18}
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The first steps in writing f(x) = 4x2 + 48x + 10 in vertex form are shown.
f(x) = 4(x2 + 12x) + 10
(twelve-halves) squared = 36
What is the function written in vertex form?
f(x) = 4(x + 6)2 + 10
f(x) = 4(x + 6)2 – 26
f(x) = 4(x + 6)2 – 134
f(x) = 4(x + 6)2 + 154
The function written in vertex form is:
f(x) = 4(x + 6)² - 26
Option B is the correct answer.
What is a function?A function is a relationship between inputs where each input is related to exactly one output.
Example:
f(x) = 2x + 1
f(1) = 2 + 1 = 3
f(2) = 2 x 2 + 1 = 4 + 1 = 5
The outputs of the functions are 3 and 5
The inputs of the function are 1 and 2.
We have,
f(x) = 4(x² + 12x) + 10
Now,
f(x) = 4(x² + 12x) + 10
f(x) = 4 (x² + 2 x (x) x 6 + 36) - 36 + 10
f(x) = 4(x + 6)² - 26
Thus,
f(x) = 4(x + 6)² - 26 is the function in vertex form.
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Answer:
B is correct
Step-by-step explanation:
I need help ASAP. I can’t figure out the answer can someone give it or explain the answer?
1.5 cm is the data range. The number sequence "4, 6, 9, 3, 7" is an example where the lowest value is 3 and the highest is 9. The range is therefore 9 3 = 6. Just like that!
What is meant by data range?In statistics, the range of your data is the range between the lowest and greatest values of the distribution. It acts as a typical sign of unpredictable behavior.Measurements of variability provide descriptive statistics for your data set's summary, together with measures of central tendency. In a list or collection of numbers, the range is the difference between the lowest and highest integers. Place all the numbers in order before attempting to determine the range. The lowest number is then subtracted (subtracted) from the greatest number. The range is the range of values, i.e., the range between the lowest and highest values. The lowest value is 3 and the highest is 9 in the example number sequence "4, 6, 9, 3, 7." As a result, the range is 9 3 = 6. Simple as that!Q3 - Q1 is the interquartile range (IQR).
The third quartile (Q3) of the box plot is the data value that exactly matches the end of the box's edge (7 cm).
The data value exactly at the box's outside edge (5.5 cm) is the first quartile (Q1).
Range between quartiles (IQR): 7 - 5.5 = 1.5 cm
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Peterson Products calculates its pension benefits as follows: Years of service × 1.98% multiplier × Average of last two annual salaries What is Mary’s monthly pension benefit if she worked for Peterson for 28 years and her last two annual salaries were $78,000 and $80,000?
Mary's monthly pension benefit is $3,649.80.
First, we have to find the average salary.
The average is the sum of the salaries divided by the number of salaries.
($78,000 + $80,000)/2 = $79,000
Next, we can find the annual retirement rate.
The annual retirement pension is the product of the average, the rate and the number of years employed.
$79,000 x 1.98% x 28 = $43,797.60
Finally, we can find the monthly retirement pension.
The monthly retirement pension is then the annual retirement pension divided by the number of months in a year.
There are 12 months in a year.
$43,797.60 / 12 = $3,649.80
Therefore, Mary's monthly pension benefit is $3,649.80.
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you decide to roll 2 6 sided dice once. what is the probability that the sum of the spots on the dice will add up to a 5
The probability of rolling a 5 with two 6-sided dice is 1/9 or approximately 0.11.
This can be found by calculating the number of combinations that add up to 5. There are 2 combinations that add up to 5: (1, 4) and (2, 3). Out of 36 possible combinations of rolling 2 dice (6 x 6), there are only 2 combinations that give us a sum of 5, so the probability is 2/36 or 1/18 or approximately 0.11.
Probability is a measure of the likelihood or chance of an event occurring. It is expressed as a number between 0 and 1, where 0 means the event is impossible, and 1 means the event is certain to happen. A probability of 0.5 means that the event has an equal chance of happening or not happening.
The probability of an event is calculated by dividing the number of favorable outcomes by the number of possible outcomes. For example, if you flip a fair coin, the probability of getting heads is 1/2 because there are two possible outcomes (heads or tails) and only one of them is favorable (heads).
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The probability of rolling a 5 with two 6-sided dice is 1/9 or approximately 0.11.
This can be found by calculating the number of combinations that add up to 5. There are 2 combinations that add up to 5: (1, 4) and (2, 3). Out of 36 possible combinations of rolling 2 dice (6 x 6), there are only 2 combinations that give us a sum of 5, so the probability is 2/36 or 1/18 or approximately 0.11.
Probability is a measure of the likelihood or chance of an event occurring. It is expressed as a number between 0 and 1, where 0 means the event is impossible, and 1 means the event is certain to happen. A probability of 0.5 means that the event has an equal chance of happening or not happening.
The probability of an event is calculated by dividing the number of favorable outcomes by the number of possible outcomes. For example, if you flip a fair coin, the probability of getting heads is 1/2 because there are two possible outcomes (heads or tails) and only one of them is favorable (heads).
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A few playing cards are missing from a standard 52-card deck. Three cards
remain when you deal the entire deck to four people. And two cards remain
when you deal the entire deck to three people OR if you deal the entire
deck to five people. How many cards are missing from the deck???
Answer:
49 cards would be left from the deck of card.good luck with future questions I hope I am right
Use the gcf and the distributive property to find the sum of 15+36
Answer: br uh is this even a high school question? anyway, look at the image that i sent you can see the answer there.
better give me brainliest
Step-by-step explanation:
Suppose A Deck Of 52 Cards Is Shuffled And The Top Two Cards Are Dealt.A) How Many Ordered
5. Suppose a deck of 52 cards is shuffled and the top two cards are dealt.
a) How many ordered pairs of cards could possibly result as outcomes?
Assuming each of these pairs has the same chance, calculate:
b) the chance that the first card is an ace;
c) the chance that the second card is an ace (explain your answer by a symmetry argument as well as by counting);
d) the chance that both cards are aces;
e) the chance of at least one ace among the two cards.
6. Repeat Exercise 5, supposing instead that after the first card is dealt, it is replaced, and shuffled into the deck before the second card is dealt.
Suppose a deck of 52 cards is shuffled and the top two cards are dealt..
[tex]\left \P {{52} \atop {2}} \right.[/tex] =52!50! = 52 ×51 = 2652.
Now assuming each of the pairs has the same chance, calculate the probabilities for the following events
the chance that the first card is an ace;
There are 4aces in a deck, so the probability is
P (A)=
[tex]\frac{4}{52}\\ =\frac{1}{13}[/tex]
the chance that the second card is an ace
Again, there are 4aces in a deck, so the probability is
P(B)=
[tex]\\ \\ \frac{4}{52}\\ =\frac{1}{13}[/tex]
the chance that both cards are aces
There are 4aces in the deck. We already have the number ofpossible ordered pairs from P(A), each of which is equally likely. How many different ordered pairs give both aces? The answer is the number of permutations of two cards among four.
= [tex]\left \ P{4} \atop {2}} \right. \\\frac{4!}{2!}[/tex]
= 4*3
= 12
The probability that both cards are aces is therefore
[tex]\frac{\left \P {{4} \atop {2}} \right. }{\left \P{{52} \atop {2}} \right. }[/tex]
=12 /2652
=1/221
the chance of at least one ace among the two cards.
How many different permutations of the first two cards give at least one ace? The number that give two aces is P42, from above. The number that give an ace as the first card but not the second card is 4×48, since there are4aces, and after choosing one ace, there are 48 that possible non-aces for the second card. Likewise there are 48 ×4ways to choose an ace as the second card, but not the first. Thus the total number of ways that the two cards can have at least one ace is
P42+ 4 ×48 + 4 ×48 = 396.
The probability of of selecting at least one ace among the first two cards
= 396/3652
P (D)= 33 /221
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PLEASE HELP ASAP
An element with a mass of 660 grams decays by 5.1% per minute. To the nearest tenth of a minute, how long will it be until there are 280 grams of the element remaining?
The time in minutes until there are 280 grams of the element remaining is given as follows:
16 minutes.
How to model the situation?A decaying exponential function is modeled as follows:
y = a(1 - r)^t.
In which the parameters are given as follows:
a is the initial amount.r is the decay rate, as a decimal.The parameter values for this problem are given as follows:
a = 660, r = 0.051.
Hence the function is modeled as follows:
y = 660(0.949)^t.
The time until there are 280 grams remaining is given as follows:
280 = 660(0.949)^t.
(0.949)^t = 280/660
tlog(0.949) = log(280/660)
t = log(280/660)/log(0.949)
t = 16 minutes.
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HELP ASAP PLS!!!!…..,,,
The first value of the given exponential expression would be 3.
What is an exponential function?
An exponential function is a mathematical function of the form f(x) = aˣ, where "a" is a positive constant and x is a real number. The function represents an exponential growth or decay, depending on the value of "a". If "a" is greater than 1, the function increases rapidly as x increases. If "a" is between 0 and 1, the function decreases as x increases.
In the exponential expression y = 3 * q⁵, the first value is 3.
Hence, the first value of the given exponential expression would be 3.
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HELP PLSSS!!!
Prove the diviibility of the following number: 45^45 x 15^15 by 75^30
The proof of divisibility is correct in this question.
DivisibilityThe capacity of one integer (the divisor) to divide another integer (the dividend) equally and without leaving a residual is known as divisibility in mathematics. Alternatively said, if a dividend is divisible by a divisor, the division will produce a whole number or an integer. The formula for this connection is "dividend divisor = integer." Using divisibility criteria, which are based on the characteristics of numbers and their prime factorizations, is a typical method of checking for divisibility. In subjects such as number theory, cryptography, and others, the ability to divide a number by another number can have significant ramifications.
According to the question
It is necessary to demonstrate that the phrase 45*45*15*15 may be divided by 75*30. We must first comprehend the characteristics of the numbers' prime factorization in order to do this.
The number 75 may be represented as 31 * 52, and when it is raised to the 30th power, it becomes 75^30 = 31 * 52^30 = 3^30 * 5^60. Similar to how 45 may be expressed as 3^2 * 5^1, 3^90 * 5^45 is equal to 45^45 = (3^2 * 5^1)^45. Additionally, 15 may be written as 3 * 5 1, which means that 15 = 3 * 5 * 15.
75 = 3^1 * 5^2,
∴ 75^30 = (3^1 * 5^2)^30 = 3^30 * 5^60.
It follows that 75^30, or 3^30 * 5^60, divides 45^45 * 15^15, or 3^90 * 5^45 * 3^15 * 5^15, as 3^30 divides 3^90 and 5^60 divides 5^45.
45 = 3^2 * 5^1,
∴ 45^45 = (3^2 * 5^1)^45 = 3^90 * 5^45.
15 = 3^1 * 5^1,
∴ 15^15 = (3^1 * 5^1)^15 = 3^15 * 5^15.
In other words, the equation 45*45*15*15 may be evenly divided by 75*30 without any residual, proving that it is divisible by 75*30. The division may be used to confirm this, but it can also be demonstrated by the fact that all of the dividend's prime factors—45*45*15*15—are included in the divisor's prime factorization, 75*30, in the multiples necessary to divide it evenly.
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The proof of divisibility is correct in this question.
Divisibility
The capacity of one integer (the divisor) to divide another integer (the dividend) equally and without leaving a residual is known as divisibility in mathematics. Alternatively said, if a dividend is divisible by a divisor, the division will produce a whole number or an integer. The formula for this connection is "dividend divisor = integer." Using divisibility criteria, which are based on the characteristics of numbers and their prime factorizations, is a typical method of checking for divisibility. In subjects such as number theory, cryptography, and others, the ability to divide a number by another number can have significant ramifications.
According to the question,
It is necessary to demonstrate that the phrase 45*45*15*15 may be divided by 75*30. We must first comprehend the characteristics of the numbers' prime factorization in order to do this.
The number 75 may be represented as 31 * 52, and when it is raised to the 30th power, it becomes [tex]75^{30}=(31*52^{30})=(3^{30}*5^{60})[/tex]. Similar to how 45 may be expressed as [tex](3^2*5^1)[/tex]. [tex](3^{90}*5^{45})[/tex] is equal to [tex]45^{45}=(3^2*5^1)^{45}[/tex]. Additionally, 15 may be written as 3 * 5 1, which means that 15 = 3 * 5 * 15.
[tex]75=3^1*5^2[/tex],
∴ [tex]75^{30}=(3^1*5^2)^{30}=3^{30}*5^{60}[/tex].
It follows that [tex]75^{30}[/tex], or [tex](3^{30}*5^{60})[/tex], divides [tex](45^{45}*15^{15})[/tex] or [tex](3^{90}*5^{45}*3^{15}*5^{15})[/tex], as [tex]3^{30}[/tex] divides [tex]3^{90}[/tex] and [tex]5^{60}[/tex] divides [tex]5^{45}[/tex].
[tex]45=3^2*5^1[/tex]
∴ [tex]45^{45}=(3^*5^1)^{45}=3^{90}*5^{45}[/tex]
[tex]15=3^1*5^1[/tex]
∴ [tex]15^{15}=(3^1*5^1)^{15}=3^{15}*5^{15}[/tex]
In other words, the equation 45*45*15*15 may be evenly divided by 75*30 without any residual, proving that it is divisible by 75*30. The division may be used to confirm this, but it can also be demonstrated by the fact that all of the dividend's prime factors—45*45*15*15—are included in the divisor's prime factorization, 75*30, in the multiples necessary to divide it evenly.
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